Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.1%	99.9%	0
0.1%	0%	99.9%	1

Compiler

Compiled 33 to 24 computations (27.3% saved)

sample1.6s (56.2%)

Results

1.6s

8256×

body

256

valid

preprocess41.0ms (1.4%)

Algorithm

2×	egg-herbie

Rules

601×	`fma-def_binary32`
498×	`fma-neg_binary32`
174×	`cancel-sign-sub-inv_binary32`
94×	`sub-neg_binary32`
89×	`unsub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	40	32
2	106	32
3	222	32
4	540	32
5	1153	32
6	1987	32
7	2325	32
8	2405	32
9	2416	32
0	3	3

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

Inputs
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
(+.f32 (-.f32 1 uy) (*.f32 uy maxCos))
(+.f32 (-.f32 1 maxCos) (*.f32 maxCos ux))
(+.f32 (-.f32 1 ux) (*.f32 ux uy))

Outputs
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
(fma.f32 ux maxCos (-.f32 1 ux))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 (-.f32 1 uy) (*.f32 uy maxCos))
(-.f32 1 (-.f32 uy (*.f32 maxCos uy)))
(fma.f32 maxCos uy (-.f32 1 uy))
(-.f32 (fma.f32 maxCos uy 1) uy)
(+.f32 (-.f32 1 maxCos) (*.f32 maxCos ux))
(+.f32 (-.f32 1 maxCos) (*.f32 ux maxCos))
(fma.f32 ux maxCos (-.f32 1 maxCos))
(-.f32 (fma.f32 ux maxCos 1) maxCos)
(+.f32 (-.f32 1 ux) (*.f32 ux uy))
(fma.f32 ux uy (-.f32 1 ux))
(-.f32 (fma.f32 ux uy 1) ux)

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify15.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

199×	`fma-def_binary32`
155×	`fma-neg_binary32`
47×	`cancel-sign-sub-inv_binary32`
34×	`sub-neg_binary32`
26×	`unsub-neg_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	8
2	35	8
3	72	8
4	167	8
5	361	8
6	618	8
7	765	8
8	797	8
9	802	8

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

Outputs
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
(fma.f32 ux maxCos (-.f32 1 ux))
(-.f32 (fma.f32 ux maxCos 1) ux)

eval1.0ms (0%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

prune1.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(-.f32 (fma.f32 ux maxCos 1) ux)
▶	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

Compiler

Compiled 19 to 13 computations (31.6% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
	0.0b	(*.f32 ux maxCos)
✓	0.0b	(*.f32 ux maxCos)
✓	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

series6.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	maxCos	@	inf	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
1.0ms	ux	@	inf	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
1.0ms	ux	@	-inf	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
1.0ms	ux	@	0	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
0.0ms	ux	@	0	(*.f32 ux maxCos)

rewrite52.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

897×	`pow1_binary32`
836×	`add-log-exp_binary32`
836×	`log1p-expm1-u_binary32`
836×	`expm1-log1p-u_binary32`
820×	`add-exp-log_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	154	12
2	2208	12

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

Inputs
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
(*.f32 ux maxCos)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 1 (.f32 ux (-.f32 1 maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 1 (fma.f32 ux maxCos (-.f32 1 ux))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 (-.f32 1 ux) (.f32 ux maxCos))) (/.f32 (pow.f32 (.f32 ux maxCos) 2) (-.f32 (-.f32 1 ux) (.f32 ux maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (.f32 ux maxCos) 1) ux)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (fma.f32 ux maxCos (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2) (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 ux maxCos) 3)) (/.f32 1 (+.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 (.f32 ux maxCos) (-.f32 (.f32 ux maxCos) (-.f32 1 ux))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (-.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (.f32 ux maxCos) 2)) (/.f32 1 (-.f32 (-.f32 1 ux) (.f32 ux maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 (.f32 ux maxCos) (-.f32 (.f32 ux maxCos) (-.f32 1 ux)))) (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 ux maxCos) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (-.f32 (-.f32 1 ux) (.f32 ux maxCos)) (-.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (.f32 ux maxCos) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 (.f32 ux maxCos) (-.f32 (.f32 ux maxCos) (-.f32 1 ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (pow.f32 (.f32 ux maxCos) 2) (-.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 (.f32 (-.f32 1 ux) ux) maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (.f32 ux maxCos) 2)) (-.f32 (-.f32 1 ux) (.f32 ux maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 ux maxCos) 3))) (neg.f32 (+.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 (.f32 ux maxCos) (-.f32 (.f32 ux maxCos) (-.f32 1 ux))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (.f32 ux maxCos) 2))) (neg.f32 (-.f32 (-.f32 1 ux) (.f32 ux maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (pow.f32 (.f32 ux (-.f32 1 maxCos)) 3)) (+.f32 1 (+.f32 (.f32 (.f32 ux (-.f32 1 maxCos)) (.f32 ux (-.f32 1 maxCos))) (.f32 ux (-.f32 1 maxCos)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (.f32 (.f32 ux (-.f32 1 maxCos)) (.f32 ux (-.f32 1 maxCos)))) (+.f32 1 (.f32 ux (-.f32 1 maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 2) (pow.f32 (-.f32 1 ux) 2)) (-.f32 (.f32 ux maxCos) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (-.f32 1 ux) (.f32 ux maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (.f32 ux maxCos) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 ux maxCos (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 maxCos ux (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (.f32 ux maxCos)) 2) (cbrt.f32 (.f32 ux maxCos)) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (-.f32 1 ux)) (.f32 ux maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (.f32 ux maxCos)) (sqrt.f32 (.f32 ux maxCos)) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (-.f32 1 ux)) (sqrt.f32 (-.f32 1 ux)) (*.f32 ux maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 1 (.f32 ux maxCos)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 ux maxCos) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 ux maxCos)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 ux maxCos)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 ux maxCos) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 ux maxCos) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 ux) maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 ux maxCos) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 ux maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 ux maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 ux maxCos)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 1 (*.f32 ux (-.f32 1 maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 1 (fma.f32 ux maxCos (-.f32 1 ux))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 (-.f32 1 ux) (*.f32 ux maxCos))) (/.f32 (pow.f32 (*.f32 ux maxCos) 2) (-.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (*.f32 ux maxCos) 1) ux)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (fma.f32 ux maxCos (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2) (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (*.f32 ux maxCos) 3)) (/.f32 1 (+.f32 (pow.f32 (-.f32 1 ux) 2) (*.f32 (*.f32 ux maxCos) (-.f32 (*.f32 ux maxCos) (-.f32 1 ux))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (*.f32 ux maxCos) 2)) (/.f32 1 (-.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 (pow.f32 (-.f32 1 ux) 2) (*.f32 (*.f32 ux maxCos) (-.f32 (*.f32 ux maxCos) (-.f32 1 ux)))) (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (*.f32 ux maxCos) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (-.f32 (-.f32 1 ux) (*.f32 ux maxCos)) (-.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (*.f32 ux maxCos) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (*.f32 ux maxCos) 3)) (+.f32 (pow.f32 (-.f32 1 ux) 2) (*.f32 (*.f32 ux maxCos) (-.f32 (*.f32 ux maxCos) (-.f32 1 ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (*.f32 ux maxCos) 3)) (+.f32 (pow.f32 (*.f32 ux maxCos) 2) (-.f32 (pow.f32 (-.f32 1 ux) 2) (*.f32 (*.f32 (-.f32 1 ux) ux) maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (*.f32 ux maxCos) 2)) (-.f32 (-.f32 1 ux) (*.f32 ux maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (*.f32 ux maxCos) 3))) (neg.f32 (+.f32 (pow.f32 (-.f32 1 ux) 2) (*.f32 (*.f32 ux maxCos) (-.f32 (*.f32 ux maxCos) (-.f32 1 ux))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (*.f32 ux maxCos) 2))) (neg.f32 (-.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (pow.f32 (*.f32 ux (-.f32 1 maxCos)) 3)) (+.f32 1 (+.f32 (*.f32 (*.f32 ux (-.f32 1 maxCos)) (*.f32 ux (-.f32 1 maxCos))) (*.f32 ux (-.f32 1 maxCos)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (*.f32 (*.f32 ux (-.f32 1 maxCos)) (*.f32 ux (-.f32 1 maxCos)))) (+.f32 1 (*.f32 ux (-.f32 1 maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (*.f32 ux maxCos) 2) (pow.f32 (-.f32 1 ux) 2)) (-.f32 (*.f32 ux maxCos) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (-.f32 1 ux) (*.f32 ux maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (*.f32 ux maxCos) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 ux maxCos (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 maxCos ux (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (*.f32 ux maxCos)) 2) (cbrt.f32 (*.f32 ux maxCos)) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (-.f32 1 ux)) (*.f32 ux maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (*.f32 ux maxCos)) (sqrt.f32 (*.f32 ux maxCos)) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (-.f32 1 ux)) (sqrt.f32 (-.f32 1 ux)) (*.f32 ux maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 1 (*.f32 ux maxCos)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 ux maxCos) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 ux maxCos)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 ux maxCos)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 ux maxCos) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 ux maxCos) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 ux) maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 ux maxCos) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 ux maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 ux maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 ux maxCos)))))))

simplify24.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

185×	`fma-def_binary32`
158×	`fma-neg_binary32`
31×	`sub-neg_binary32`
25×	`unsub-neg_binary32`
22×	`cancel-sign-sub-inv_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	303
1	45	267
2	107	267
3	227	267
4	461	267
5	662	267
6	762	267
7	780	267

Stop Event

1×

saturated

Counts

98 → 60

Calls

Call 1

Inputs
1
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(*.f32 (-.f32 maxCos 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(-.f32 1 ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)

Outputs
1
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (+.f32 maxCos -1) ux)
(-.f32 (*.f32 maxCos ux) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))
(*.f32 (+.f32 maxCos -1) ux)
(-.f32 (*.f32 maxCos ux) ux)
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 1 ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)

localize13.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.f32 (fma.f32 ux maxCos 1) ux)
✓	0.0b	(-.f32 (fma.f32 ux maxCos 1) ux)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	ux	@	-inf	(-.f32 (fma.f32 ux maxCos 1) ux)
0.0ms	ux	@	0	(-.f32 (fma.f32 ux maxCos 1) ux)
0.0ms	maxCos	@	-inf	(-.f32 (fma.f32 ux maxCos 1) ux)
0.0ms	maxCos	@	inf	(-.f32 (fma.f32 ux maxCos 1) ux)
0.0ms	maxCos	@	0	(-.f32 (fma.f32 ux maxCos 1) ux)

rewrite40.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

672×	`pow1_binary32`
624×	`add-log-exp_binary32`
624×	`log1p-expm1-u_binary32`
624×	`expm1-log1p-u_binary32`
610×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	124	8
2	1632	8

