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 (55.8%)

Results

1.6s

8256×

body

256

valid

preprocess68.0ms (2.3%)

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	1152	32
6	1980	32
7	2318	32
8	2398	32
9	2409	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 (-.f32 1 uy) (*.f32 uy maxCos))
(+.f32 (-.f32 1 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 ux maxCos) (-.f32 1 maxCos))
(fma.f32 ux maxCos (-.f32 1 maxCos))
(-.f32 (fma.f32 ux maxCos 1) maxCos)
(fma.f32 maxCos (+.f32 ux -1) 1)
(+.f32 (-.f32 1 ux) (*.f32 ux uy))
(fma.f32 ux uy (-.f32 1 ux))
(-.f32 (fma.f32 ux uy 1) ux)
(fma.f32 ux (-.f32 uy 1) 1)

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify23.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

199×	`fma-def_binary32`
151×	`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	363	8
6	626	8
7	768	8
8	800	8
9	805	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
▶	0.1b	(-.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)

localize21.0ms (0.7%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 10 computations (47.4% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite60.0ms (2%)

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	10
1	154	8
2	2215	8

Stop Event

1×	node limit

Counts

1 → 39

Calls

Call 1

Inputs
(+.f32 (-.f32 1 ux) (*.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 1 (+.f32 ux (.f32 ux maxCos)))) (/.f32 (pow.f32 (.f32 ux maxCos) 2) (-.f32 1 (+.f32 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 1 (+.f32 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 1 (+.f32 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 1 (+.f32 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 1 (+.f32 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 expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(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 exp.f32 (log.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))))))

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 1 (+.f32 ux (*.f32 ux maxCos)))) (/.f32 (pow.f32 (*.f32 ux maxCos) 2) (-.f32 1 (+.f32 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 1 (+.f32 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 1 (+.f32 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 1 (+.f32 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 1 (+.f32 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 expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(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 exp.f32 (log.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))))))

simplify27.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

185×	`fma-def_binary32`
162×	`fma-neg_binary32`
31×	`sub-neg_binary32`
25×	`unsub-neg_binary32`
23×	`cancel-sign-sub-inv_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	207
1	45	171
2	111	171
3	230	171
4	465	171
5	664	171
6	772	171
7	790	171

Stop Event

1×

saturated

Counts

63 → 49

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

localize17.0ms (0.6%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(-.f32 (fma.f32 ux maxCos 1) ux)

Compiler

Compiled 16 to 9 computations (43.8% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite49.0ms (1.7%)

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	1637	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 expm1.f32 (log1p.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(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 exp.f32 (log.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))))))

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 expm1.f32 (log1p.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(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 exp.f32 (log.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))))))

simplify27.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

185×	`fma-def_binary32`
162×	`fma-neg_binary32`
31×	`sub-neg_binary32`
25×	`unsub-neg_binary32`
23×	`cancel-sign-sub-inv_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	207
1	45	171
2	111	171
3	230	171
4	465	171
5	664	171
6	772	171
7	790	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 ux (+.f32 maxCos -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 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))
(*.f32 (+.f32 maxCos -1) ux)
(-.f32 (*.f32 maxCos ux) ux)
(*.f32 ux (+.f32 maxCos -1))
(+.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)

eval24.0ms (0.8%)

Compiler: Compiled 1223 to 740 computations (39.5% saved)

prune18.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	93	5	98

Error

Counts

98 → 5

Alt Table

Click to see full alt table

Status	Error	Program
	8.2b	1
▶	0.4b	(/.f32 (-.f32 1 (.f32 (.f32 ux (-.f32 1 maxCos)) (.f32 ux (-.f32 1 maxCos)))) (+.f32 1 (.f32 ux (-.f32 1 maxCos))))
✓	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
▶	0.0b	(-.f32 1 (*.f32 ux (-.f32 1 maxCos)))
▶	0.8b	(-.f32 1 ux)

Compiler

Compiled 54 to 42 computations (22.2% saved)

localize8.0ms (0.3%)

Compiler: Compiled 8 to 6 computations (25% saved)

localize22.0ms (0.7%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 21 to 14 computations (33.3% saved)

series5.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

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

rewrite57.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

847×	`pow1_binary32`
787×	`add-log-exp_binary32`
787×	`log1p-expm1-u_binary32`
787×	`expm1-log1p-u_binary32`
773×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	154	17
2	2077	17

Stop Event

1×	node limit

Counts

2 → 45

Calls

Call 1

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

Outputs

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

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

simplify36.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

203×	`fma-def_binary32`
147×	`fma-neg_binary32`
52×	`cancel-sign-sub-inv_binary32`
36×	`sub-neg_binary32`
32×	`associate--r+_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	367
1	45	331
2	96	331
3	180	331
4	377	331
5	620	331
6	784	331
7	839	331
8	848	331

Stop Event

1×

saturated

Counts

93 → 61

Calls

Call 1

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

localize51.0ms (1.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
	0.0b	(*.f32 ux (-.f32 1 maxCos))
✓	0.1b	(.f32 (.f32 ux (-.f32 1 maxCos)) (*.f32 ux (-.f32 1 maxCos)))
✓	0.4b	(/.f32 (-.f32 1 (.f32 (.f32 ux (-.f32 1 maxCos)) (.f32 ux (-.f32 1 maxCos)))) (+.f32 1 (.f32 ux (-.f32 1 maxCos))))

Compiler

Compiled 66 to 45 computations (31.8% saved)

series11.0ms (0.4%)

Counts

3 → 72

Calls

18 calls:

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

rewrite81.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

642×	`log-prod_binary32`
444×	`fma-def_binary32`
311×	`pow2_binary32`
262×	`fma-neg_binary32`
213×	`pow1/3_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	45
1	234	28
2	3611	28

Stop Event

1×	node limit

Counts

3 → 155

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

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

simplify58.0ms (2%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-def_binary32`
567×	`times-frac_binary32`
464×	`associate-r_binary32`
427×	`associate-l_binary32`
348×	`associate-/l*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	113	1584
1	432	1370
2	1600	1238

