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)

sample1.5s (49%)

Results

1.5s	8255×	body	128	valid
0.0ms	1×	body	256	valid

preprocess41.0ms (1.3%)

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	1153	32
6	1987	32
7	2325	32
8	2405	32
9	2416	32
0	3	3

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

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

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

Compiler

Compiled 10 to 7 computations (30% saved)

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune2.0ms (0.1%)

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 38 to 26 computations (31.6% saved)

localize17.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

series5.0ms (0.2%)

Counts

2 → 48

Calls

12 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))
0.0ms	ux	@	0	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
0.0ms	ux	@	0	(*.f32 ux maxCos)
0.0ms	maxCos	@	inf	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

rewrite42.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

836×	`log1p-expm1-u_binary32`
836×	`expm1-log1p-u_binary32`
81×	`add-sqr-sqrt_binary32`
79×	`*-un-lft-identity_binary32`
79×	`pow1_binary32`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

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

Outputs

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

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

simplify22.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×

saturated

Counts

102 → 64

Calls

Call 1

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

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

eval14.0ms (0.5%)

Compiler: Compiled 795 to 455 computations (42.8% saved)

prune95.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	62	4	66

Error

Counts

66 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
	0.4b	(log.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
	0.3b	(.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))))))
▶	0.0b	(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))

Compiler

Compiled 120 to 85 computations (29.2% saved)

localize17.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

series5.0ms (0.2%)

Counts

2 → 27

Calls

12 calls:

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

rewrite38.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

799×	`pow1_binary32`
742×	`log1p-expm1-u_binary32`
742×	`expm1-log1p-u_binary32`
79×	`add-sqr-sqrt_binary32`
76×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 53

Calls

Call 1

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

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

Outputs

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

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

simplify24.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×

saturated

Counts

80 → 65

Calls

Call 1

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

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

eval16.0ms (0.5%)

Compiler: Compiled 745 to 556 computations (25.4% saved)

prune89.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	66	3	69

Error

Counts

69 → 3

Alt Table

Click to see full alt table

Status

Error

Program

0.4b

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

✓

0.0b

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

▶

0.0b

(+.f32 1 (log1p.f32 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux))))

Compiler

Compiled 94 to 75 computations (20.2% saved)

localize25.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (log1p.f32 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux))))
✓	0.1b	(expm1.f32 (*.f32 (+.f32 maxCos -1) ux))
✓	0.1b	(*.f32 (+.f32 maxCos -1) ux)
✓	0.1b	(log1p.f32 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux)))

series7.0ms (0.2%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
1.0ms	maxCos	@	0	(expm1.f32 (*.f32 (+.f32 maxCos -1) ux))
1.0ms	ux	@	0	(expm1.f32 (*.f32 (+.f32 maxCos -1) ux))
0.0ms	maxCos	@	0	(log1p.f32 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux)))
0.0ms	maxCos	@	-inf	(expm1.f32 (*.f32 (+.f32 maxCos -1) ux))
0.0ms	ux	@	inf	(expm1.f32 (*.f32 (+.f32 maxCos -1) ux))

rewrite50.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

882×	`expm1-log1p-u_binary32`
881×	`log1p-expm1-u_binary32`
92×	`add-sqr-sqrt_binary32`
90×	`pow1_binary32`
89×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	188	31
2	2331	31

Stop Event

1×	node limit

Counts

4 → 108

Calls

Call 1

Inputs
(log1p.f32 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux)))
(*.f32 (+.f32 maxCos -1) ux)
(expm1.f32 (*.f32 (+.f32 maxCos -1) ux))
(+.f32 1 (log1p.f32 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux))))

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

simplify41.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

448×	`associate-l_binary32`
436×	`associate-r_binary32`
385×	`fma-neg_binary32`
320×	`fma-def_binary32`
267×	`distribute-rgt-out_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	938
1	198	869
2	606	848
3	3361	843