Stop Event

1×	node limit

Counts

1 → 37

Calls

Call 1

Inputs
(-.f32 (fma.f32 ux maxCos 1) ux)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 ux maxCos 1) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 ux maxCos 1) (.f32 (neg.f32 ux) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (fma.f32 (neg.f32 ux) 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (fma.f32 (neg.f32 (cbrt.f32 ux)) (pow.f32 (cbrt.f32 ux) 2) ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (fma.f32 (neg.f32 (sqrt.f32 ux)) (sqrt.f32 ux) ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 ux maxCos) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 ux maxCos) (+.f32 1 (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (neg.f32 ux) (fma.f32 ux maxCos 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (-.f32 (fma.f32 ux maxCos 1) ux))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (-.f32 (fma.f32 ux maxCos 1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) (pow.f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 2) (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) (sqrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3)) (/.f32 1 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux (+.f32 ux (fma.f32 ux maxCos 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux ux)) (/.f32 1 (+.f32 ux (fma.f32 ux maxCos 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (+.f32 (sqrt.f32 (fma.f32 ux maxCos 1)) (sqrt.f32 ux)) (-.f32 (sqrt.f32 (fma.f32 ux maxCos 1)) (sqrt.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux (+.f32 ux (fma.f32 ux maxCos 1)))) (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 ux (fma.f32 ux maxCos 1)) (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3)) (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux (+.f32 ux (fma.f32 ux maxCos 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux ux)) (+.f32 ux (fma.f32 ux maxCos 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3))) (neg.f32 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux (+.f32 ux (fma.f32 ux maxCos 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux ux))) (neg.f32 (+.f32 ux (fma.f32 ux maxCos 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 (neg.f32 ux) 3)) (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (-.f32 (.f32 (neg.f32 ux) (neg.f32 ux)) (.f32 (fma.f32 ux maxCos 1) (neg.f32 ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 (neg.f32 ux) (neg.f32 ux))) (-.f32 (fma.f32 ux maxCos 1) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (fma.f32 ux maxCos 1) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (fma.f32 ux maxCos 1)) 2) (cbrt.f32 (fma.f32 ux maxCos 1)) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (fma.f32 ux maxCos 1)) (sqrt.f32 (fma.f32 ux maxCos 1)) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 ux maxCos 1) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 ux maxCos 1) (*.f32 (neg.f32 ux) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (fma.f32 (neg.f32 ux) 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (fma.f32 (neg.f32 (cbrt.f32 ux)) (pow.f32 (cbrt.f32 ux) 2) ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (fma.f32 (neg.f32 (sqrt.f32 ux)) (sqrt.f32 ux) ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 ux maxCos) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 ux maxCos) (+.f32 1 (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (neg.f32 ux) (fma.f32 ux maxCos 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (-.f32 (fma.f32 ux maxCos 1) ux))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) (pow.f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 2) (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) (sqrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3)) (/.f32 1 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux (+.f32 ux (fma.f32 ux maxCos 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux ux)) (/.f32 1 (+.f32 ux (fma.f32 ux maxCos 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 (sqrt.f32 (fma.f32 ux maxCos 1)) (sqrt.f32 ux)) (-.f32 (sqrt.f32 (fma.f32 ux maxCos 1)) (sqrt.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux (+.f32 ux (fma.f32 ux maxCos 1)))) (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 ux (fma.f32 ux maxCos 1)) (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3)) (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux (+.f32 ux (fma.f32 ux maxCos 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux ux)) (+.f32 ux (fma.f32 ux maxCos 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3))) (neg.f32 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux (+.f32 ux (fma.f32 ux maxCos 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux ux))) (neg.f32 (+.f32 ux (fma.f32 ux maxCos 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 (neg.f32 ux) 3)) (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (-.f32 (*.f32 (neg.f32 ux) (neg.f32 ux)) (*.f32 (fma.f32 ux maxCos 1) (neg.f32 ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 (neg.f32 ux) (neg.f32 ux))) (-.f32 (fma.f32 ux maxCos 1) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (fma.f32 ux maxCos 1) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (fma.f32 ux maxCos 1)) 2) (cbrt.f32 (fma.f32 ux maxCos 1)) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (fma.f32 ux maxCos 1)) (sqrt.f32 (fma.f32 ux maxCos 1)) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))))

simplify19.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

185×	`fma-def_binary32`
158×	`fma-neg_binary32`
31×	`sub-neg_binary32`
25×	`unsub-neg_binary32`
22×	`cancel-sign-sub-inv_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	207
1	45	171
2	107	171
3	227	171
4	461	171
5	662	171
6	762	171
7	780	171

Stop Event

1×

saturated

Counts

61 → 47

Calls

Call 1

Inputs
1
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(*.f32 (-.f32 maxCos 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(-.f32 1 ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)

Outputs
1
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (+.f32 maxCos -1) ux)
(-.f32 (*.f32 maxCos ux) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))
(*.f32 (+.f32 maxCos -1) ux)
(-.f32 (*.f32 maxCos ux) ux)
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 1 ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)

eval27.0ms (0.9%)

Compiler: Compiled 1330 to 802 computations (39.7% saved)

prune17.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	104	5	109

Error

Counts

109 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
	8.4b	1
▶	0.5b	(-.f32 1 ux)
▶	0.0b	(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
▶	0.0b	(/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 2) (pow.f32 (-.f32 1 ux) 2)) (-.f32 (.f32 ux maxCos) (-.f32 1 ux)))

Compiler

Compiled 52 to 39 computations (25% saved)

localize37.0ms (1.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.3b	(/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 2) (pow.f32 (-.f32 1 ux) 2)) (-.f32 (.f32 ux maxCos) (-.f32 1 ux)))
	0.2b	(pow.f32 (*.f32 ux maxCos) 2)
	0.0b	(-.f32 (*.f32 ux maxCos) (-.f32 1 ux))
	0.0b	(*.f32 ux maxCos)
✓	0.0b	(-.f32 (*.f32 ux maxCos) (-.f32 1 ux))
✓	0.2b	(pow.f32 (*.f32 ux maxCos) 2)
✓	0.3b	(/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 2) (pow.f32 (-.f32 1 ux) 2)) (-.f32 (.f32 ux maxCos) (-.f32 1 ux)))
✓	0.4b	(pow.f32 (-.f32 1 ux) 2)

series13.0ms (0.4%)

Counts

4 → 84

Calls

21 calls:

Time	Variable		Point	Expression
2.0ms	ux	@	-inf	(/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 2) (pow.f32 (-.f32 1 ux) 2)) (-.f32 (.f32 ux maxCos) (-.f32 1 ux)))
1.0ms	ux	@	inf	(/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 2) (pow.f32 (-.f32 1 ux) 2)) (-.f32 (.f32 ux maxCos) (-.f32 1 ux)))
1.0ms	maxCos	@	0	(/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 2) (pow.f32 (-.f32 1 ux) 2)) (-.f32 (.f32 ux maxCos) (-.f32 1 ux)))
1.0ms	ux	@	inf	(pow.f32 (-.f32 1 ux) 2)
1.0ms	ux	@	0	(/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 2) (pow.f32 (-.f32 1 ux) 2)) (-.f32 (.f32 ux maxCos) (-.f32 1 ux)))

rewrite94.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

682×	`log-prod_binary32`
662×	`fma-def_binary32`
371×	`fma-neg_binary32`
235×	`expm1-udef_binary32`
235×	`log1p-udef_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	52
1	284	30
2	4162	30

Stop Event

1×	node limit

Counts

4 → 309

Calls

Call 1

Inputs
(pow.f32 (-.f32 1 ux) 2)
(/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 2) (pow.f32 (-.f32 1 ux) 2)) (-.f32 (.f32 ux maxCos) (-.f32 1 ux)))
(pow.f32 (*.f32 ux maxCos) 2)
(-.f32 (*.f32 ux maxCos) (-.f32 1 ux))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 1 ux) (.f32 (neg.f32 ux) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 1 ux) (.f32 (-.f32 1 ux) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (pow.f32 (-.f32 1 ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (pow.f32 (-.f32 1 ux) 2))) (cbrt.f32 (exp.f32 (pow.f32 (-.f32 1 ux) 2))))) (log.f32 (cbrt.f32 (exp.f32 (pow.f32 (-.f32 1 ux) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (pow.f32 (-.f32 1 ux) 2)))) (log.f32 (sqrt.f32 (exp.f32 (pow.f32 (-.f32 1 ux) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (pow.f32 (-.f32 1 ux) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (pow.f32 (-.f32 1 ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (-.f32 1 ux) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (-.f32 1 ux) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (pow.f32 (-.f32 1 ux) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (.f32 (cbrt.f32 (-.f32 1 ux)) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 4)) (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (-.f32 1 ux)) (.f32 (sqrt.f32 (-.f32 1 ux)) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (sqrt.f32 (-.f32 1 ux)) 3) (sqrt.f32 (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (-.f32 1 ux) (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2)) (cbrt.f32 (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (-.f32 1 (.f32 ux ux)) (-.f32 1 (.f32 ux ux))) (.f32 (+.f32 1 ux) (+.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (-.f32 1 (pow.f32 ux 3)) (-.f32 1 (pow.f32 ux 3))) (.f32 (+.f32 1 (fma.f32 ux ux ux)) (+.f32 1 (fma.f32 ux ux ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (-.f32 1 (.f32 ux ux)) (-.f32 1 (pow.f32 ux 3))) (.f32 (+.f32 1 ux) (+.f32 1 (fma.f32 ux ux ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (-.f32 1 (pow.f32 ux 3)) (-.f32 1 (.f32 ux ux))) (.f32 (+.f32 1 (fma.f32 ux ux ux)) (+.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (-.f32 1 (pow.f32 ux 3)) (-.f32 1 ux)) (+.f32 1 (fma.f32 ux ux ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (-.f32 1 (.f32 ux ux)) (-.f32 1 ux)) (+.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (-.f32 1 ux) (-.f32 1 (pow.f32 ux 3))) (+.f32 1 (fma.f32 ux ux ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (-.f32 1 ux) (-.f32 1 (.f32 ux ux))) (+.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (-.f32 1 ux) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (pow.f32 (-.f32 1 ux) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (pow.f32 (-.f32 1 ux) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (-.f32 1 ux) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (pow.f32 (-.f32 1 ux) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (pow.f32 (-.f32 1 ux) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (-.f32 1 ux) (.f32 (neg.f32 ux) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (-.f32 1 ux) (.f32 (-.f32 1 ux) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (-.f32 1 ux) 1 (.f32 (neg.f32 ux) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (-.f32 1 ux) 1 (.f32 (-.f32 1 ux) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (-.f32 1 ux)) (.f32 (neg.f32 ux) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (-.f32 1 ux)) (.f32 (-.f32 1 ux) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (cbrt.f32 (-.f32 1 ux)) (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (.f32 (neg.f32 ux) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (cbrt.f32 (-.f32 1 ux)) (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (.f32 (-.f32 1 ux) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (-.f32 1 ux)) (sqrt.f32 (-.f32 1 ux)) (.f32 (neg.f32 ux) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (-.f32 1 ux)) (sqrt.f32 (-.f32 1 ux)) (.f32 (-.f32 1 ux) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (.f32 (neg.f32 ux) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (.f32 (-.f32 1 ux) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (-.f32 1 (.f32 ux ux)) (/.f32 1 (+.f32 1 ux)) (.f32 (neg.f32 ux) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (-.f32 1 (.f32 ux ux)) (/.f32 1 (+.f32 1 ux)) (.f32 (-.f32 1 ux) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 4))) (sqrt.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2)) (.f32 (neg.f32 ux) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 4))) (sqrt.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2)) (.f32 (-.f32 1 ux) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 2 (log1p.f32 (neg.f32 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 2 (log1p.f32 (neg.f32 ux))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 1 ux) (.f32 ux maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 ux maxCos) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (fma.f32 ux maxCos (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (pow.f32 (.f32 ux maxCos) 2) (+.f32 ux (fma.f32 ux maxCos -1))) (neg.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (+.f32 ux (fma.f32 ux maxCos -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 ux maxCos 1) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) (cbrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux)))))) (log.f32 (cbrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))) (log.f32 (sqrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (pow.f32 (.f32 ux maxCos) 2) (+.f32 ux (fma.f32 ux maxCos -1))) (/.f32 (pow.f32 (-.f32 1 ux) 2) (+.f32 ux (fma.f32 ux maxCos -1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (fma.f32 ux maxCos 1) ux)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (fma.f32 ux maxCos (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (-.f32 (pow.f32 (.f32 ux maxCos) 2) (pow.f32 (-.f32 1 ux) 2)) (/.f32 1 (+.f32 ux (fma.f32 ux maxCos -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2) (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 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(#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 maxCos) 2) (.f32 (cbrt.f32 maxCos) ux) (neg.f32 (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 maxCos) 2) (.f32 (cbrt.f32 maxCos) ux) (.f32 (neg.f32 (-.f32 1 ux)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (+.f32 ux (fma.f32 ux maxCos -1))) (sqrt.f32 (+.f32 ux (fma.f32 ux maxCos -1))) (fma.f32 (neg.f32 (-.f32 1 ux)) 1 (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (+.f32 ux (fma.f32 ux maxCos -1))) (sqrt.f32 (+.f32 ux (fma.f32 ux maxCos -1))) (fma.f32 (neg.f32 (cbrt.f32 (-.f32 1 ux))) (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (+.f32 ux (fma.f32 ux maxCos -1))) (sqrt.f32 (+.f32 ux (fma.f32 ux maxCos -1))) (+.f32 (neg.f32 (-.f32 1 ux)) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (.f32 ux maxCos)) (sqrt.f32 (.f32 ux maxCos)) (neg.f32 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(cbrt.f32 ux) 2)) (cbrt.f32 ux) (neg.f32 (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (.f32 maxCos (pow.f32 (cbrt.f32 ux) 2)) (cbrt.f32 ux) (.f32 (neg.f32 (-.f32 1 ux)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (.f32 maxCos (sqrt.f32 ux)) (sqrt.f32 ux) (neg.f32 (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (.f32 maxCos (sqrt.f32 ux)) (sqrt.f32 ux) (.f32 (neg.f32 (-.f32 1 ux)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (+.f32 ux (fma.f32 ux maxCos -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (+.f32 ux (fma.f32 ux maxCos -1))) 1))))))