Stop Event

1×	node limit

Counts

227 → 201

Calls

Call 1

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

Outputs
1
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(fma.f32 (+.f32 maxCos -1) ux 1)
(fma.f32 ux (+.f32 maxCos -1) 1)
(+.f32 1 (+.f32 (.f32 (-.f32 (.f32 -1 (pow.f32 (-.f32 1 maxCos) 2)) (.f32 (-.f32 maxCos 1) (-.f32 1 maxCos))) (pow.f32 ux 2)) (.f32 (-.f32 maxCos 1) ux)))
(+.f32 1 (fma.f32 (-.f32 (neg.f32 (pow.f32 (-.f32 1 maxCos) 2)) (.f32 (+.f32 maxCos -1) (-.f32 1 maxCos))) (.f32 ux ux) (*.f32 (+.f32 maxCos -1) ux)))
(+.f32 (fma.f32 (+.f32 maxCos -1) ux 1) (.f32 (.f32 ux ux) (fma.f32 -1 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 (-.f32 1 maxCos) 2))))
(fma.f32 (.f32 ux ux) (.f32 0 (pow.f32 (-.f32 1 maxCos) 2)) (fma.f32 ux (+.f32 maxCos -1) 1))
(+.f32 1 (+.f32 (.f32 -1 (.f32 (-.f32 1 maxCos) (.f32 (pow.f32 ux 3) (-.f32 (.f32 -1 (pow.f32 (-.f32 1 maxCos) 2)) (.f32 (-.f32 1 maxCos) (-.f32 maxCos 1)))))) (+.f32 (.f32 (-.f32 (.f32 -1 (pow.f32 (-.f32 1 maxCos) 2)) (.f32 (-.f32 maxCos 1) (-.f32 1 maxCos))) (pow.f32 ux 2)) (*.f32 (-.f32 maxCos 1) ux))))
(+.f32 1 (fma.f32 -1 (.f32 (-.f32 1 maxCos) (.f32 (pow.f32 ux 3) (-.f32 (neg.f32 (pow.f32 (-.f32 1 maxCos) 2)) (.f32 (+.f32 maxCos -1) (-.f32 1 maxCos))))) (fma.f32 (-.f32 (neg.f32 (pow.f32 (-.f32 1 maxCos) 2)) (.f32 (+.f32 maxCos -1) (-.f32 1 maxCos))) (.f32 ux ux) (.f32 (+.f32 maxCos -1) ux))))
(+.f32 (fma.f32 (+.f32 maxCos -1) ux (.f32 (.f32 ux ux) (fma.f32 -1 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 (-.f32 1 maxCos) 2)))) (-.f32 1 (.f32 (pow.f32 ux 3) (.f32 (fma.f32 -1 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 (-.f32 1 maxCos) 2)) (-.f32 1 maxCos)))))
(+.f32 (.f32 (.f32 0 (pow.f32 (-.f32 1 maxCos) 2)) (+.f32 (.f32 ux ux) (.f32 (pow.f32 ux 3) (+.f32 maxCos -1)))) (fma.f32 ux (+.f32 maxCos -1) 1))
(.f32 -1 (.f32 (-.f32 1 maxCos) ux))
(neg.f32 (*.f32 ux (-.f32 1 maxCos)))
(*.f32 ux (neg.f32 (-.f32 1 maxCos)))
(-.f32 (*.f32 maxCos ux) ux)
(+.f32 1 (.f32 -1 (.f32 (-.f32 1 maxCos) ux)))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(fma.f32 (+.f32 maxCos -1) ux 1)
(fma.f32 ux (+.f32 maxCos -1) 1)
(+.f32 1 (.f32 -1 (.f32 (-.f32 1 maxCos) ux)))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(fma.f32 (+.f32 maxCos -1) ux 1)
(fma.f32 ux (+.f32 maxCos -1) 1)
(+.f32 1 (.f32 -1 (.f32 (-.f32 1 maxCos) ux)))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(fma.f32 (+.f32 maxCos -1) ux 1)
(fma.f32 ux (+.f32 maxCos -1) 1)
(.f32 -1 (.f32 (-.f32 1 maxCos) ux))
(neg.f32 (*.f32 ux (-.f32 1 maxCos)))
(*.f32 ux (neg.f32 (-.f32 1 maxCos)))
(-.f32 (*.f32 maxCos ux) ux)
(+.f32 1 (.f32 -1 (.f32 (-.f32 1 maxCos) ux)))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(fma.f32 (+.f32 maxCos -1) ux 1)
(fma.f32 ux (+.f32 maxCos -1) 1)
(+.f32 1 (.f32 -1 (.f32 (-.f32 1 maxCos) ux)))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(fma.f32 (+.f32 maxCos -1) ux 1)
(fma.f32 ux (+.f32 maxCos -1) 1)
(+.f32 1 (.f32 -1 (.f32 (-.f32 1 maxCos) ux)))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(fma.f32 (+.f32 maxCos -1) ux 1)
(fma.f32 ux (+.f32 maxCos -1) 1)
(/.f32 (-.f32 1 (pow.f32 ux 2)) (+.f32 1 ux))
(/.f32 (-.f32 1 (*.f32 ux ux)) (+.f32 1 ux))
(-.f32 (+.f32 (/.f32 1 (+.f32 1 ux)) (.f32 (-.f32 (.f32 2 (/.f32 (pow.f32 ux 2) (+.f32 1 ux))) (.f32 -1 (/.f32 (.f32 ux (-.f32 1 (pow.f32 ux 2))) (pow.f32 (+.f32 1 ux) 2)))) maxCos)) (/.f32 (pow.f32 ux 2) (+.f32 1 ux)))