Stop Event

1×	node limit

Counts

204 → 118

Calls

Call 1

Inputs
(*.f32 -1 ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 -1 ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(-.f32 (exp.f32 (*.f32 -1 ux)) 1)
(-.f32 (+.f32 (exp.f32 (.f32 -1 ux)) (.f32 (exp.f32 (.f32 -1 ux)) (.f32 maxCos ux))) 1)
(-.f32 (+.f32 (exp.f32 (.f32 -1 ux)) (+.f32 (.f32 (exp.f32 (.f32 -1 ux)) (.f32 maxCos ux)) (.f32 1/2 (.f32 (exp.f32 (.f32 -1 ux)) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)))))) 1)
(-.f32 (+.f32 (.f32 1/6 (.f32 (exp.f32 (.f32 -1 ux)) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3)))) (+.f32 (exp.f32 (.f32 -1 ux)) (+.f32 (.f32 (exp.f32 (.f32 -1 ux)) (.f32 maxCos ux)) (.f32 1/2 (.f32 (exp.f32 (.f32 -1 ux)) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))))))) 1)
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(-.f32 (exp.f32 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))) 1)
(-.f32 (exp.f32 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))) 1)
(-.f32 (exp.f32 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))) 1)
(-.f32 (exp.f32 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))) 1)
(*.f32 (-.f32 maxCos 1) ux)
(+.f32 (.f32 1/2 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2))) (*.f32 (-.f32 maxCos 1) ux))
(+.f32 (.f32 1/2 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2))) (+.f32 (.f32 1/6 (.f32 (pow.f32 (-.f32 maxCos 1) 3) (pow.f32 ux 3))) (*.f32 (-.f32 maxCos 1) ux)))
(+.f32 (.f32 1/2 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2))) (+.f32 (.f32 1/24 (.f32 (pow.f32 (-.f32 maxCos 1) 4) (pow.f32 ux 4))) (+.f32 (.f32 1/6 (.f32 (pow.f32 (-.f32 maxCos 1) 3) (pow.f32 ux 3))) (*.f32 (-.f32 maxCos 1) ux))))
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
1
(+.f32 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 (-.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))