simplify53.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary32`
701×	`times-frac_binary32`
518×	`associate-/r*_binary32`
497×	`associate-/l*_binary32`
353×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	1854
1	600	1665
2	2172	1532

Stop Event

1×	node limit

Counts

393 → 368

Calls

Call 1

Inputs
1
(+.f32 1 (*.f32 -2 ux))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(pow.f32 ux 2)
(+.f32 (pow.f32 ux 2) (*.f32 -2 ux))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(pow.f32 ux 2)
(+.f32 (pow.f32 ux 2) (*.f32 -2 ux))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
1
(+.f32 (.f32 -1 (.f32 ux (+.f32 2 (*.f32 -1 (+.f32 1 maxCos))))) 1)
(+.f32 (.f32 -1 (.f32 ux (+.f32 2 (.f32 -1 (+.f32 1 maxCos))))) (+.f32 1 (.f32 (-.f32 (.f32 -1 (-.f32 (pow.f32 maxCos 2) 1)) (.f32 (+.f32 2 (*.f32 -1 (+.f32 1 maxCos))) (+.f32 1 maxCos))) (pow.f32 ux 2))))
(+.f32 (.f32 -1 (.f32 ux (+.f32 2 (.f32 -1 (+.f32 1 maxCos))))) (+.f32 1 (+.f32 (.f32 (-.f32 (.f32 -1 (-.f32 (pow.f32 maxCos 2) 1)) (.f32 (+.f32 2 (.f32 -1 (+.f32 1 maxCos))) (+.f32 1 maxCos))) (.f32 (pow.f32 ux 3) (+.f32 1 maxCos))) (.f32 (-.f32 (.f32 -1 (-.f32 (pow.f32 maxCos 2) 1)) (.f32 (+.f32 2 (.f32 -1 (+.f32 1 maxCos))) (+.f32 1 maxCos))) (pow.f32 ux 2)))))
(/.f32 (*.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (+.f32 1 maxCos))
(-.f32 (+.f32 (/.f32 (.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (+.f32 1 maxCos)) (.f32 2 (/.f32 1 (+.f32 1 maxCos)))) (*.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (+.f32 1 maxCos) 2))))
(-.f32 (+.f32 (/.f32 (.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (+.f32 1 maxCos)) (+.f32 (.f32 -1 (/.f32 (+.f32 (/.f32 1 (+.f32 1 maxCos)) (.f32 -1 (/.f32 (-.f32 (.f32 2 (/.f32 1 (+.f32 1 maxCos))) (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (+.f32 1 maxCos) 2)))) (+.f32 1 maxCos)))) ux)) (.f32 2 (/.f32 1 (+.f32 1 maxCos))))) (*.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (+.f32 1 maxCos) 2))))
(-.f32 (+.f32 (/.f32 (.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (+.f32 1 maxCos)) (+.f32 (.f32 -1 (/.f32 (+.f32 (/.f32 1 (+.f32 1 maxCos)) (.f32 -1 (/.f32 (-.f32 (.f32 2 (/.f32 1 (+.f32 1 maxCos))) (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (+.f32 1 maxCos) 2)))) (+.f32 1 maxCos)))) ux)) (+.f32 (.f32 2 (/.f32 1 (+.f32 1 maxCos))) (.f32 -1 (/.f32 (+.f32 (/.f32 1 (pow.f32 (+.f32 1 maxCos) 2)) (.f32 -1 (/.f32 (-.f32 (.f32 2 (/.f32 1 (+.f32 1 maxCos))) (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (+.f32 1 maxCos) 2)))) (pow.f32 (+.f32 1 maxCos) 2)))) (pow.f32 ux 2)))))) (*.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (+.f32 1 maxCos) 2))))
(.f32 -1 (/.f32 (.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (-.f32 (*.f32 -1 maxCos) 1)))
(+.f32 (.f32 -1 (+.f32 (.f32 2 (/.f32 1 (-.f32 (.f32 -1 maxCos) 1))) (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 2))))) (.f32 -1 (/.f32 (.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (-.f32 (.f32 -1 maxCos) 1))))
(+.f32 (.f32 -1 (+.f32 (.f32 2 (/.f32 1 (-.f32 (.f32 -1 maxCos) 1))) (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 2))))) (+.f32 (/.f32 1 (.f32 ux (-.f32 (.f32 -1 maxCos) 1))) (+.f32 (.f32 2 (/.f32 1 (.f32 ux (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 2)))) (+.f32 (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (.f32 ux (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 3)))) (.f32 -1 (/.f32 (.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (-.f32 (.f32 -1 maxCos) 1)))))))
(+.f32 (.f32 -1 (+.f32 (.f32 2 (/.f32 1 (-.f32 (.f32 -1 maxCos) 1))) (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 2))))) (+.f32 (/.f32 1 (.f32 ux (-.f32 (.f32 -1 maxCos) 1))) (+.f32 (.f32 2 (/.f32 1 (.f32 ux (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 2)))) (+.f32 (.f32 -1 (/.f32 (+.f32 (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 4))) (+.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 2)) (.f32 2 (/.f32 1 (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 3))))) (pow.f32 ux 2))) (+.f32 (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (.f32 ux (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 3)))) (.f32 -1 (/.f32 (.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (-.f32 (.f32 -1 maxCos) 1))))))))
(*.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 ux 1)))
(+.f32 (/.f32 (.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 maxCos ux)) (pow.f32 (-.f32 ux 1) 2)) (*.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 ux 1))))
(+.f32 (/.f32 (.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 maxCos ux)) (pow.f32 (-.f32 ux 1) 2)) (+.f32 (.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 ux 1))) (.f32 (pow.f32 maxCos 2) (-.f32 (/.f32 (pow.f32 ux 2) (-.f32 ux 1)) (/.f32 (*.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 ux 2)) (pow.f32 (-.f32 ux 1) 3))))))
(+.f32 (/.f32 (.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 maxCos ux)) (pow.f32 (-.f32 ux 1) 2)) (+.f32 (.f32 -1 (/.f32 (.f32 (pow.f32 maxCos 3) (.f32 ux (-.f32 (/.f32 (pow.f32 ux 2) (-.f32 ux 1)) (/.f32 (.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 ux 2)) (pow.f32 (-.f32 ux 1) 3))))) (-.f32 ux 1))) (+.f32 (.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 ux 1))) (.f32 (pow.f32 maxCos 2) (-.f32 (/.f32 (pow.f32 ux 2) (-.f32 ux 1)) (/.f32 (*.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 ux 2)) (pow.f32 (-.f32 ux 1) 3)))))))
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 (.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 maxCos ux))) (+.f32 1 (.f32 maxCos ux))) (+.f32 (/.f32 (.f32 (-.f32 ux 1) (-.f32 1 ux)) (*.f32 maxCos ux)) ux))
(-.f32 (+.f32 (.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 maxCos ux))) (+.f32 1 (+.f32 (.f32 -1 (/.f32 (.f32 (-.f32 ux 1) (-.f32 (.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux)) (/.f32 (.f32 (-.f32 ux 1) (-.f32 1 ux)) ux))) (.f32 (pow.f32 maxCos 2) ux))) (.f32 maxCos ux)))) (+.f32 (/.f32 (.f32 (-.f32 ux 1) (-.f32 1 ux)) (.f32 maxCos ux)) ux))
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (+.f32 (.f32 -1 (/.f32 (-.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux) (.f32 -1 (/.f32 (.f32 (-.f32 ux 1) (-.f32 1 ux)) ux))) maxCos)) (.f32 maxCos ux))) ux)
(-.f32 (+.f32 1 (+.f32 (.f32 -1 (/.f32 (-.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux) (.f32 -1 (/.f32 (.f32 (-.f32 ux 1) (-.f32 1 ux)) ux))) maxCos)) (+.f32 (/.f32 (.f32 (-.f32 ux 1) (-.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux) (.f32 -1 (/.f32 (.f32 (-.f32 ux 1) (-.f32 1 ux)) ux)))) (.f32 (pow.f32 maxCos 2) ux)) (.f32 maxCos ux)))) ux)
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
-1
(-.f32 (*.f32 ux (+.f32 1 maxCos)) 1)
(-.f32 (*.f32 ux (+.f32 1 maxCos)) 1)
(-.f32 (*.f32 ux (+.f32 1 maxCos)) 1)
(*.f32 ux (+.f32 1 maxCos))
(-.f32 (*.f32 ux (+.f32 1 maxCos)) 1)
(-.f32 (*.f32 ux (+.f32 1 maxCos)) 1)
(-.f32 (*.f32 ux (+.f32 1 maxCos)) 1)
(.f32 -1 (.f32 ux (-.f32 (*.f32 -1 maxCos) 1)))
(-.f32 (.f32 -1 (.f32 ux (-.f32 (*.f32 -1 maxCos) 1))) 1)
(-.f32 (.f32 -1 (.f32 ux (-.f32 (*.f32 -1 maxCos) 1))) 1)
(-.f32 (.f32 -1 (.f32 ux (-.f32 (*.f32 -1 maxCos) 1))) 1)
(-.f32 ux 1)
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(*.f32 maxCos ux)
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(*.f32 maxCos ux)
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)