(+.f32 (/.f32 1 (+.f32 1 ux)) (-.f32 (.f32 maxCos (-.f32 (.f32 2 (/.f32 (.f32 ux ux) (+.f32 1 ux))) (neg.f32 (/.f32 ux (/.f32 (pow.f32 (+.f32 1 ux) 2) (-.f32 1 (.f32 ux ux))))))) (/.f32 (*.f32 ux ux) (+.f32 1 ux))))
(+.f32 (.f32 maxCos (fma.f32 2 (/.f32 ux (/.f32 (+.f32 1 ux) ux)) (.f32 (/.f32 ux (pow.f32 (+.f32 1 ux) 2)) (-.f32 1 (.f32 ux ux))))) (/.f32 (-.f32 1 (.f32 ux ux)) (+.f32 1 ux)))
(fma.f32 maxCos (fma.f32 2 (.f32 ux (/.f32 ux (+.f32 1 ux))) (/.f32 (+.f32 ux (neg.f32 (pow.f32 ux 3))) (pow.f32 (+.f32 1 ux) 2))) (/.f32 (-.f32 1 (.f32 ux ux)) (+.f32 1 ux)))
(-.f32 (+.f32 (/.f32 1 (+.f32 1 ux)) (+.f32 (.f32 (pow.f32 maxCos 2) (-.f32 (.f32 -1 (/.f32 (pow.f32 ux 2) (+.f32 1 ux))) (.f32 -1 (/.f32 (.f32 (-.f32 (.f32 2 (/.f32 (pow.f32 ux 2) (+.f32 1 ux))) (.f32 -1 (/.f32 (.f32 ux (-.f32 1 (pow.f32 ux 2))) (pow.f32 (+.f32 1 ux) 2)))) ux) (+.f32 1 ux))))) (.f32 (-.f32 (.f32 2 (/.f32 (pow.f32 ux 2) (+.f32 1 ux))) (.f32 -1 (/.f32 (*.f32 ux (-.f32 1 (pow.f32 ux 2))) (pow.f32 (+.f32 1 ux) 2)))) maxCos))) (/.f32 (pow.f32 ux 2) (+.f32 1 ux)))
(+.f32 (/.f32 1 (+.f32 1 ux)) (-.f32 (fma.f32 (.f32 maxCos maxCos) (.f32 -1 (-.f32 (/.f32 (.f32 ux ux) (+.f32 1 ux)) (/.f32 (-.f32 (.f32 2 (/.f32 (.f32 ux ux) (+.f32 1 ux))) (neg.f32 (/.f32 ux (/.f32 (pow.f32 (+.f32 1 ux) 2) (-.f32 1 (.f32 ux ux)))))) (/.f32 (+.f32 1 ux) ux)))) (.f32 maxCos (-.f32 (.f32 2 (/.f32 (.f32 ux ux) (+.f32 1 ux))) (neg.f32 (/.f32 ux (/.f32 (pow.f32 (+.f32 1 ux) 2) (-.f32 1 (.f32 ux ux)))))))) (/.f32 (*.f32 ux ux) (+.f32 1 ux))))
(+.f32 (fma.f32 (.f32 maxCos maxCos) (fma.f32 -1 (/.f32 ux (/.f32 (+.f32 1 ux) ux)) (.f32 (/.f32 (fma.f32 2 (/.f32 ux (/.f32 (+.f32 1 ux) ux)) (.f32 (/.f32 ux (pow.f32 (+.f32 1 ux) 2)) (-.f32 1 (.f32 ux ux)))) (+.f32 1 ux)) ux)) (.f32 maxCos (fma.f32 2 (/.f32 ux (/.f32 (+.f32 1 ux) ux)) (.f32 (/.f32 ux (pow.f32 (+.f32 1 ux) 2)) (-.f32 1 (.f32 ux ux)))))) (/.f32 (-.f32 1 (.f32 ux ux)) (+.f32 1 ux)))
(+.f32 (.f32 maxCos (+.f32 (fma.f32 2 (.f32 ux (/.f32 ux (+.f32 1 ux))) (/.f32 (+.f32 ux (neg.f32 (pow.f32 ux 3))) (pow.f32 (+.f32 1 ux) 2))) (.f32 (-.f32 (.f32 (/.f32 ux (+.f32 1 ux)) (fma.f32 2 (.f32 ux (/.f32 ux (+.f32 1 ux))) (/.f32 (+.f32 ux (neg.f32 (pow.f32 ux 3))) (pow.f32 (+.f32 1 ux) 2)))) (.f32 ux (/.f32 ux (+.f32 1 ux)))) maxCos))) (/.f32 (-.f32 1 (*.f32 ux ux)) (+.f32 1 ux)))
(-.f32 (+.f32 (/.f32 (.f32 (pow.f32 maxCos 3) (.f32 (-.f32 (.f32 -1 (/.f32 (pow.f32 ux 2) (+.f32 1 ux))) (.f32 -1 (/.f32 (.f32 (-.f32 (.f32 2 (/.f32 (pow.f32 ux 2) (+.f32 1 ux))) (.f32 -1 (/.f32 (.f32 ux (-.f32 1 (pow.f32 ux 2))) (pow.f32 (+.f32 1 ux) 2)))) ux) (+.f32 1 ux)))) ux)) (+.f32 1 ux)) (+.f32 (/.f32 1 (+.f32 1 ux)) (+.f32 (.f32 (pow.f32 maxCos 2) (-.f32 (.f32 -1 (/.f32 (pow.f32 ux 2) (+.f32 1 ux))) (.f32 -1 (/.f32 (.f32 (-.f32 (.f32 2 (/.f32 (pow.f32 ux 2) (+.f32 1 ux))) (.f32 -1 (/.f32 (.f32 ux (-.f32 1 (pow.f32 ux 2))) (pow.f32 (+.f32 1 ux) 2)))) ux) (+.f32 1 ux))))) (.f32 (-.f32 (.f32 2 (/.f32 (pow.f32 ux 2) (+.f32 1 ux))) (.f32 -1 (/.f32 (*.f32 ux (-.f32 1 (pow.f32 ux 2))) (pow.f32 (+.f32 1 ux) 2)))) maxCos)))) (/.f32 (pow.f32 ux 2) (+.f32 1 ux)))
(+.f32 (/.f32 (pow.f32 maxCos 3) (/.f32 (+.f32 1 ux) (.f32 ux (.f32 -1 (-.f32 (/.f32 (.f32 ux ux) (+.f32 1 ux)) (/.f32 (-.f32 (.f32 2 (/.f32 (.f32 ux ux) (+.f32 1 ux))) (neg.f32 (/.f32 ux (/.f32 (pow.f32 (+.f32 1 ux) 2) (-.f32 1 (.f32 ux ux)))))) (/.f32 (+.f32 1 ux) ux))))))) (+.f32 (/.f32 1 (+.f32 1 ux)) (-.f32 (fma.f32 (.f32 maxCos maxCos) (.f32 -1 (-.f32 (/.f32 (.f32 ux ux) (+.f32 1 ux)) (/.f32 (-.f32 (.f32 2 (/.f32 (.f32 ux ux) (+.f32 1 ux))) (neg.f32 (/.f32 ux (/.f32 (pow.f32 (+.f32 1 ux) 2) (-.f32 1 (.f32 ux ux)))))) (/.f32 (+.f32 1 ux) ux)))) (.f32 maxCos (-.f32 (.f32 2 (/.f32 (.f32 ux ux) (+.f32 1 ux))) (neg.f32 (/.f32 ux (/.f32 (pow.f32 (+.f32 1 ux) 2) (-.f32 1 (.f32 ux ux)))))))) (/.f32 (*.f32 ux ux) (+.f32 1 ux)))))