Outputs
(*.f32 -1 ux)
(neg.f32 ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 -1 ux)
(neg.f32 ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (exp.f32 (*.f32 -1 ux)) 1)
(expm1.f32 (neg.f32 ux))
(-.f32 (+.f32 (exp.f32 (.f32 -1 ux)) (.f32 (exp.f32 (.f32 -1 ux)) (.f32 maxCos ux))) 1)
(+.f32 (exp.f32 (neg.f32 ux)) (-.f32 (.f32 (.f32 ux maxCos) (exp.f32 (neg.f32 ux))) 1))
(+.f32 -1 (*.f32 (fma.f32 ux maxCos 1) (exp.f32 (neg.f32 ux))))
(fma.f32 (fma.f32 ux maxCos 1) (exp.f32 (neg.f32 ux)) -1)
(fma.f32 (exp.f32 (neg.f32 ux)) (fma.f32 ux maxCos 1) -1)
(-.f32 (+.f32 (exp.f32 (.f32 -1 ux)) (+.f32 (.f32 (exp.f32 (.f32 -1 ux)) (.f32 maxCos ux)) (.f32 1/2 (.f32 (exp.f32 (.f32 -1 ux)) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)))))) 1)
(+.f32 (exp.f32 (neg.f32 ux)) (-.f32 (fma.f32 (exp.f32 (neg.f32 ux)) (.f32 ux maxCos) (.f32 1/2 (.f32 (exp.f32 (neg.f32 ux)) (.f32 (.f32 ux ux) (.f32 maxCos maxCos))))) 1))
(+.f32 -1 (+.f32 (.f32 (fma.f32 ux maxCos 1) (exp.f32 (neg.f32 ux))) (.f32 1/2 (.f32 (exp.f32 (neg.f32 ux)) (.f32 ux (.f32 ux (.f32 maxCos maxCos)))))))
(+.f32 -1 (.f32 (exp.f32 (neg.f32 ux)) (+.f32 (fma.f32 ux maxCos 1) (.f32 ux (.f32 (.f32 ux (*.f32 maxCos maxCos)) 1/2)))))
(fma.f32 (exp.f32 (neg.f32 ux)) (+.f32 (fma.f32 ux maxCos 1) (.f32 ux (.f32 (.f32 ux (.f32 maxCos maxCos)) 1/2))) -1)
(-.f32 (+.f32 (.f32 1/6 (.f32 (exp.f32 (.f32 -1 ux)) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3)))) (+.f32 (exp.f32 (.f32 -1 ux)) (+.f32 (.f32 (exp.f32 (.f32 -1 ux)) (.f32 maxCos ux)) (.f32 1/2 (.f32 (exp.f32 (.f32 -1 ux)) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))))))) 1)
(+.f32 (fma.f32 1/6 (.f32 (exp.f32 (neg.f32 ux)) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3))) (+.f32 (exp.f32 (neg.f32 ux)) (fma.f32 (exp.f32 (neg.f32 ux)) (.f32 ux maxCos) (.f32 1/2 (.f32 (exp.f32 (neg.f32 ux)) (.f32 (.f32 ux ux) (.f32 maxCos maxCos))))))) -1)
(fma.f32 1/6 (.f32 (exp.f32 (neg.f32 ux)) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3))) (+.f32 -1 (+.f32 (.f32 (fma.f32 ux maxCos 1) (exp.f32 (neg.f32 ux))) (.f32 1/2 (.f32 (exp.f32 (neg.f32 ux)) (.f32 ux (.f32 ux (.f32 maxCos maxCos))))))))
(+.f32 (.f32 (exp.f32 (neg.f32 ux)) (+.f32 (.f32 1/6 (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3))) (fma.f32 ux maxCos 1))) (fma.f32 (.f32 ux (.f32 ux (.f32 maxCos maxCos))) (/.f32 1/2 (exp.f32 ux)) -1))
(+.f32 (/.f32 (fma.f32 ux maxCos 1) (exp.f32 ux)) (fma.f32 (exp.f32 (neg.f32 ux)) (.f32 (.f32 ux ux) (+.f32 (.f32 1/2 (.f32 maxCos maxCos)) (.f32 1/6 (.f32 ux (pow.f32 maxCos 3))))) -1))
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(-.f32 (exp.f32 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(-.f32 (exp.f32 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(-.f32 (exp.f32 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(-.f32 (exp.f32 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 (.f32 1/2 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2))) (*.f32 (-.f32 maxCos 1) ux))