Outputs
1
(+.f32 1 (*.f32 -2 ux))
(fma.f32 -2 ux 1)
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (+.f32 1 (.f32 -2 ux)) (.f32 ux ux))
(fma.f32 ux ux (fma.f32 -2 ux 1))
(fma.f32 ux (+.f32 -2 ux) 1)
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (+.f32 1 (.f32 -2 ux)) (.f32 ux ux))
(fma.f32 ux ux (fma.f32 -2 ux 1))
(fma.f32 ux (+.f32 -2 ux) 1)
(pow.f32 ux 2)
(*.f32 ux ux)
(+.f32 (pow.f32 ux 2) (*.f32 -2 ux))
(+.f32 (.f32 -2 ux) (.f32 ux ux))
(*.f32 ux (+.f32 -2 ux))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (+.f32 1 (.f32 -2 ux)) (.f32 ux ux))
(fma.f32 ux ux (fma.f32 -2 ux 1))
(fma.f32 ux (+.f32 -2 ux) 1)
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (+.f32 1 (.f32 -2 ux)) (.f32 ux ux))
(fma.f32 ux ux (fma.f32 -2 ux 1))
(fma.f32 ux (+.f32 -2 ux) 1)
(pow.f32 ux 2)
(*.f32 ux ux)
(+.f32 (pow.f32 ux 2) (*.f32 -2 ux))
(+.f32 (.f32 -2 ux) (.f32 ux ux))
(*.f32 ux (+.f32 -2 ux))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (+.f32 1 (.f32 -2 ux)) (.f32 ux ux))
(fma.f32 ux ux (fma.f32 -2 ux 1))
(fma.f32 ux (+.f32 -2 ux) 1)
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (+.f32 1 (.f32 -2 ux)) (.f32 ux ux))
(fma.f32 ux ux (fma.f32 -2 ux 1))
(fma.f32 ux (+.f32 -2 ux) 1)
1
(+.f32 (.f32 -1 (.f32 ux (+.f32 2 (*.f32 -1 (+.f32 1 maxCos))))) 1)
(fma.f32 -1 (*.f32 ux (+.f32 2 (neg.f32 (+.f32 1 maxCos)))) 1)
(fma.f32 (neg.f32 ux) (+.f32 1 (neg.f32 maxCos)) 1)
(-.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(+.f32 (.f32 -1 (.f32 ux (+.f32 2 (.f32 -1 (+.f32 1 maxCos))))) (+.f32 1 (.f32 (-.f32 (.f32 -1 (-.f32 (pow.f32 maxCos 2) 1)) (.f32 (+.f32 2 (*.f32 -1 (+.f32 1 maxCos))) (+.f32 1 maxCos))) (pow.f32 ux 2))))
(+.f32 (fma.f32 -1 (.f32 ux (+.f32 2 (neg.f32 (+.f32 1 maxCos)))) 1) (.f32 (.f32 ux ux) (-.f32 (neg.f32 (+.f32 (.f32 maxCos maxCos) -1)) (*.f32 (+.f32 1 maxCos) (+.f32 2 (neg.f32 (+.f32 1 maxCos)))))))
(-.f32 (fma.f32 (.f32 ux ux) (fma.f32 -1 (fma.f32 maxCos maxCos -1) (.f32 (+.f32 1 (neg.f32 maxCos)) (-.f32 -1 maxCos))) 1) (*.f32 ux (+.f32 1 (neg.f32 maxCos))))
(-.f32 (fma.f32 (.f32 ux ux) (-.f32 (.f32 (-.f32 1 maxCos) (-.f32 -1 maxCos)) (fma.f32 maxCos maxCos -1)) 1) (*.f32 ux (-.f32 1 maxCos)))
(+.f32 (.f32 -1 (.f32 ux (+.f32 2 (.f32 -1 (+.f32 1 maxCos))))) (+.f32 1 (+.f32 (.f32 (-.f32 (.f32 -1 (-.f32 (pow.f32 maxCos 2) 1)) (.f32 (+.f32 2 (.f32 -1 (+.f32 1 maxCos))) (+.f32 1 maxCos))) (.f32 (pow.f32 ux 3) (+.f32 1 maxCos))) (.f32 (-.f32 (.f32 -1 (-.f32 (pow.f32 maxCos 2) 1)) (.f32 (+.f32 2 (.f32 -1 (+.f32 1 maxCos))) (+.f32 1 maxCos))) (pow.f32 ux 2)))))
(+.f32 (fma.f32 -1 (.f32 ux (+.f32 2 (neg.f32 (+.f32 1 maxCos)))) 1) (.f32 (-.f32 (neg.f32 (+.f32 (.f32 maxCos maxCos) -1)) (.f32 (+.f32 1 maxCos) (+.f32 2 (neg.f32 (+.f32 1 maxCos))))) (+.f32 (.f32 (+.f32 1 maxCos) (pow.f32 ux 3)) (.f32 ux ux))))
(-.f32 (fma.f32 (fma.f32 -1 (fma.f32 maxCos maxCos -1) (.f32 (+.f32 1 (neg.f32 maxCos)) (-.f32 -1 maxCos))) (fma.f32 (+.f32 1 maxCos) (pow.f32 ux 3) (.f32 ux ux)) 1) (*.f32 ux (+.f32 1 (neg.f32 maxCos))))
(fma.f32 (-.f32 (.f32 (-.f32 1 maxCos) (-.f32 -1 maxCos)) (fma.f32 maxCos maxCos -1)) (.f32 (+.f32 (fma.f32 ux maxCos ux) 1) (.f32 ux ux)) (-.f32 1 (.f32 ux (-.f32 1 maxCos))))
(/.f32 (*.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (+.f32 1 maxCos))
(/.f32 (+.f32 (*.f32 maxCos maxCos) -1) (/.f32 (+.f32 1 maxCos) ux))
(/.f32 (fma.f32 maxCos maxCos -1) (/.f32 (+.f32 1 maxCos) ux))
(*.f32 (/.f32 (fma.f32 maxCos maxCos -1) (+.f32 1 maxCos)) ux)
(-.f32 (+.f32 (/.f32 (.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (+.f32 1 maxCos)) (.f32 2 (/.f32 1 (+.f32 1 maxCos)))) (*.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (+.f32 1 maxCos) 2))))
(+.f32 (/.f32 (+.f32 (.f32 maxCos maxCos) -1) (/.f32 (+.f32 1 maxCos) ux)) (-.f32 (/.f32 2 (+.f32 1 maxCos)) (/.f32 (neg.f32 (+.f32 (.f32 maxCos maxCos) -1)) (pow.f32 (+.f32 1 maxCos) 2))))
(+.f32 (/.f32 2 (+.f32 1 maxCos)) (+.f32 (/.f32 (fma.f32 maxCos maxCos -1) (/.f32 (+.f32 1 maxCos) ux)) (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (+.f32 1 maxCos) 2))))
(+.f32 (/.f32 -2 (-.f32 -1 maxCos)) (*.f32 (/.f32 (fma.f32 maxCos maxCos -1) (+.f32 1 maxCos)) (-.f32 ux (/.f32 -1 (+.f32 1 maxCos)))))
(-.f32 (+.f32 (/.f32 (.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (+.f32 1 maxCos)) (+.f32 (.f32 -1 (/.f32 (+.f32 (/.f32 1 (+.f32 1 maxCos)) (.f32 -1 (/.f32 (-.f32 (.f32 2 (/.f32 1 (+.f32 1 maxCos))) (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (+.f32 1 maxCos) 2)))) (+.f32 1 maxCos)))) ux)) (.f32 2 (/.f32 1 (+.f32 1 maxCos))))) (*.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (+.f32 1 maxCos) 2))))
(+.f32 (/.f32 (+.f32 (.f32 maxCos maxCos) -1) (/.f32 (+.f32 1 maxCos) ux)) (-.f32 (fma.f32 -1 (/.f32 (+.f32 (/.f32 1 (+.f32 1 maxCos)) (neg.f32 (/.f32 (-.f32 (/.f32 2 (+.f32 1 maxCos)) (/.f32 (neg.f32 (+.f32 (.f32 maxCos maxCos) -1)) (pow.f32 (+.f32 1 maxCos) 2))) (+.f32 1 maxCos)))) ux) (/.f32 2 (+.f32 1 maxCos))) (/.f32 (neg.f32 (+.f32 (*.f32 maxCos maxCos) -1)) (pow.f32 (+.f32 1 maxCos) 2))))
(+.f32 (-.f32 (/.f32 2 (+.f32 1 maxCos)) (/.f32 (-.f32 (/.f32 1 (+.f32 1 maxCos)) (/.f32 (+.f32 (/.f32 2 (+.f32 1 maxCos)) (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (+.f32 1 maxCos) 2))) (+.f32 1 maxCos))) ux)) (+.f32 (/.f32 (fma.f32 maxCos maxCos -1) (/.f32 (+.f32 1 maxCos) ux)) (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (+.f32 1 maxCos) 2))))
(+.f32 (-.f32 (/.f32 -2 (-.f32 -1 maxCos)) (/.f32 (-.f32 (/.f32 1 (+.f32 1 maxCos)) (+.f32 (/.f32 2 (pow.f32 (+.f32 1 maxCos) 2)) (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (+.f32 1 maxCos) 3)))) ux)) (*.f32 (/.f32 (fma.f32 maxCos maxCos -1) (+.f32 1 maxCos)) (-.f32 ux (/.f32 -1 (+.f32 1 maxCos)))))
(-.f32 (+.f32 (/.f32 (.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (+.f32 1 maxCos)) (+.f32 (.f32 -1 (/.f32 (+.f32 (/.f32 1 (+.f32 1 maxCos)) (.f32 -1 (/.f32 (-.f32 (.f32 2 (/.f32 1 (+.f32 1 maxCos))) (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (+.f32 1 maxCos) 2)))) (+.f32 1 maxCos)))) ux)) (+.f32 (.f32 2 (/.f32 1 (+.f32 1 maxCos))) (.f32 -1 (/.f32 (+.f32 (/.f32 1 (pow.f32 (+.f32 1 maxCos) 2)) (.f32 -1 (/.f32 (-.f32 (.f32 2 (/.f32 1 (+.f32 1 maxCos))) (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (+.f32 1 maxCos) 2)))) (pow.f32 (+.f32 1 maxCos) 2)))) (pow.f32 ux 2)))))) (*.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (+.f32 1 maxCos) 2))))
(+.f32 (/.f32 (+.f32 (.f32 maxCos maxCos) -1) (/.f32 (+.f32 1 maxCos) ux)) (-.f32 (+.f32 (fma.f32 -1 (/.f32 (+.f32 (/.f32 1 (+.f32 1 maxCos)) (neg.f32 (/.f32 (-.f32 (/.f32 2 (+.f32 1 maxCos)) (/.f32 (neg.f32 (+.f32 (.f32 maxCos maxCos) -1)) (pow.f32 (+.f32 1 maxCos) 2))) (+.f32 1 maxCos)))) ux) (/.f32 2 (+.f32 1 maxCos))) (neg.f32 (/.f32 (+.f32 (/.f32 1 (pow.f32 (+.f32 1 maxCos) 2)) (neg.f32 (/.f32 (-.f32 (/.f32 2 (+.f32 1 maxCos)) (/.f32 (neg.f32 (+.f32 (.f32 maxCos maxCos) -1)) (pow.f32 (+.f32 1 maxCos) 2))) (pow.f32 (+.f32 1 maxCos) 2)))) (.f32 ux ux)))) (/.f32 (neg.f32 (+.f32 (*.f32 maxCos maxCos) -1)) (pow.f32 (+.f32 1 maxCos) 2))))
(+.f32 (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (+.f32 1 maxCos) 2)) (+.f32 (-.f32 (/.f32 2 (+.f32 1 maxCos)) (/.f32 (-.f32 (/.f32 1 (pow.f32 (+.f32 1 maxCos) 2)) (/.f32 (+.f32 (/.f32 2 (+.f32 1 maxCos)) (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (+.f32 1 maxCos) 2))) (pow.f32 (+.f32 1 maxCos) 2))) (*.f32 ux ux))) (-.f32 (/.f32 (fma.f32 maxCos maxCos -1) (/.f32 (+.f32 1 maxCos) ux)) (/.f32 (-.f32 (/.f32 1 (+.f32 1 maxCos)) (/.f32 (+.f32 (/.f32 2 (+.f32 1 maxCos)) (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (+.f32 1 maxCos) 2))) (+.f32 1 maxCos))) ux))))