(+.f32 (+.f32 (fma.f32 (.f32 maxCos maxCos) (fma.f32 -1 (/.f32 ux (/.f32 (+.f32 1 ux) ux)) (.f32 (/.f32 (fma.f32 2 (/.f32 ux (/.f32 (+.f32 1 ux) ux)) (.f32 (/.f32 ux (pow.f32 (+.f32 1 ux) 2)) (-.f32 1 (.f32 ux ux)))) (+.f32 1 ux)) ux)) (.f32 maxCos (fma.f32 2 (/.f32 ux (/.f32 (+.f32 1 ux) ux)) (.f32 (/.f32 ux (pow.f32 (+.f32 1 ux) 2)) (-.f32 1 (.f32 ux ux)))))) (/.f32 (-.f32 1 (.f32 ux ux)) (+.f32 1 ux))) (.f32 (/.f32 (pow.f32 maxCos 3) (+.f32 1 ux)) (.f32 ux (fma.f32 -1 (/.f32 ux (/.f32 (+.f32 1 ux) ux)) (.f32 (/.f32 (fma.f32 2 (/.f32 ux (/.f32 (+.f32 1 ux) ux)) (.f32 (/.f32 ux (pow.f32 (+.f32 1 ux) 2)) (-.f32 1 (*.f32 ux ux)))) (+.f32 1 ux)) ux)))))
(+.f32 (fma.f32 (/.f32 (pow.f32 maxCos 3) (+.f32 1 ux)) (.f32 ux (-.f32 (.f32 (/.f32 ux (+.f32 1 ux)) (fma.f32 2 (.f32 ux (/.f32 ux (+.f32 1 ux))) (/.f32 (+.f32 ux (neg.f32 (pow.f32 ux 3))) (pow.f32 (+.f32 1 ux) 2)))) (.f32 ux (/.f32 ux (+.f32 1 ux))))) (.f32 maxCos (+.f32 (fma.f32 2 (.f32 ux (/.f32 ux (+.f32 1 ux))) (/.f32 (+.f32 ux (neg.f32 (pow.f32 ux 3))) (pow.f32 (+.f32 1 ux) 2))) (.f32 (-.f32 (.f32 (/.f32 ux (+.f32 1 ux)) (fma.f32 2 (.f32 ux (/.f32 ux (+.f32 1 ux))) (/.f32 (+.f32 ux (neg.f32 (pow.f32 ux 3))) (pow.f32 (+.f32 1 ux) 2)))) (.f32 ux (/.f32 ux (+.f32 1 ux)))) maxCos)))) (/.f32 (-.f32 1 (*.f32 ux ux)) (+.f32 1 ux)))
(*.f32 maxCos ux)
(-.f32 (+.f32 (.f32 -2 ux) (.f32 maxCos ux)) (*.f32 -1 (+.f32 1 ux)))
(-.f32 (*.f32 ux (+.f32 -2 maxCos)) (neg.f32 (+.f32 1 ux)))
(fma.f32 ux (+.f32 maxCos -2) (+.f32 1 ux))
(+.f32 (fma.f32 ux (+.f32 maxCos -2) 1) ux)
(-.f32 (+.f32 (.f32 -2 ux) (+.f32 (.f32 -1 (/.f32 (-.f32 1 (pow.f32 ux 2)) (.f32 maxCos ux))) (.f32 maxCos ux))) (+.f32 (.f32 -1 (/.f32 (.f32 (-.f32 (.f32 -2 ux) (.f32 -1 (+.f32 1 ux))) (+.f32 1 ux)) (.f32 maxCos ux))) (.f32 -1 (+.f32 1 ux))))
(-.f32 (fma.f32 -2 ux (fma.f32 -1 (/.f32 (-.f32 1 (.f32 ux ux)) (.f32 maxCos ux)) (.f32 maxCos ux))) (fma.f32 -1 (.f32 (/.f32 (-.f32 (*.f32 ux -2) (neg.f32 (+.f32 1 ux))) maxCos) (/.f32 (+.f32 1 ux) ux)) (neg.f32 (+.f32 1 ux))))
(-.f32 (fma.f32 ux -2 (-.f32 (.f32 maxCos ux) (/.f32 (-.f32 1 (.f32 ux ux)) (*.f32 maxCos ux)))) (neg.f32 (fma.f32 (/.f32 (fma.f32 ux -2 (+.f32 1 ux)) maxCos) (/.f32 (+.f32 1 ux) ux) (+.f32 1 ux))))
(+.f32 (+.f32 (fma.f32 ux (+.f32 maxCos -2) 1) ux) (/.f32 (+.f32 (fma.f32 (/.f32 (+.f32 (fma.f32 ux -2 1) ux) ux) (+.f32 1 ux) ux) (/.f32 -1 ux)) maxCos))
(-.f32 (+.f32 (.f32 -2 ux) (+.f32 (.f32 -1 (/.f32 (-.f32 1 (pow.f32 ux 2)) (.f32 maxCos ux))) (+.f32 (/.f32 (.f32 (-.f32 (.f32 -1 (/.f32 (-.f32 1 (pow.f32 ux 2)) ux)) (.f32 -1 (/.f32 (.f32 (-.f32 (.f32 -2 ux) (.f32 -1 (+.f32 1 ux))) (+.f32 1 ux)) ux))) (+.f32 1 ux)) (.f32 (pow.f32 maxCos 2) ux)) (.f32 maxCos ux)))) (+.f32 (.f32 -1 (/.f32 (.f32 (-.f32 (.f32 -2 ux) (.f32 -1 (+.f32 1 ux))) (+.f32 1 ux)) (.f32 maxCos ux))) (*.f32 -1 (+.f32 1 ux))))
(-.f32 (fma.f32 -2 ux (fma.f32 -1 (/.f32 (-.f32 1 (.f32 ux ux)) (.f32 maxCos ux)) (+.f32 (.f32 maxCos ux) (.f32 (/.f32 (.f32 -1 (-.f32 (/.f32 (-.f32 1 (.f32 ux ux)) ux) (/.f32 (-.f32 (.f32 ux -2) (neg.f32 (+.f32 1 ux))) (/.f32 ux (+.f32 1 ux))))) (.f32 maxCos maxCos)) (/.f32 (+.f32 1 ux) ux))))) (fma.f32 -1 (.f32 (/.f32 (-.f32 (.f32 ux -2) (neg.f32 (+.f32 1 ux))) maxCos) (/.f32 (+.f32 1 ux) ux)) (neg.f32 (+.f32 1 ux))))