(fma.f32 1/2 (.f32 (.f32 ux ux) (pow.f32 (+.f32 maxCos -1) 2)) (*.f32 ux (+.f32 maxCos -1)))
(fma.f32 ux (+.f32 -1 maxCos) (.f32 1/2 (.f32 (*.f32 ux ux) (pow.f32 (+.f32 -1 maxCos) 2))))
(.f32 ux (+.f32 (.f32 (pow.f32 (+.f32 -1 maxCos) 2) (*.f32 1/2 ux)) (+.f32 -1 maxCos)))
(.f32 (+.f32 -1 maxCos) (+.f32 ux (.f32 (.f32 ux ux) (.f32 (+.f32 -1 maxCos) 1/2))))
(+.f32 (.f32 1/2 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2))) (+.f32 (.f32 1/6 (.f32 (pow.f32 (-.f32 maxCos 1) 3) (pow.f32 ux 3))) (*.f32 (-.f32 maxCos 1) ux)))
(fma.f32 1/2 (.f32 (.f32 ux ux) (pow.f32 (+.f32 maxCos -1) 2)) (fma.f32 1/6 (.f32 (pow.f32 ux 3) (pow.f32 (+.f32 maxCos -1) 3)) (.f32 ux (+.f32 maxCos -1))))
(fma.f32 1/2 (.f32 (.f32 ux ux) (pow.f32 (+.f32 -1 maxCos) 2)) (fma.f32 ux (+.f32 -1 maxCos) (.f32 1/6 (.f32 (pow.f32 ux 3) (pow.f32 (+.f32 -1 maxCos) 3)))))
(fma.f32 1/6 (.f32 (pow.f32 ux 3) (pow.f32 (+.f32 -1 maxCos) 3)) (.f32 ux (+.f32 (.f32 (pow.f32 (+.f32 -1 maxCos) 2) (.f32 1/2 ux)) (+.f32 -1 maxCos))))
(fma.f32 1/6 (.f32 (pow.f32 ux 3) (pow.f32 (+.f32 -1 maxCos) 3)) (.f32 (+.f32 -1 maxCos) (+.f32 ux (.f32 (.f32 ux ux) (*.f32 (+.f32 -1 maxCos) 1/2)))))
(+.f32 (.f32 1/2 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2))) (+.f32 (.f32 1/24 (.f32 (pow.f32 (-.f32 maxCos 1) 4) (pow.f32 ux 4))) (+.f32 (.f32 1/6 (.f32 (pow.f32 (-.f32 maxCos 1) 3) (pow.f32 ux 3))) (*.f32 (-.f32 maxCos 1) ux))))
(fma.f32 1/2 (.f32 (.f32 ux ux) (pow.f32 (+.f32 maxCos -1) 2)) (fma.f32 1/24 (.f32 (pow.f32 (+.f32 maxCos -1) 4) (pow.f32 ux 4)) (fma.f32 1/6 (.f32 (pow.f32 ux 3) (pow.f32 (+.f32 maxCos -1) 3)) (*.f32 ux (+.f32 maxCos -1)))))
(fma.f32 1/2 (.f32 (.f32 ux ux) (pow.f32 (+.f32 -1 maxCos) 2)) (fma.f32 1/24 (.f32 (pow.f32 (+.f32 -1 maxCos) 4) (pow.f32 ux 4)) (fma.f32 ux (+.f32 -1 maxCos) (.f32 1/6 (*.f32 (pow.f32 ux 3) (pow.f32 (+.f32 -1 maxCos) 3))))))
(fma.f32 1/24 (.f32 (pow.f32 (+.f32 -1 maxCos) 4) (pow.f32 ux 4)) (fma.f32 1/6 (.f32 (pow.f32 ux 3) (pow.f32 (+.f32 -1 maxCos) 3)) (.f32 ux (+.f32 (.f32 (pow.f32 (+.f32 -1 maxCos) 2) (*.f32 1/2 ux)) (+.f32 -1 maxCos)))))
(fma.f32 1/2 (.f32 (.f32 ux ux) (pow.f32 (+.f32 -1 maxCos) 2)) (fma.f32 ux (+.f32 -1 maxCos) (.f32 (pow.f32 ux 3) (+.f32 (.f32 1/6 (pow.f32 (+.f32 -1 maxCos) 3)) (.f32 (.f32 1/24 (pow.f32 (+.f32 -1 maxCos) 4)) ux)))))
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(-.f32 (exp.f32 (*.f32 (-.f32 maxCos 1) ux)) 1)
(expm1.f32 (*.f32 ux (+.f32 maxCos -1)))
(expm1.f32 (*.f32 ux (+.f32 -1 maxCos)))
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
1
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(fma.f32 ux (+.f32 -1 maxCos) 1)
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))