(+.f32 (+.f32 (/.f32 -2 (-.f32 -1 maxCos)) (+.f32 (/.f32 (+.f32 (+.f32 (/.f32 2 (pow.f32 (+.f32 1 maxCos) 3)) (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (+.f32 1 maxCos) 4))) (/.f32 -1 (pow.f32 (+.f32 1 maxCos) 2))) (.f32 ux ux)) (/.f32 (+.f32 (+.f32 (/.f32 2 (pow.f32 (+.f32 1 maxCos) 2)) (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (+.f32 1 maxCos) 3))) (/.f32 -1 (+.f32 1 maxCos))) ux))) (.f32 (/.f32 (fma.f32 maxCos maxCos -1) (+.f32 1 maxCos)) (-.f32 ux (/.f32 -1 (+.f32 1 maxCos)))))
(.f32 -1 (/.f32 (.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (-.f32 (*.f32 -1 maxCos) 1)))
(neg.f32 (/.f32 (+.f32 (*.f32 maxCos maxCos) -1) (/.f32 (fma.f32 -1 maxCos -1) ux)))
(/.f32 (neg.f32 (fma.f32 maxCos maxCos -1)) (/.f32 (-.f32 -1 maxCos) ux))
(+.f32 (.f32 -1 (+.f32 (.f32 2 (/.f32 1 (-.f32 (.f32 -1 maxCos) 1))) (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 2))))) (.f32 -1 (/.f32 (.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (-.f32 (.f32 -1 maxCos) 1))))
(fma.f32 -1 (+.f32 (/.f32 2 (fma.f32 -1 maxCos -1)) (/.f32 (neg.f32 (+.f32 (.f32 maxCos maxCos) -1)) (pow.f32 (fma.f32 -1 maxCos -1) 2))) (neg.f32 (/.f32 (+.f32 (.f32 maxCos maxCos) -1) (/.f32 (fma.f32 -1 maxCos -1) ux))))
(-.f32 (/.f32 (neg.f32 (fma.f32 maxCos maxCos -1)) (/.f32 (-.f32 -1 maxCos) ux)) (-.f32 (/.f32 2 (-.f32 -1 maxCos)) (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (-.f32 -1 maxCos) 2))))
(+.f32 (/.f32 -2 (-.f32 -1 maxCos)) (neg.f32 (*.f32 (/.f32 (fma.f32 maxCos maxCos -1) (-.f32 -1 maxCos)) (+.f32 (/.f32 1 (+.f32 1 maxCos)) ux))))
(+.f32 (.f32 -1 (+.f32 (.f32 2 (/.f32 1 (-.f32 (.f32 -1 maxCos) 1))) (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 2))))) (+.f32 (/.f32 1 (.f32 ux (-.f32 (.f32 -1 maxCos) 1))) (+.f32 (.f32 2 (/.f32 1 (.f32 ux (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 2)))) (+.f32 (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (.f32 ux (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 3)))) (.f32 -1 (/.f32 (.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (-.f32 (.f32 -1 maxCos) 1)))))))
(fma.f32 -1 (+.f32 (/.f32 2 (fma.f32 -1 maxCos -1)) (/.f32 (neg.f32 (+.f32 (.f32 maxCos maxCos) -1)) (pow.f32 (fma.f32 -1 maxCos -1) 2))) (+.f32 (/.f32 1 (.f32 ux (fma.f32 -1 maxCos -1))) (+.f32 (/.f32 2 (.f32 ux (pow.f32 (fma.f32 -1 maxCos -1) 2))) (fma.f32 -1 (/.f32 (+.f32 (.f32 maxCos maxCos) -1) (.f32 ux (pow.f32 (fma.f32 -1 maxCos -1) 3))) (neg.f32 (/.f32 (+.f32 (.f32 maxCos maxCos) -1) (/.f32 (fma.f32 -1 maxCos -1) ux)))))))
(-.f32 (+.f32 (/.f32 1 (.f32 ux (-.f32 -1 maxCos))) (-.f32 (-.f32 (/.f32 2 (.f32 ux (pow.f32 (-.f32 -1 maxCos) 2))) (/.f32 (fma.f32 maxCos maxCos -1) (.f32 ux (pow.f32 (-.f32 -1 maxCos) 3)))) (.f32 (/.f32 (fma.f32 maxCos maxCos -1) (-.f32 -1 maxCos)) ux))) (-.f32 (/.f32 2 (-.f32 -1 maxCos)) (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (-.f32 -1 maxCos) 2))))
(+.f32 (-.f32 (+.f32 (/.f32 -2 (-.f32 -1 maxCos)) (+.f32 (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (+.f32 1 maxCos) 2)) (/.f32 -1 (fma.f32 ux maxCos ux)))) (fma.f32 (/.f32 (fma.f32 maxCos maxCos -1) (-.f32 -1 maxCos)) ux (/.f32 (fma.f32 maxCos maxCos -1) (.f32 ux (pow.f32 (-.f32 -1 maxCos) 3))))) (/.f32 2 (.f32 ux (pow.f32 (+.f32 1 maxCos) 2))))
(+.f32 (.f32 -1 (+.f32 (.f32 2 (/.f32 1 (-.f32 (.f32 -1 maxCos) 1))) (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 2))))) (+.f32 (/.f32 1 (.f32 ux (-.f32 (.f32 -1 maxCos) 1))) (+.f32 (.f32 2 (/.f32 1 (.f32 ux (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 2)))) (+.f32 (.f32 -1 (/.f32 (+.f32 (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 4))) (+.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 2)) (.f32 2 (/.f32 1 (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 3))))) (pow.f32 ux 2))) (+.f32 (.f32 -1 (/.f32 (-.f32 (pow.f32 maxCos 2) 1) (.f32 ux (pow.f32 (-.f32 (.f32 -1 maxCos) 1) 3)))) (.f32 -1 (/.f32 (.f32 (-.f32 (pow.f32 maxCos 2) 1) ux) (-.f32 (.f32 -1 maxCos) 1))))))))
(fma.f32 -1 (+.f32 (/.f32 2 (fma.f32 -1 maxCos -1)) (/.f32 (neg.f32 (+.f32 (.f32 maxCos maxCos) -1)) (pow.f32 (fma.f32 -1 maxCos -1) 2))) (+.f32 (/.f32 1 (.f32 ux (fma.f32 -1 maxCos -1))) (+.f32 (/.f32 2 (.f32 ux (pow.f32 (fma.f32 -1 maxCos -1) 2))) (fma.f32 -1 (/.f32 (fma.f32 -1 (/.f32 (+.f32 (.f32 maxCos maxCos) -1) (pow.f32 (fma.f32 -1 maxCos -1) 4)) (+.f32 (/.f32 1 (pow.f32 (fma.f32 -1 maxCos -1) 2)) (/.f32 2 (pow.f32 (fma.f32 -1 maxCos -1) 3)))) (.f32 ux ux)) (fma.f32 -1 (/.f32 (+.f32 (.f32 maxCos maxCos) -1) (.f32 ux (pow.f32 (fma.f32 -1 maxCos -1) 3))) (neg.f32 (/.f32 (+.f32 (.f32 maxCos maxCos) -1) (/.f32 (fma.f32 -1 maxCos -1) ux))))))))
(-.f32 (+.f32 (/.f32 1 (.f32 ux (-.f32 -1 maxCos))) (+.f32 (-.f32 (-.f32 (/.f32 2 (.f32 ux (pow.f32 (-.f32 -1 maxCos) 2))) (/.f32 (fma.f32 maxCos maxCos -1) (.f32 ux (pow.f32 (-.f32 -1 maxCos) 3)))) (.f32 (/.f32 (fma.f32 maxCos maxCos -1) (-.f32 -1 maxCos)) ux)) (/.f32 (neg.f32 (-.f32 (+.f32 (/.f32 1 (pow.f32 (-.f32 -1 maxCos) 2)) (/.f32 2 (pow.f32 (-.f32 -1 maxCos) 3))) (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (-.f32 -1 maxCos) 4)))) (*.f32 ux ux)))) (-.f32 (/.f32 2 (-.f32 -1 maxCos)) (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (-.f32 -1 maxCos) 2))))
(+.f32 (/.f32 -1 (fma.f32 ux maxCos ux)) (+.f32 (-.f32 (+.f32 (/.f32 2 (.f32 ux (pow.f32 (+.f32 1 maxCos) 2))) (/.f32 (+.f32 (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (+.f32 1 maxCos) 4)) (+.f32 (/.f32 2 (pow.f32 (+.f32 1 maxCos) 3)) (/.f32 -1 (pow.f32 (+.f32 1 maxCos) 2)))) (.f32 ux ux))) (fma.f32 (/.f32 (fma.f32 maxCos maxCos -1) (-.f32 -1 maxCos)) ux (/.f32 (fma.f32 maxCos maxCos -1) (*.f32 ux (pow.f32 (-.f32 -1 maxCos) 3))))) (+.f32 (/.f32 -2 (-.f32 -1 maxCos)) (/.f32 (fma.f32 maxCos maxCos -1) (pow.f32 (+.f32 1 maxCos) 2)))))
(*.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 ux 1)))
(neg.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (+.f32 ux -1)))
(/.f32 (neg.f32 (pow.f32 (-.f32 1 ux) 2)) (+.f32 ux -1))
(+.f32 (/.f32 (.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 maxCos ux)) (pow.f32 (-.f32 ux 1) 2)) (*.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 ux 1))))
(+.f32 (neg.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (+.f32 ux -1))) (/.f32 (pow.f32 (-.f32 1 ux) 2) (/.f32 (pow.f32 (+.f32 ux -1) 2) (*.f32 ux maxCos))))
(-.f32 (/.f32 (*.f32 ux maxCos) (/.f32 (pow.f32 (+.f32 ux -1) 2) (pow.f32 (-.f32 1 ux) 2))) (/.f32 (pow.f32 (-.f32 1 ux) 2) (+.f32 ux -1)))
(*.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (+.f32 ux -1)) (+.f32 -1 (/.f32 maxCos (/.f32 (+.f32 ux -1) ux))))
(+.f32 (/.f32 (.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 maxCos ux)) (pow.f32 (-.f32 ux 1) 2)) (+.f32 (.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 ux 1))) (.f32 (pow.f32 maxCos 2) (-.f32 (/.f32 (pow.f32 ux 2) (-.f32 ux 1)) (/.f32 (*.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 ux 2)) (pow.f32 (-.f32 ux 1) 3))))))
(+.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (/.f32 (pow.f32 (+.f32 ux -1) 2) (.f32 ux maxCos))) (fma.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (+.f32 ux -1)) (.f32 (.f32 maxCos maxCos) (-.f32 (/.f32 (.f32 ux ux) (+.f32 ux -1)) (/.f32 (pow.f32 (-.f32 1 ux) 2) (/.f32 (pow.f32 (+.f32 ux -1) 3) (*.f32 ux ux)))))))
(+.f32 (/.f32 (.f32 ux maxCos) (/.f32 (pow.f32 (+.f32 ux -1) 2) (pow.f32 (-.f32 1 ux) 2))) (fma.f32 (.f32 maxCos maxCos) (-.f32 (/.f32 ux (/.f32 (+.f32 ux -1) ux)) (.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (+.f32 ux -1) 3)) (.f32 ux ux))) (/.f32 (neg.f32 (pow.f32 (-.f32 1 ux) 2)) (+.f32 ux -1))))
(fma.f32 maxCos (.f32 maxCos (-.f32 (.f32 (/.f32 ux (+.f32 ux -1)) ux) (.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (+.f32 ux -1) 3)) (.f32 ux ux)))) (*.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (+.f32 ux -1)) (+.f32 -1 (/.f32 maxCos (/.f32 (+.f32 ux -1) ux)))))