(-.f32 (fma.f32 ux -2 (-.f32 (fma.f32 (/.f32 (fma.f32 -1 (/.f32 (-.f32 1 (.f32 ux ux)) ux) (.f32 (/.f32 (fma.f32 ux -2 (+.f32 1 ux)) ux) (+.f32 1 ux))) (.f32 maxCos maxCos)) (/.f32 (+.f32 1 ux) ux) (.f32 maxCos ux)) (/.f32 (-.f32 1 (.f32 ux ux)) (.f32 maxCos ux)))) (neg.f32 (fma.f32 (/.f32 (fma.f32 ux -2 (+.f32 1 ux)) maxCos) (/.f32 (+.f32 1 ux) ux) (+.f32 1 ux))))
(+.f32 (+.f32 1 ux) (+.f32 (/.f32 (+.f32 (fma.f32 (/.f32 (+.f32 (fma.f32 ux -2 1) ux) ux) (+.f32 1 ux) ux) (/.f32 -1 ux)) maxCos) (fma.f32 ux (+.f32 maxCos -2) (.f32 (/.f32 (+.f32 (fma.f32 (/.f32 (+.f32 (fma.f32 ux -2 1) ux) ux) (+.f32 1 ux) ux) (/.f32 -1 ux)) (.f32 maxCos (*.f32 maxCos ux))) (+.f32 1 ux)))))
(*.f32 maxCos ux)
(-.f32 (+.f32 (.f32 -2 ux) (.f32 maxCos ux)) (*.f32 -1 (+.f32 1 ux)))
(-.f32 (*.f32 ux (+.f32 -2 maxCos)) (neg.f32 (+.f32 1 ux)))
(fma.f32 ux (+.f32 maxCos -2) (+.f32 1 ux))
(+.f32 (fma.f32 ux (+.f32 maxCos -2) 1) ux)
(-.f32 (+.f32 (.f32 -1 (/.f32 (-.f32 (/.f32 1 ux) (+.f32 ux (/.f32 (.f32 (-.f32 (.f32 -2 ux) (.f32 -1 (+.f32 1 ux))) (+.f32 1 ux)) ux))) maxCos)) (+.f32 (.f32 -2 ux) (.f32 maxCos ux))) (*.f32 -1 (+.f32 1 ux)))
(-.f32 (fma.f32 -2 ux (fma.f32 -1 (/.f32 (-.f32 1 (.f32 ux ux)) (.f32 maxCos ux)) (.f32 maxCos ux))) (fma.f32 -1 (.f32 (/.f32 (-.f32 (*.f32 ux -2) (neg.f32 (+.f32 1 ux))) maxCos) (/.f32 (+.f32 1 ux) ux)) (neg.f32 (+.f32 1 ux))))
(-.f32 (fma.f32 ux -2 (-.f32 (.f32 maxCos ux) (/.f32 (-.f32 1 (.f32 ux ux)) (*.f32 maxCos ux)))) (neg.f32 (fma.f32 (/.f32 (fma.f32 ux -2 (+.f32 1 ux)) maxCos) (/.f32 (+.f32 1 ux) ux) (+.f32 1 ux))))
(+.f32 (+.f32 (fma.f32 ux (+.f32 maxCos -2) 1) ux) (/.f32 (+.f32 (fma.f32 (/.f32 (+.f32 (fma.f32 ux -2 1) ux) ux) (+.f32 1 ux) ux) (/.f32 -1 ux)) maxCos))
(-.f32 (+.f32 (.f32 -1 (/.f32 (-.f32 (/.f32 1 ux) (+.f32 ux (/.f32 (.f32 (-.f32 (.f32 -2 ux) (.f32 -1 (+.f32 1 ux))) (+.f32 1 ux)) ux))) maxCos)) (+.f32 (.f32 -2 ux) (+.f32 (.f32 -1 (/.f32 (.f32 (-.f32 (/.f32 1 ux) (+.f32 ux (/.f32 (.f32 (-.f32 (.f32 -2 ux) (.f32 -1 (+.f32 1 ux))) (+.f32 1 ux)) ux))) (+.f32 1 ux)) (.f32 (pow.f32 maxCos 2) ux))) (.f32 maxCos ux)))) (*.f32 -1 (+.f32 1 ux)))
(-.f32 (fma.f32 -2 ux (fma.f32 -1 (/.f32 (-.f32 1 (.f32 ux ux)) (.f32 maxCos ux)) (+.f32 (.f32 maxCos ux) (.f32 (/.f32 (.f32 -1 (-.f32 (/.f32 (-.f32 1 (.f32 ux ux)) ux) (/.f32 (-.f32 (.f32 ux -2) (neg.f32 (+.f32 1 ux))) (/.f32 ux (+.f32 1 ux))))) (.f32 maxCos maxCos)) (/.f32 (+.f32 1 ux) ux))))) (fma.f32 -1 (.f32 (/.f32 (-.f32 (.f32 ux -2) (neg.f32 (+.f32 1 ux))) maxCos) (/.f32 (+.f32 1 ux) ux)) (neg.f32 (+.f32 1 ux))))
(-.f32 (fma.f32 ux -2 (-.f32 (fma.f32 (/.f32 (fma.f32 -1 (/.f32 (-.f32 1 (.f32 ux ux)) ux) (.f32 (/.f32 (fma.f32 ux -2 (+.f32 1 ux)) ux) (+.f32 1 ux))) (.f32 maxCos maxCos)) (/.f32 (+.f32 1 ux) ux) (.f32 maxCos ux)) (/.f32 (-.f32 1 (.f32 ux ux)) (.f32 maxCos ux)))) (neg.f32 (fma.f32 (/.f32 (fma.f32 ux -2 (+.f32 1 ux)) maxCos) (/.f32 (+.f32 1 ux) ux) (+.f32 1 ux))))
(+.f32 (+.f32 1 ux) (+.f32 (/.f32 (+.f32 (fma.f32 (/.f32 (+.f32 (fma.f32 ux -2 1) ux) ux) (+.f32 1 ux) ux) (/.f32 -1 ux)) maxCos) (fma.f32 ux (+.f32 maxCos -2) (.f32 (/.f32 (+.f32 (fma.f32 (/.f32 (+.f32 (fma.f32 ux -2 1) ux) ux) (+.f32 1 ux) ux) (/.f32 -1 ux)) (.f32 maxCos (*.f32 maxCos ux))) (+.f32 1 ux)))))
(*.f32 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 ux 2))
(.f32 (pow.f32 (-.f32 1 maxCos) 2) (.f32 ux ux))
(.f32 ux (.f32 (pow.f32 (-.f32 1 maxCos) 2) ux))
(*.f32 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 ux 2))
(.f32 (pow.f32 (-.f32 1 maxCos) 2) (.f32 ux ux))
(.f32 ux (.f32 (pow.f32 (-.f32 1 maxCos) 2) ux))