eval35.0ms (1.1%)

Compiler: Compiled 1640 to 1232 computations (24.9% saved)

prune254.0ms (8.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	119	2	121

Error

Counts

121 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 38 to 27 computations (28.9% saved)

localize25.0ms (0.8%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (.f32 (sqrt.f32 ux) (.f32 (sqrt.f32 ux) (+.f32 maxCos -1))))
✓	0.1b	(*.f32 (sqrt.f32 ux) (+.f32 maxCos -1))
✓	0.5b	(.f32 (sqrt.f32 ux) (.f32 (sqrt.f32 ux) (+.f32 maxCos -1)))

series8.0ms (0.3%)

Counts

3 → 52

Calls

18 calls:

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

rewrite51.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

686×	`prod-diff_binary32`
397×	`fma-def_binary32`
180×	`fma-neg_binary32`
179×	`expm1-udef_binary32`
179×	`log1p-udef_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	213	24
2	2838	24

Stop Event

1×	node limit

Counts

3 → 132

Calls

Call 1

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

Outputs

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

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

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

simplify39.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

301×	`fma-def_binary32`
248×	`fma-neg_binary32`
81×	`cancel-sign-sub-inv_binary32`
42×	`distribute-rgt-in_binary32`
41×	`sub-neg_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	399
1	43	368
2	66	368
3	87	368
4	132	368
5	215	368
6	437	368
7	753	368
8	1071	368
9	1176	368
10	1200	368
11	1201	368

Stop Event

1×

saturated

Counts

184 → 148

Calls

Call 1

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

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

eval38.0ms (1.2%)

Compiler: Compiled 2044 to 1222 computations (40.2% saved)

prune514.0ms (16.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	148	2	150

Error

Counts

150 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 24 to 17 computations (29.2% saved)

regimes26.0ms (0.8%)

Accuracy

Total -0.8b remaining (-5020.8%)

Threshold costs -0.8b (-5020.8%)

Counts

8 → 1

Calls

Call 1

Inputs
(+.f32 1 (.f32 (sqrt.f32 ux) (.f32 (sqrt.f32 ux) (+.f32 maxCos -1))))
(.f32 (+.f32 1 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 3)) (/.f32 1 (+.f32 1 (-.f32 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 2) (.f32 (+.f32 maxCos -1) ux)))))
(+.f32 1 (log1p.f32 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux))))
(log.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
(.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))))))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

Outputs
(+.f32 1 (log1p.f32 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux))))

Results

Time	Error	Segments	Branch
5.0ms	0.0b	1	`ux`
6.0ms	0.0b	1	`uy`
5.0ms	0.0b	1	`maxCos`
7.0ms	0.0b	1	`(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))`

Compiler

Compiled 131 to 90 computations (31.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary32`
1×	`*-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	15	14

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f32 1 (log1p.f32 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux))))

Outputs
(+.f32 1 (log1p.f32 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux))))

end16.0ms (0.5%)

Stop Event

1×

done

Compiler

Compiled 24 to 20 computations (16.7% saved)

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

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

Details

analyze1.0ms (0%)

sample1.5s (49%)

preprocess41.0ms (1.3%)

simplify14.0ms (0.5%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize17.0ms (0.5%)

series5.0ms (0.2%)

rewrite42.0ms (1.3%)

simplify22.0ms (0.7%)

eval14.0ms (0.5%)

prune95.0ms (3.1%)

localize17.0ms (0.5%)

series5.0ms (0.2%)

rewrite38.0ms (1.2%)

simplify24.0ms (0.8%)

eval16.0ms (0.5%)

prune89.0ms (2.9%)

localize25.0ms (0.8%)

series7.0ms (0.2%)

rewrite50.0ms (1.6%)

simplify41.0ms (1.3%)

eval35.0ms (1.1%)

prune254.0ms (8.2%)

localize25.0ms (0.8%)

series8.0ms (0.3%)

rewrite51.0ms (1.6%)

simplify39.0ms (1.2%)

eval38.0ms (1.2%)

prune514.0ms (16.7%)

regimes26.0ms (0.8%)

simplify2.0ms (0.1%)

end16.0ms (0.5%)

Profiling

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