(+.f32 (/.f32 (.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 maxCos ux)) (pow.f32 (-.f32 ux 1) 2)) (+.f32 (.f32 -1 (/.f32 (.f32 (pow.f32 maxCos 3) (.f32 ux (-.f32 (/.f32 (pow.f32 ux 2) (-.f32 ux 1)) (/.f32 (.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 ux 2)) (pow.f32 (-.f32 ux 1) 3))))) (-.f32 ux 1))) (+.f32 (.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 ux 1))) (.f32 (pow.f32 maxCos 2) (-.f32 (/.f32 (pow.f32 ux 2) (-.f32 ux 1)) (/.f32 (*.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 ux 2)) (pow.f32 (-.f32 ux 1) 3)))))))
(+.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (/.f32 (pow.f32 (+.f32 ux -1) 2) (.f32 ux maxCos))) (fma.f32 -1 (/.f32 (.f32 (pow.f32 maxCos 3) (.f32 ux (-.f32 (/.f32 (.f32 ux ux) (+.f32 ux -1)) (/.f32 (pow.f32 (-.f32 1 ux) 2) (/.f32 (pow.f32 (+.f32 ux -1) 3) (.f32 ux ux)))))) (+.f32 ux -1)) (fma.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (+.f32 ux -1)) (.f32 (.f32 maxCos maxCos) (-.f32 (/.f32 (.f32 ux ux) (+.f32 ux -1)) (/.f32 (pow.f32 (-.f32 1 ux) 2) (/.f32 (pow.f32 (+.f32 ux -1) 3) (*.f32 ux ux))))))))
(+.f32 (/.f32 (.f32 ux maxCos) (/.f32 (pow.f32 (+.f32 ux -1) 2) (pow.f32 (-.f32 1 ux) 2))) (-.f32 (fma.f32 (.f32 maxCos maxCos) (-.f32 (/.f32 ux (/.f32 (+.f32 ux -1) ux)) (.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (+.f32 ux -1) 3)) (.f32 ux ux))) (/.f32 (neg.f32 (pow.f32 (-.f32 1 ux) 2)) (+.f32 ux -1))) (.f32 (/.f32 (pow.f32 maxCos 3) (+.f32 ux -1)) (.f32 ux (-.f32 (/.f32 ux (/.f32 (+.f32 ux -1) ux)) (.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (+.f32 ux -1) 3)) (.f32 ux ux)))))))
(-.f32 (fma.f32 maxCos (.f32 maxCos (-.f32 (.f32 (/.f32 ux (+.f32 ux -1)) ux) (.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (+.f32 ux -1) 3)) (.f32 ux ux)))) (.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (+.f32 ux -1)) (+.f32 -1 (/.f32 maxCos (/.f32 (+.f32 ux -1) ux))))) (.f32 (/.f32 (pow.f32 maxCos 3) (+.f32 ux -1)) (.f32 ux (-.f32 (.f32 (/.f32 ux (+.f32 ux -1)) ux) (.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (+.f32 ux -1) 3)) (.f32 ux ux))))))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (-.f32 (*.f32 ux maxCos) ux))
(-.f32 (fma.f32 ux maxCos 1) ux)
(-.f32 (+.f32 (.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 maxCos ux))) (+.f32 1 (.f32 maxCos ux))) (+.f32 (/.f32 (.f32 (-.f32 ux 1) (-.f32 1 ux)) (*.f32 maxCos ux)) ux))
(-.f32 (fma.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 ux maxCos)) (+.f32 1 (.f32 ux maxCos))) (+.f32 ux (*.f32 (/.f32 (+.f32 ux -1) maxCos) (/.f32 (-.f32 1 ux) ux))))
(-.f32 (-.f32 (fma.f32 ux maxCos 1) (/.f32 (pow.f32 (-.f32 1 ux) 2) (*.f32 ux maxCos))) (fma.f32 (/.f32 (+.f32 ux -1) maxCos) (/.f32 (-.f32 1 ux) ux) ux))
(+.f32 (fma.f32 ux maxCos (/.f32 (-.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux) (/.f32 (pow.f32 (-.f32 1 ux) 2) ux)) maxCos)) (-.f32 1 ux))
(-.f32 (+.f32 (.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 maxCos ux))) (+.f32 1 (+.f32 (.f32 -1 (/.f32 (.f32 (-.f32 ux 1) (-.f32 (.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux)) (/.f32 (.f32 (-.f32 ux 1) (-.f32 1 ux)) ux))) (.f32 (pow.f32 maxCos 2) ux))) (.f32 maxCos ux)))) (+.f32 (/.f32 (.f32 (-.f32 ux 1) (-.f32 1 ux)) (.f32 maxCos ux)) ux))
(-.f32 (fma.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 ux maxCos)) (+.f32 1 (fma.f32 -1 (/.f32 (+.f32 ux -1) (/.f32 (.f32 ux (.f32 maxCos maxCos)) (-.f32 (neg.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux)) (/.f32 (+.f32 ux -1) (/.f32 ux (-.f32 1 ux)))))) (.f32 ux maxCos)))) (+.f32 ux (*.f32 (/.f32 (+.f32 ux -1) maxCos) (/.f32 (-.f32 1 ux) ux))))
(-.f32 (+.f32 (-.f32 (fma.f32 ux maxCos 1) (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 ux maxCos))) (/.f32 (neg.f32 (+.f32 ux -1)) (/.f32 ux (/.f32 (-.f32 (/.f32 (neg.f32 (pow.f32 (-.f32 1 ux) 2)) ux) (.f32 (/.f32 (+.f32 ux -1) ux) (-.f32 1 ux))) (*.f32 maxCos maxCos))))) (fma.f32 (/.f32 (+.f32 ux -1) maxCos) (/.f32 (-.f32 1 ux) ux) ux))
(+.f32 (fma.f32 ux maxCos (fma.f32 (/.f32 (+.f32 ux -1) (*.f32 maxCos maxCos)) (/.f32 (-.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux) (/.f32 (pow.f32 (-.f32 1 ux) 2) ux)) ux) (/.f32 (-.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux) (/.f32 (pow.f32 (-.f32 1 ux) 2) ux)) maxCos))) (-.f32 1 ux))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (-.f32 (*.f32 ux maxCos) ux))
(-.f32 (fma.f32 ux maxCos 1) ux)
(-.f32 (+.f32 1 (+.f32 (.f32 -1 (/.f32 (-.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux) (.f32 -1 (/.f32 (.f32 (-.f32 ux 1) (-.f32 1 ux)) ux))) maxCos)) (.f32 maxCos ux))) ux)
(-.f32 (fma.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 ux maxCos)) (+.f32 1 (.f32 ux maxCos))) (+.f32 ux (*.f32 (/.f32 (+.f32 ux -1) maxCos) (/.f32 (-.f32 1 ux) ux))))
(-.f32 (-.f32 (fma.f32 ux maxCos 1) (/.f32 (pow.f32 (-.f32 1 ux) 2) (*.f32 ux maxCos))) (fma.f32 (/.f32 (+.f32 ux -1) maxCos) (/.f32 (-.f32 1 ux) ux) ux))
(+.f32 (fma.f32 ux maxCos (/.f32 (-.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux) (/.f32 (pow.f32 (-.f32 1 ux) 2) ux)) maxCos)) (-.f32 1 ux))
(-.f32 (+.f32 1 (+.f32 (.f32 -1 (/.f32 (-.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux) (.f32 -1 (/.f32 (.f32 (-.f32 ux 1) (-.f32 1 ux)) ux))) maxCos)) (+.f32 (/.f32 (.f32 (-.f32 ux 1) (-.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux) (.f32 -1 (/.f32 (.f32 (-.f32 ux 1) (-.f32 1 ux)) ux)))) (.f32 (pow.f32 maxCos 2) ux)) (.f32 maxCos ux)))) ux)
(-.f32 (fma.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 ux maxCos)) (+.f32 1 (fma.f32 -1 (/.f32 (+.f32 ux -1) (/.f32 (.f32 ux (.f32 maxCos maxCos)) (-.f32 (neg.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux)) (/.f32 (+.f32 ux -1) (/.f32 ux (-.f32 1 ux)))))) (.f32 ux maxCos)))) (+.f32 ux (*.f32 (/.f32 (+.f32 ux -1) maxCos) (/.f32 (-.f32 1 ux) ux))))
(-.f32 (+.f32 (-.f32 (fma.f32 ux maxCos 1) (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 ux maxCos))) (/.f32 (neg.f32 (+.f32 ux -1)) (/.f32 ux (/.f32 (-.f32 (/.f32 (neg.f32 (pow.f32 (-.f32 1 ux) 2)) ux) (.f32 (/.f32 (+.f32 ux -1) ux) (-.f32 1 ux))) (*.f32 maxCos maxCos))))) (fma.f32 (/.f32 (+.f32 ux -1) maxCos) (/.f32 (-.f32 1 ux) ux) ux))
(+.f32 (fma.f32 ux maxCos (fma.f32 (/.f32 (+.f32 ux -1) (*.f32 maxCos maxCos)) (/.f32 (-.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux) (/.f32 (pow.f32 (-.f32 1 ux) 2) ux)) ux) (/.f32 (-.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux) (/.f32 (pow.f32 (-.f32 1 ux) 2) ux)) maxCos))) (-.f32 1 ux))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
-1
(-.f32 (*.f32 ux (+.f32 1 maxCos)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(-.f32 (*.f32 ux (+.f32 1 maxCos)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(-.f32 (*.f32 ux (+.f32 1 maxCos)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(*.f32 ux (+.f32 1 maxCos))
(+.f32 ux (*.f32 ux maxCos))
(fma.f32 ux maxCos ux)
(-.f32 (*.f32 ux (+.f32 1 maxCos)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(-.f32 (*.f32 ux (+.f32 1 maxCos)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(-.f32 (*.f32 ux (+.f32 1 maxCos)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(.f32 -1 (.f32 ux (-.f32 (*.f32 -1 maxCos) 1)))
(+.f32 ux (*.f32 ux maxCos))
(fma.f32 ux maxCos ux)
(-.f32 (.f32 -1 (.f32 ux (-.f32 (*.f32 -1 maxCos) 1))) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(-.f32 (.f32 -1 (.f32 ux (-.f32 (*.f32 -1 maxCos) 1))) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(-.f32 (.f32 -1 (.f32 ux (-.f32 (*.f32 -1 maxCos) 1))) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(-.f32 ux 1)
(+.f32 ux -1)
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))
(-.f32 (+.f32 ux (*.f32 maxCos ux)) 1)
(fma.f32 ux (+.f32 1 maxCos) -1)
(+.f32 ux (fma.f32 ux maxCos -1))
(fma.f32 ux maxCos (+.f32 ux -1))