(*.f32 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 ux 2))
(.f32 (pow.f32 (-.f32 1 maxCos) 2) (.f32 ux ux))
(.f32 ux (.f32 (pow.f32 (-.f32 1 maxCos) 2) ux))
(*.f32 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 ux 2))
(.f32 (pow.f32 (-.f32 1 maxCos) 2) (.f32 ux ux))
(.f32 ux (.f32 (pow.f32 (-.f32 1 maxCos) 2) ux))
(*.f32 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 ux 2))
(.f32 (pow.f32 (-.f32 1 maxCos) 2) (.f32 ux ux))
(.f32 ux (.f32 (pow.f32 (-.f32 1 maxCos) 2) ux))
(*.f32 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 ux 2))
(.f32 (pow.f32 (-.f32 1 maxCos) 2) (.f32 ux ux))
(.f32 ux (.f32 (pow.f32 (-.f32 1 maxCos) 2) ux))
(*.f32 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 ux 2))
(.f32 (pow.f32 (-.f32 1 maxCos) 2) (.f32 ux ux))
(.f32 ux (.f32 (pow.f32 (-.f32 1 maxCos) 2) ux))
(*.f32 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 ux 2))
(.f32 (pow.f32 (-.f32 1 maxCos) 2) (.f32 ux ux))
(.f32 ux (.f32 (pow.f32 (-.f32 1 maxCos) 2) ux))
(*.f32 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 ux 2))
(.f32 (pow.f32 (-.f32 1 maxCos) 2) (.f32 ux ux))
(.f32 ux (.f32 (pow.f32 (-.f32 1 maxCos) 2) ux))
(*.f32 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 ux 2))
(.f32 (pow.f32 (-.f32 1 maxCos) 2) (.f32 ux ux))
(.f32 ux (.f32 (pow.f32 (-.f32 1 maxCos) 2) ux))
(*.f32 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 ux 2))
(.f32 (pow.f32 (-.f32 1 maxCos) 2) (.f32 ux ux))
(.f32 ux (.f32 (pow.f32 (-.f32 1 maxCos) 2) ux))
(*.f32 (pow.f32 (-.f32 1 maxCos) 2) (pow.f32 ux 2))
(.f32 (pow.f32 (-.f32 1 maxCos) 2) (.f32 ux ux))
(.f32 ux (.f32 (pow.f32 (-.f32 1 maxCos) 2) ux))
(pow.f32 ux 2)
(*.f32 ux ux)
(+.f32 (pow.f32 ux 2) (.f32 -2 (.f32 maxCos (pow.f32 ux 2))))
(+.f32 (.f32 ux ux) (.f32 (.f32 -2 maxCos) (.f32 ux ux)))
(.f32 (+.f32 (.f32 maxCos -2) 1) (*.f32 ux ux))
(.f32 (fma.f32 maxCos -2 1) (.f32 ux ux))
(+.f32 (pow.f32 ux 2) (+.f32 (.f32 -2 (.f32 maxCos (pow.f32 ux 2))) (*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))))
(+.f32 (.f32 ux ux) (fma.f32 -2 (.f32 maxCos (.f32 ux ux)) (.f32 (.f32 ux ux) (.f32 maxCos maxCos))))
(fma.f32 ux ux (.f32 (.f32 ux ux) (+.f32 (.f32 maxCos -2) (.f32 maxCos maxCos))))
(fma.f32 (.f32 ux ux) (.f32 maxCos (+.f32 maxCos -2)) (*.f32 ux ux))
(+.f32 (pow.f32 ux 2) (+.f32 (.f32 -2 (.f32 maxCos (pow.f32 ux 2))) (*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))))
(+.f32 (.f32 ux ux) (fma.f32 -2 (.f32 maxCos (.f32 ux ux)) (.f32 (.f32 ux ux) (.f32 maxCos maxCos))))
(fma.f32 ux ux (.f32 (.f32 ux ux) (+.f32 (.f32 maxCos -2) (.f32 maxCos maxCos))))
(fma.f32 (.f32 ux ux) (.f32 maxCos (+.f32 maxCos -2)) (*.f32 ux ux))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 ux (.f32 maxCos (*.f32 maxCos ux)))
(.f32 (.f32 maxCos ux) (*.f32 maxCos ux))
(+.f32 (.f32 -2 (.f32 maxCos (pow.f32 ux 2))) (*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)))
(fma.f32 -2 (.f32 maxCos (.f32 ux ux)) (.f32 (.f32 ux ux) (*.f32 maxCos maxCos)))
(.f32 (.f32 ux ux) (+.f32 (.f32 maxCos -2) (.f32 maxCos maxCos)))
(.f32 ux (.f32 ux (*.f32 maxCos (+.f32 maxCos -2))))
(+.f32 (pow.f32 ux 2) (+.f32 (.f32 -2 (.f32 maxCos (pow.f32 ux 2))) (*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))))
(+.f32 (.f32 ux ux) (fma.f32 -2 (.f32 maxCos (.f32 ux ux)) (.f32 (.f32 ux ux) (.f32 maxCos maxCos))))
(fma.f32 ux ux (.f32 (.f32 ux ux) (+.f32 (.f32 maxCos -2) (.f32 maxCos maxCos))))
(fma.f32 (.f32 ux ux) (.f32 maxCos (+.f32 maxCos -2)) (*.f32 ux ux))
(+.f32 (pow.f32 ux 2) (+.f32 (.f32 -2 (.f32 maxCos (pow.f32 ux 2))) (*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))))
(+.f32 (.f32 ux ux) (fma.f32 -2 (.f32 maxCos (.f32 ux ux)) (.f32 (.f32 ux ux) (.f32 maxCos maxCos))))
(fma.f32 ux ux (.f32 (.f32 ux ux) (+.f32 (.f32 maxCos -2) (.f32 maxCos maxCos))))
(fma.f32 (.f32 ux ux) (.f32 maxCos (+.f32 maxCos -2)) (*.f32 ux ux))
(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
(.f32 (.f32 ux ux) (*.f32 maxCos maxCos))
(.f32 ux (.f32 maxCos (*.f32 maxCos ux)))
(.f32 (.f32 maxCos ux) (*.f32 maxCos ux))
(+.f32 (.f32 -2 (.f32 maxCos (pow.f32 ux 2))) (*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)))
(fma.f32 -2 (.f32 maxCos (.f32 ux ux)) (.f32 (.f32 ux ux) (*.f32 maxCos maxCos)))
(.f32 (.f32 ux ux) (+.f32 (.f32 maxCos -2) (.f32 maxCos maxCos)))
(.f32 ux (.f32 ux (*.f32 maxCos (+.f32 maxCos -2))))
(+.f32 (pow.f32 ux 2) (+.f32 (.f32 -2 (.f32 maxCos (pow.f32 ux 2))) (*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))))
(+.f32 (.f32 ux ux) (fma.f32 -2 (.f32 maxCos (.f32 ux ux)) (.f32 (.f32 ux ux) (.f32 maxCos maxCos))))
(fma.f32 ux ux (.f32 (.f32 ux ux) (+.f32 (.f32 maxCos -2) (.f32 maxCos maxCos))))
(fma.f32 (.f32 ux ux) (.f32 maxCos (+.f32 maxCos -2)) (*.f32 ux ux))
(+.f32 (pow.f32 ux 2) (+.f32 (.f32 -2 (.f32 maxCos (pow.f32 ux 2))) (*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))))
(+.f32 (.f32 ux ux) (fma.f32 -2 (.f32 maxCos (.f32 ux ux)) (.f32 (.f32 ux ux) (.f32 maxCos maxCos))))
(fma.f32 ux ux (.f32 (.f32 ux ux) (+.f32 (.f32 maxCos -2) (.f32 maxCos maxCos))))
(fma.f32 (.f32 ux ux) (.f32 maxCos (+.f32 maxCos -2)) (*.f32 ux ux))
1
(+.f32 1 (*.f32 (-.f32 1 maxCos) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(+.f32 1 (*.f32 (-.f32 1 maxCos) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(+.f32 1 (*.f32 (-.f32 1 maxCos) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(*.f32 (-.f32 1 maxCos) ux)
(*.f32 ux (-.f32 1 maxCos))
(-.f32 ux (*.f32 maxCos ux))
(+.f32 1 (*.f32 (-.f32 1 maxCos) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(+.f32 1 (*.f32 (-.f32 1 maxCos) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(+.f32 1 (*.f32 (-.f32 1 maxCos) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(*.f32 (-.f32 1 maxCos) ux)
(*.f32 ux (-.f32 1 maxCos))
(-.f32 ux (*.f32 maxCos ux))
(+.f32 1 (*.f32 (-.f32 1 maxCos) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(+.f32 1 (*.f32 (-.f32 1 maxCos) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(+.f32 1 (*.f32 (-.f32 1 maxCos) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(+.f32 1 ux)
(+.f32 1 (+.f32 (.f32 -1 (.f32 maxCos ux)) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(+.f32 1 (+.f32 (.f32 -1 (.f32 maxCos ux)) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(+.f32 1 (+.f32 (.f32 -1 (.f32 maxCos ux)) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(.f32 -1 (.f32 maxCos ux))
(neg.f32 (*.f32 maxCos ux))
(+.f32 1 (+.f32 (.f32 -1 (.f32 maxCos ux)) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(+.f32 1 (+.f32 (.f32 -1 (.f32 maxCos ux)) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(+.f32 1 (+.f32 (.f32 -1 (.f32 maxCos ux)) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(.f32 -1 (.f32 maxCos ux))
(neg.f32 (*.f32 maxCos ux))
(+.f32 1 (+.f32 (.f32 -1 (.f32 maxCos ux)) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(+.f32 1 (+.f32 (.f32 -1 (.f32 maxCos ux)) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)
(+.f32 1 (+.f32 (.f32 -1 (.f32 maxCos ux)) ux))
(+.f32 1 (*.f32 ux (-.f32 1 maxCos)))
(fma.f32 ux (-.f32 1 maxCos) 1)