localize17.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f32 (-.f32 maxCos 1) ux)
	0.0b	(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
✓	0.0b	(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
✓	0.1b	(*.f32 (-.f32 maxCos 1) ux)

series5.0ms (0.2%)

Counts

2 → 27

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	maxCos	@	-inf	(*.f32 (-.f32 maxCos 1) ux)
0.0ms	maxCos	@	0	(*.f32 (-.f32 maxCos 1) ux)
0.0ms	ux	@	-inf	(*.f32 (-.f32 maxCos 1) ux)
0.0ms	ux	@	inf	(*.f32 (-.f32 maxCos 1) ux)
0.0ms	ux	@	0	(*.f32 (-.f32 maxCos 1) ux)

rewrite45.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

799×	`pow1_binary32`
743×	`add-log-exp_binary32`
742×	`log1p-expm1-u_binary32`
742×	`expm1-log1p-u_binary32`
729×	`add-exp-log_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	152	15
2	2042	15

Stop Event

1×	node limit

Counts

2 → 49

Calls

Call 1

Inputs
(*.f32 (-.f32 maxCos 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 maxCos ux) (*.f32 -1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 ux maxCos) (*.f32 ux -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 (pow.f32 maxCos 3) -1) ux) (fma.f32 maxCos maxCos (+.f32 maxCos 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (fma.f32 maxCos maxCos -1) ux) (+.f32 maxCos 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 ux (+.f32 (pow.f32 maxCos 3) -1)) (fma.f32 maxCos maxCos (+.f32 maxCos 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 ux (fma.f32 maxCos maxCos -1)) (+.f32 maxCos 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (+.f32 maxCos -1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 ux) (+.f32 maxCos -1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 (+.f32 maxCos -1) ux)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 1 (fma.f32 (+.f32 maxCos -1) ux 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 1 (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))) (/.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (fma.f32 (+.f32 maxCos -1) ux 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) (pow.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 2) (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) (sqrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3)) (/.f32 1 (+.f32 1 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (*.f32 (+.f32 maxCos -1) ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2)) (/.f32 1 (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 1 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (*.f32 (+.f32 maxCos -1) ux))) (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (-.f32 1 (*.f32 (+.f32 maxCos -1) ux)) (-.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3)) (+.f32 1 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3)) (+.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2)) (-.f32 1 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3))) (neg.f32 (+.f32 1 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (*.f32 (+.f32 maxCos -1) ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2))) (neg.f32 (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) 1) (-.f32 (*.f32 (+.f32 maxCos -1) ux) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (*.f32 (+.f32 maxCos -1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (+.f32 maxCos -1) ux 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 ux (+.f32 maxCos -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 2) (cbrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (*.f32 (+.f32 maxCos -1) ux)) (sqrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))))))

simplify26.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

186×	`fma-def_binary32`
186×	`fma-neg_binary32`
59×	`cancel-sign-sub-inv_binary32`
32×	`sub-neg_binary32`
31×	`associate--r+_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	201
1	31	173
2	46	173
3	64	173
4	96	173
5	155	173
6	311	173
7	522	173
8	733	173
9	822	173
10	846	173
11	847	173

Stop Event

1×

saturated

Counts

76 → 61

Calls

Call 1

Inputs
(*.f32 -1 ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
1
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)

Outputs
(*.f32 -1 ux)
(neg.f32 ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
1
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)

localize6.0ms (0.2%)

eval202.0ms (7%)

Compiler: Compiled 10496 to 6780 computations (35.4% saved)

prune62.0ms (2.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	427	2	429
Fresh	1	0	1
Picked	0	1	1
Done	1	2	3
Total	429	5	434

Error

Counts

434 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(/.f32 (neg.f32 (pow.f32 (-.f32 1 ux) 2)) (+.f32 ux -1))
	8.4b	1
✓	0.5b	(-.f32 1 ux)
✓	0.0b	(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
✓	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

Compiler

Compiled 43 to 35 computations (18.6% saved)

localize25.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(/.f32 (neg.f32 (pow.f32 (-.f32 1 ux) 2)) (+.f32 ux -1))
	0.4b	(pow.f32 (-.f32 1 ux) 2)
	0.4b	(pow.f32 (-.f32 1 ux) 2)
✓	0.4b	(/.f32 (neg.f32 (pow.f32 (-.f32 1 ux) 2)) (+.f32 ux -1))

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	ux	@	0	(/.f32 (neg.f32 (pow.f32 (-.f32 1 ux) 2)) (+.f32 ux -1))
1.0ms	ux	@	inf	(/.f32 (neg.f32 (pow.f32 (-.f32 1 ux) 2)) (+.f32 ux -1))
0.0ms	ux	@	-inf	(/.f32 (neg.f32 (pow.f32 (-.f32 1 ux) 2)) (+.f32 ux -1))

rewrite45.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

969×	`pow1_binary32`
905×	`add-log-exp_binary32`
903×	`log1p-expm1-u_binary32`
903×	`expm1-log1p-u_binary32`
107×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	220	13
2	2942	13

Stop Event

1×	node limit

Counts

1 → 39

Calls

Call 1

Inputs
(/.f32 (neg.f32 (pow.f32 (-.f32 1 ux) 2)) (+.f32 ux -1))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 0 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 0 (+.f32 ux -1)) (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 1 ux) (*.f32 (-.f32 1 ux) (/.f32 -1 (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (-.f32 1 ux) 2) (/.f32 -1 (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (-.f32 1 ux) 2) (/.f32 1 (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))) (pow.f32 (cbrt.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))) 2) (cbrt.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 4)) (*.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (/.f32 -1 (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (-.f32 1 ux) (sqrt.f32 (-.f32 1 ux))) (/.f32 (-.f32 1 ux) (sqrt.f32 (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 -1 (-.f32 1 ux)) (pow.f32 (-.f32 1 ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (-.f32 1 ux) 1) (/.f32 (-.f32 1 ux) (+.f32 ux -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (cbrt.f32 (pow.f32 (+.f32 ux -1) 2))) (/.f32 (pow.f32 (-.f32 1 ux) 2) (cbrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (-.f32 1 ux) (cbrt.f32 (pow.f32 (+.f32 ux -1) 2))) (/.f32 (-.f32 1 ux) (cbrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (sqrt.f32 (+.f32 ux -1))) (/.f32 (pow.f32 (-.f32 1 ux) 2) (sqrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 4)) 1) (/.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (+.f32 ux -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 -1 (cbrt.f32 (pow.f32 (+.f32 ux -1) 2))) (/.f32 (pow.f32 (-.f32 1 ux) 2) (cbrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 4)) (cbrt.f32 (pow.f32 (+.f32 ux -1) 2))) (cbrt.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 -1 (sqrt.f32 (+.f32 ux -1))) (/.f32 (pow.f32 (-.f32 1 ux) 2) (sqrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 4)) (sqrt.f32 (+.f32 ux -1))) (/.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (sqrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (+.f32 -1 (pow.f32 ux 3))) (fma.f32 ux ux (-.f32 1 (neg.f32 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (fma.f32 ux ux -1)) (+.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (-.f32 1 ux) (sqrt.f32 (-.f32 1 ux))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (-.f32 1 ux) (pow.f32 (-.f32 1 ux) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (/.f32 (pow.f32 (-.f32 1 ux) 4) (pow.f32 (-.f32 1 ux) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (pow.f32 (pow.f32 (-.f32 1 ux) 2) 3) (pow.f32 (+.f32 ux -1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (-.f32 (*.f32 2 (log1p.f32 (neg.f32 ux))) (log1p.f32 (neg.f32 ux))))))))

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

7×	`sub-neg_binary32`
6×	`fma-def_binary32`
4×	`+-commutative_binary32`
3×	`associate-+l-_binary32`
3×	`associate--r+_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	52
1	12	43
2	15	43
3	19	43
4	25	43
5	35	43
6	46	43
7	58	43
8	61	43

Stop Event

1×

saturated

Counts

51 → 44

Calls

Call 1

Inputs
1
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (*.f32 -1 ux) 1)
(*.f32 -1 ux)
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (*.f32 -1 ux) 1)
(*.f32 -1 ux)
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (*.f32 -1 ux) 1)

Outputs
1
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(*.f32 -1 ux)
(neg.f32 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(*.f32 -1 ux)
(neg.f32 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)

eval35.0ms (1.2%)

Compiler: Compiled 1543 to 1173 computations (24% saved)

prune16.0ms (0.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	0	1
Picked	1	0	1
Done	0	3	3
Total	100	5	105

Error

Counts

105 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(/.f32 (neg.f32 (*.f32 (-.f32 1 ux) (-.f32 1 ux))) (+.f32 ux -1))
✓	0.0b	(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
✓	0.5b	(-.f32 1 ux)
	8.4b	1
✓	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

Compiler

Compiled 45 to 36 computations (20% saved)

localize25.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(/.f32 (neg.f32 (*.f32 (-.f32 1 ux) (-.f32 1 ux))) (+.f32 ux -1))
	0.4b	(*.f32 (-.f32 1 ux) (-.f32 1 ux))
✓	0.4b	(*.f32 (-.f32 1 ux) (-.f32 1 ux))
✓	0.4b	(/.f32 (neg.f32 (*.f32 (-.f32 1 ux) (-.f32 1 ux))) (+.f32 ux -1))

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	ux	@	0	(/.f32 (neg.f32 (*.f32 (-.f32 1 ux) (-.f32 1 ux))) (+.f32 ux -1))
0.0ms	ux	@	inf	(/.f32 (neg.f32 (*.f32 (-.f32 1 ux) (-.f32 1 ux))) (+.f32 ux -1))
0.0ms	ux	@	inf	(*.f32 (-.f32 1 ux) (-.f32 1 ux))
0.0ms	ux	@	-inf	(/.f32 (neg.f32 (*.f32 (-.f32 1 ux) (-.f32 1 ux))) (+.f32 ux -1))
0.0ms	ux	@	-inf	(*.f32 (-.f32 1 ux) (-.f32 1 ux))

rewrite50.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

949×	`pow1_binary32`
888×	`add-log-exp_binary32`
886×	`log1p-expm1-u_binary32`
886×	`expm1-log1p-u_binary32`
100×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	199	20
2	2898	20