eval211.0ms (7.2%)

Compiler: Compiled 8052 to 5826 computations (27.6% saved)

prune51.0ms (1.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	330	1	331
Fresh	0	1	1
Picked	1	0	1
Done	0	3	3
Total	331	5	336

Error

Counts

336 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.1b	(/.f32 (-.f32 1 (*.f32 ux ux)) (+.f32 1 ux))
	8.2b	1
✓	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
✓	0.0b	(-.f32 1 (*.f32 ux (-.f32 1 maxCos)))
✓	0.8b	(-.f32 1 ux)

Compiler

Compiled 42 to 33 computations (21.4% saved)

localize25.0ms (0.9%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f32 1 (*.f32 ux ux))
✓	0.4b	(/.f32 (-.f32 1 (*.f32 ux ux)) (+.f32 1 ux))

Compiler

Compiled 25 to 14 computations (44% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite64.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

920×	`pow1_binary32`
864×	`add-log-exp_binary32`
863×	`log1p-expm1-u_binary32`
863×	`expm1-log1p-u_binary32`
846×	`add-exp-log_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	161	11
2	2401	11

Stop Event

1×	node limit

Counts

2 → 65

Calls

Call 1

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

Outputs

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

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

simplify54.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

632×	`fma-neg_binary32`
553×	`fma-def_binary32`
472×	`associate-l_binary32`
434×	`unswap-sqr_binary32`
371×	`distribute-lft-neg-in_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	146
1	23	119
2	37	119
3	70	119
4	176	119
5	535	119
6	1915	119
7	4817	119

Stop Event

1×	node limit

Counts

89 → 73

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

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

eval19.0ms (0.6%)

Compiler: Compiled 899 to 596 computations (33.7% saved)

prune13.0ms (0.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	73	5	78

Error

Counts

78 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.1b	(/.f32 (-.f32 1 (*.f32 ux ux)) (+.f32 1 ux))
	8.2b	1
✓	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
✓	0.0b	(-.f32 1 (*.f32 ux (-.f32 1 maxCos)))
✓	0.8b	(-.f32 1 ux)

Compiler

Compiled 42 to 33 computations (21.4% saved)

eval0.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

prune2.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	4	4
Total	5	5

Error

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.1b	(/.f32 (-.f32 1 (*.f32 ux ux)) (+.f32 1 ux))
	8.2b	1
✓	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
✓	0.0b	(-.f32 1 (*.f32 ux (-.f32 1 maxCos)))
✓	0.8b	(-.f32 1 ux)

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes125.0ms (4.3%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

5 calls:

69.0ms	maxCos
6.0ms	uy
6.0ms	ux
5.0ms	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
5.0ms	(+.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 89 to 62 computations (30.3% saved)

regimes33.0ms (1.1%)

Accuracy

Total -7.4b remaining (-961.9%)

Threshold costs -7.4b (-961.9%)

Counts

2 → 1

Calls

Call 1

Inputs
1
(-.f32 1 ux)

Outputs
(-.f32 1 ux)

Calls

3 calls:

24.0ms	maxCos
4.0ms	ux
4.0ms	uy

Results

Error	Segments	Branch
0.8b	1	`ux`
0.8b	1	`uy`
0.8b	1	`maxCos`

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary32`
7×	`sub-neg_binary32`
6×	`distribute-neg-in_binary32`
6×	`cancel-sign-sub-inv_binary32`
5×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	19	15
2	34	15
3	46	15
4	62	15
5	72	15

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 20 to 17 computations (15% saved)

soundness0.0ms (0%)

end18.0ms (0.6%)

Compiler: Compiled 14 to 11 computations (21.4% saved)

Iter	Nodes	Cost
0	18	367
1	45	331
2	96	331
3	180	331
4	377	331
5	620	331
6	784	331
7	839	331
8	848	331

Iter	Nodes	Cost
0	18	367
1	45	331
2	96	331
3	180	331
4	377	331
5	620	331
6	784	331
7	839	331
8	848	331

Details

analyze1.0ms (0%)

sample1.6s (55.8%)

preprocess68.0ms (2.3%)

simplify23.0ms (0.8%)

eval1.0ms (0%)

prune1.0ms (0%)

localize21.0ms (0.7%)

series3.0ms (0.1%)

rewrite60.0ms (2%)

simplify27.0ms (0.9%)

localize17.0ms (0.6%)

series3.0ms (0.1%)

rewrite49.0ms (1.7%)

simplify27.0ms (0.9%)

eval24.0ms (0.8%)

prune18.0ms (0.6%)

localize8.0ms (0.3%)

localize22.0ms (0.7%)

series5.0ms (0.2%)

rewrite57.0ms (2%)

simplify36.0ms (1.2%)

localize51.0ms (1.7%)

series11.0ms (0.4%)

rewrite81.0ms (2.8%)

simplify58.0ms (2%)

eval211.0ms (7.2%)

prune51.0ms (1.7%)

localize25.0ms (0.9%)

series2.0ms (0.1%)

rewrite64.0ms (2.2%)

simplify54.0ms (1.8%)

eval19.0ms (0.6%)

prune13.0ms (0.4%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes125.0ms (4.3%)

regimes33.0ms (1.1%)

simplify4.0ms (0.1%)

soundness0.0ms (0%)

end18.0ms (0.6%)

Profiling

Iter	Nodes	Cost
0	18	367
1	45	331
2	96	331
3	180	331
4	377	331
5	620	331
6	784	331
7	839	331
8	848	331