Stop Event

1×	node limit

Counts

2 → 80

Calls

Call 1

Inputs
(/.f32 (neg.f32 (*.f32 (-.f32 1 ux) (-.f32 1 ux))) (+.f32 ux -1))
(*.f32 (-.f32 1 ux) (-.f32 1 ux))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 0 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 0 (+.f32 ux -1)) (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 1 ux) (*.f32 (neg.f32 (-.f32 1 ux)) (/.f32 1 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 1 ux) (*.f32 (-.f32 1 ux) (/.f32 1 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (-.f32 1 ux) 2) (/.f32 1 (+.f32 ux -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (-.f32 1 ux) 2) (/.f32 1 (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 -1 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))) (pow.f32 (cbrt.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))) 2) (cbrt.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 4)) (*.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (/.f32 1 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (-.f32 1 ux) (sqrt.f32 (+.f32 ux -1))) (/.f32 (-.f32 1 ux) (sqrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (-.f32 1 ux) (sqrt.f32 (+.f32 ux -1))) (/.f32 (neg.f32 (-.f32 1 ux)) (sqrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (+.f32 ux -1)) (pow.f32 (-.f32 1 ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (neg.f32 (-.f32 1 ux)) (*.f32 (-.f32 1 ux) (/.f32 1 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (-.f32 1 ux) 1) (/.f32 (neg.f32 (-.f32 1 ux)) (+.f32 ux -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (-.f32 1 ux) 1) (/.f32 (-.f32 1 ux) (+.f32 ux -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 4)) 1) (/.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (+.f32 ux -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (neg.f32 (-.f32 1 ux)) 1) (/.f32 (-.f32 1 ux) (+.f32 ux -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (pow.f32 (cbrt.f32 (+.f32 ux -1)) 2)) (/.f32 (pow.f32 (-.f32 1 ux) 2) (cbrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (-.f32 1 ux) (pow.f32 (cbrt.f32 (+.f32 ux -1)) 2)) (/.f32 (neg.f32 (-.f32 1 ux)) (cbrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (-.f32 1 ux) (pow.f32 (cbrt.f32 (+.f32 ux -1)) 2)) (/.f32 (-.f32 1 ux) (cbrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 -1 (pow.f32 (cbrt.f32 (+.f32 ux -1)) 2)) (/.f32 (pow.f32 (-.f32 1 ux) 2) (cbrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 4)) (pow.f32 (cbrt.f32 (+.f32 ux -1)) 2)) (cbrt.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (neg.f32 (-.f32 1 ux)) (pow.f32 (cbrt.f32 (+.f32 ux -1)) 2)) (/.f32 (-.f32 1 ux) (cbrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (sqrt.f32 (+.f32 ux -1))) (/.f32 (pow.f32 (-.f32 1 ux) 2) (sqrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (neg.f32 (-.f32 1 ux)) (sqrt.f32 (+.f32 ux -1))) (/.f32 (-.f32 1 ux) (sqrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 -1 (sqrt.f32 (+.f32 ux -1))) (/.f32 (pow.f32 (-.f32 1 ux) 2) (sqrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 4)) (sqrt.f32 (+.f32 ux -1))) (/.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (sqrt.f32 (+.f32 ux -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (+.f32 -1 (pow.f32 ux 3))) (fma.f32 ux ux (-.f32 1 (neg.f32 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (fma.f32 ux ux -1)) (+.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (-.f32 1 ux) (sqrt.f32 (+.f32 ux -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (-.f32 1 ux) (pow.f32 (-.f32 1 ux) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (/.f32 (pow.f32 (-.f32 1 ux) 4) (pow.f32 (-.f32 1 ux) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (pow.f32 (pow.f32 (-.f32 1 ux) 2) 3) (pow.f32 (+.f32 ux -1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (-.f32 (*.f32 (log1p.f32 (neg.f32 ux)) 2) (log1p.f32 (neg.f32 ux))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 1 ux) (*.f32 (neg.f32 ux) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 1 ux) (*.f32 (-.f32 1 ux) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (pow.f32 (-.f32 1 ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (neg.f32 (-.f32 1 ux)) (*.f32 (neg.f32 ux) (neg.f32 (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (neg.f32 (-.f32 1 ux)) 1) (*.f32 (neg.f32 (-.f32 1 ux)) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 0 (pow.f32 (-.f32 1 ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (pow.f32 (-.f32 1 ux) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (-.f32 1 (*.f32 ux ux)) (-.f32 1 (*.f32 ux ux))) (*.f32 (+.f32 1 ux) (+.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (-.f32 1 (pow.f32 ux 3)) (-.f32 1 (pow.f32 ux 3))) (*.f32 (+.f32 1 (fma.f32 ux ux ux)) (+.f32 1 (fma.f32 ux ux ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (-.f32 1 (*.f32 ux ux)) (-.f32 1 (pow.f32 ux 3))) (*.f32 (+.f32 1 ux) (+.f32 1 (fma.f32 ux ux ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (-.f32 1 (pow.f32 ux 3)) (-.f32 1 (*.f32 ux ux))) (*.f32 (+.f32 1 (fma.f32 ux ux ux)) (+.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 0 (pow.f32 (pow.f32 (-.f32 1 ux) 2) 3)) (+.f32 0 (+.f32 (pow.f32 (-.f32 1 ux) 4) (*.f32 0 (pow.f32 (-.f32 1 ux) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 0 (pow.f32 (-.f32 1 ux) 4)) (pow.f32 (-.f32 1 ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (-.f32 1 (pow.f32 ux 3)) (neg.f32 (-.f32 1 ux))) (+.f32 1 (fma.f32 ux ux ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (-.f32 1 (*.f32 ux ux)) (neg.f32 (-.f32 1 ux))) (+.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (-.f32 1 (pow.f32 ux 3)) (-.f32 1 ux)) (+.f32 1 (fma.f32 ux ux ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (-.f32 1 (*.f32 ux ux)) (-.f32 1 ux)) (+.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (neg.f32 (-.f32 1 ux)) (-.f32 1 (pow.f32 ux 3))) (+.f32 1 (fma.f32 ux ux ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (neg.f32 (-.f32 1 ux)) (-.f32 1 (*.f32 ux ux))) (+.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (-.f32 1 ux) (-.f32 1 (pow.f32 ux 3))) (+.f32 1 (fma.f32 ux ux ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (-.f32 1 ux) (-.f32 1 (*.f32 ux ux))) (+.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (-.f32 1 ux) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (-.f32 1 ux) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (-.f32 1 ux) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (pow.f32 (-.f32 1 ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (-.f32 1 ux) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (pow.f32 (-.f32 1 ux) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (pow.f32 (-.f32 1 ux) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (pow.f32 (-.f32 1 ux) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (pow.f32 (-.f32 1 ux) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (pow.f32 (-.f32 1 ux) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log1p.f32 (neg.f32 ux)) 2))))))

simplify41.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-neg_binary32`
451×	`fma-def_binary32`
434×	`unswap-sqr_binary32`
367×	`associate--l+_binary32`
358×	`associate--r+_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	166
1	29	125
2	56	119
3	95	119
4	197	119
5	471	119
6	1455	119
7	3179	119
8	4600	119

Stop Event

1×	node limit

Counts

104 → 93

Calls

Call 1

Inputs
1
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (*.f32 -1 ux) 1)
(*.f32 -1 ux)
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (*.f32 -1 ux) 1)
(*.f32 -1 ux)
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (*.f32 -1 ux) 1)
1
(+.f32 1 (*.f32 -2 ux))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(pow.f32 ux 2)
(+.f32 (pow.f32 ux 2) (*.f32 -2 ux))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(pow.f32 ux 2)
(+.f32 (pow.f32 ux 2) (*.f32 -2 ux))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))

Outputs
1
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(*.f32 -1 ux)
(neg.f32 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(*.f32 -1 ux)
(neg.f32 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
1
(+.f32 1 (*.f32 -2 ux))
(+.f32 1 (*.f32 ux -2))
(fma.f32 ux -2 1)
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (+.f32 1 (.f32 ux -2)) (.f32 ux ux))
(fma.f32 ux ux (fma.f32 ux -2 1))
(fma.f32 ux (+.f32 ux -2) 1)
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (+.f32 1 (.f32 ux -2)) (.f32 ux ux))
(fma.f32 ux ux (fma.f32 ux -2 1))
(fma.f32 ux (+.f32 ux -2) 1)
(pow.f32 ux 2)
(*.f32 ux ux)
(+.f32 (pow.f32 ux 2) (*.f32 -2 ux))
(+.f32 (.f32 ux -2) (.f32 ux ux))
(*.f32 ux (+.f32 ux -2))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (+.f32 1 (.f32 ux -2)) (.f32 ux ux))
(fma.f32 ux ux (fma.f32 ux -2 1))
(fma.f32 ux (+.f32 ux -2) 1)
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (+.f32 1 (.f32 ux -2)) (.f32 ux ux))
(fma.f32 ux ux (fma.f32 ux -2 1))
(fma.f32 ux (+.f32 ux -2) 1)
(pow.f32 ux 2)
(*.f32 ux ux)
(+.f32 (pow.f32 ux 2) (*.f32 -2 ux))
(+.f32 (.f32 ux -2) (.f32 ux ux))
(*.f32 ux (+.f32 ux -2))
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (+.f32 1 (.f32 ux -2)) (.f32 ux ux))
(fma.f32 ux ux (fma.f32 ux -2 1))
(fma.f32 ux (+.f32 ux -2) 1)
(+.f32 (pow.f32 ux 2) (+.f32 1 (*.f32 -2 ux)))
(+.f32 (+.f32 1 (.f32 ux -2)) (.f32 ux ux))
(fma.f32 ux ux (fma.f32 ux -2 1))
(fma.f32 ux (+.f32 ux -2) 1)

eval56.0ms (1.9%)

Compiler: Compiled 1360 to 1049 computations (22.9% saved)

prune22.0ms (0.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	93	5	98

Error

Counts

98 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f32 (neg.f32 (*.f32 (-.f32 1 ux) (-.f32 1 ux))) (+.f32 ux -1))
✓	0.0b	(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
✓	0.5b	(-.f32 1 ux)
	8.4b	1
✓	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

Compiler

Compiled 45 to 36 computations (20% saved)

regimes35.0ms (1.2%)

Counts

10 → 1

Calls

Call 1

Inputs
1
1
1
(-.f32 1 ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
(/.f32 (neg.f32 (*.f32 (-.f32 1 ux) (-.f32 1 ux))) (+.f32 ux -1))
(-.f32 (fma.f32 ux maxCos 1) ux)
(/.f32 (neg.f32 (pow.f32 (-.f32 1 ux) 2)) (+.f32 ux -1))
(/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 2) (pow.f32 (-.f32 1 ux) 2)) (-.f32 (.f32 ux maxCos) (-.f32 1 ux)))

Outputs
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))

Calls

5 calls:

7.0ms	ux
7.0ms	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
6.0ms	uy
6.0ms	maxCos
6.0ms	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

Results

Error	Segments	Branch
0.0b	1	`ux`
0.0b	1	`uy`
0.0b	1	`maxCos`
0.0b	1	`(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))`
0.0b	1	`(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))`

Compiler

Compiled 102 to 71 computations (30.4% saved)

regimes13.0ms (0.4%)

Counts

4 → 1

Calls

Call 1

Inputs
1
1
1
(-.f32 1 ux)

Outputs
(-.f32 1 ux)

Calls

3 calls:

4.0ms	ux
4.0ms	uy
4.0ms	maxCos

Results

Error	Segments	Branch
0.5b	1	`ux`
0.5b	1	`uy`
0.5b	1	`maxCos`

Compiler

Compiled 21 to 17 computations (19% saved)

regimes14.0ms (0.5%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

3 → 1

Calls

Call 1

Inputs
1
1
1

Outputs
1

Calls

3 calls:

6.0ms	maxCos
4.0ms	uy
4.0ms	ux

Results

Error	Segments	Branch
8.4b	1	`ux`
8.4b	1	`uy`
8.4b	1	`maxCos`

Compiler

Compiled 18 to 15 computations (16.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary32`
3×	`sub-neg_binary32`
2×	`*-commutative_binary32`
1×	`neg-sub0_binary32`
1×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	17	15
2	21	15
3	23	15
4	24	15

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(-.f32 1 ux)
1

Outputs
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 1 ux)
1

end42.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 34 to 28 computations (17.6% saved)

Iter	Nodes	Cost
0	13	201
1	31	173
2	46	173
3	64	173
4	96	173
5	155	173
6	311	173
7	522	173
8	733	173
9	822	173
10	846	173
11	847	173

Iter	Nodes	Cost
0	13	201
1	31	173
2	46	173
3	64	173
4	96	173
5	155	173
6	311	173
7	522	173
8	733	173
9	822	173
10	846	173
11	847	173

Details

analyze1.0ms (0%)

sample1.6s (56.2%)

preprocess41.0ms (1.4%)

simplify15.0ms (0.5%)

eval1.0ms (0%)

prune1.0ms (0%)

localize16.0ms (0.5%)

series6.0ms (0.2%)

rewrite52.0ms (1.8%)

simplify24.0ms (0.8%)

localize13.0ms (0.4%)

series3.0ms (0.1%)

rewrite40.0ms (1.4%)

simplify19.0ms (0.7%)

eval27.0ms (0.9%)

prune17.0ms (0.6%)

localize37.0ms (1.3%)

series13.0ms (0.4%)

rewrite94.0ms (3.2%)

simplify53.0ms (1.8%)

localize17.0ms (0.6%)

series5.0ms (0.2%)

rewrite45.0ms (1.5%)

simplify26.0ms (0.9%)

localize6.0ms (0.2%)

eval202.0ms (7%)

prune62.0ms (2.2%)

localize25.0ms (0.9%)

series2.0ms (0.1%)

rewrite45.0ms (1.6%)

simplify9.0ms (0.3%)

eval35.0ms (1.2%)

prune16.0ms (0.5%)

localize25.0ms (0.9%)

series2.0ms (0.1%)

rewrite50.0ms (1.7%)

simplify41.0ms (1.4%)

eval56.0ms (1.9%)

prune22.0ms (0.7%)

regimes35.0ms (1.2%)

regimes13.0ms (0.4%)

regimes14.0ms (0.5%)

simplify2.0ms (0.1%)

end42.0ms (1.5%)

Profiling

Iter	Nodes	Cost
0	13	201
1	31	173
2	46	173
3	64	173
4	96	173
5	155	173
6	311	173
7	522	173
8	733	173
9	822	173
10	846	173
11	847	173