Details

analyze105.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.3%	87.7%	0
0%	12.3%	87.7%	1
6.2%	6.2%	87.7%	2
6.2%	6.2%	87.7%	3
9.2%	3.1%	87.7%	4
9.2%	3.1%	87.7%	5
10.8%	1.5%	87.7%	6
10.8%	1.5%	87.7%	7
11.5%	0.8%	87.7%	8
11.5%	0.8%	87.7%	9
11.9%	0.4%	87.7%	10
11.9%	0.4%	87.7%	11
12.1%	0.2%	87.7%	12
12.1%	0.2%	87.7%	13
12.1%	0.1%	87.8%	14

Compiler

Compiled 42 to 32 computations (23.8% saved)

sample2.2s (15.9%)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 111 to 85 computations (23.4% saved)

simplify44.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

940×	`fma-neg_binary32`
929×	`fma-def_binary32`
740×	`times-frac_binary32`
329×	`div-sub_binary32`
317×	`associate-l_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	45	35
2	107	35
3	264	33
4	605	33
5	2500	33
6	3754	33
7	5049	33

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.7b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Status

Error

Program

▶

0.5b

(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))

0.7b

(/.f32 1 (+.f32 (+.f32 1 c) (*.f32 (*.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Compiler

Compiled 148 to 113 computations (23.6% saved)

localize64.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f32 (fma.f32 cosTheta -2 1))
✓	0.3b	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
✓	0.3b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
✓	0.4b	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

series125.0ms (0.9%)

Counts

4 → 38

Calls

4 calls:

81.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
26.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
11.0ms	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
7.0ms	(sqrt.f32 (fma.f32 cosTheta -2 1))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary32`
32×	`add-exp-log_binary32`
22×	`add-sqr-sqrt_binary32`
21×	`times-frac_binary32`
21×	`add-cube-cbrt_binary32`

Counts

4 → 117

Calls

4 calls:

10.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
6.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
5.0ms	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
1.0ms	(sqrt.f32 (fma.f32 cosTheta -2 1))

simplify122.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

449×	`cancel-sign-sub-inv_binary32`
348×	`associate-r_binary32`
306×	`associate-l_binary32`
287×	`unswap-sqr_binary32`
281×	`fma-def_binary32`

Counts

155 → 200

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	364	5718
1	1029	5271
2	3838	5255
3	5406	5255

prune320.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	191	9	200
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	193	9	202

Error

0.0b

Counts

202 → 9

Alt Table

Status	Error	Program
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
▶	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))))))
	0.9b	(/.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	3.1b	(exp.f32 (neg.f32 (log1p.f32 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))))
	1.0b	(fma.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (-.f32 -1 c) (.f32 (PI.f32) (.f32 cosTheta cosTheta))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))
	14.9b	(.f32 (/.f32 1 (-.f32 (.f32 (+.f32 1 c) (+.f32 1 c)) (/.f32 (fma.f32 cosTheta -2 1) (.f32 (PI.f32) (.f32 (.f32 cosTheta cosTheta) (pow.f32 (exp.f32 (.f32 cosTheta cosTheta)) 2)))))) (-.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.7b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.7b	(/.f32 (/.f32 1 (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))

Compiler

Compiled 8009 to 4564 computations (43% saved)

localize74.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))))
✓	0.3b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))))))
✓	0.3b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))
✓	0.5b	(.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))

series272.0ms (2%)

Counts

4 → 46

Calls

4 calls:

156.0ms	(.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))
79.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))))))
26.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))))
11.0ms	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))

rewrite55.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary32`
34×	`add-cbrt-cube_binary32`
33×	`add-exp-log_binary32`
22×	`add-sqr-sqrt_binary32`
22×	`add-cube-cbrt_binary32`

Counts

4 → 128

Calls

4 calls:

14.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))))
12.0ms	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))
11.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))))))
6.0ms	(.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))

simplify213.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

451×	`associate-r_binary32`
420×	`associate-l_binary32`
302×	`fma-def_binary32`
250×	`*-commutative_binary32`
216×	`associate-/r*_binary32`

Counts

174 → 216

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	7546
1	1150	6371
2	4302	6345
3	4901	6345
4	4989	6345
5	4945	6345

prune282.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	213	3	216
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	216	9	225

Error

0.0b

Counts

225 → 9

Alt Table

Status	Error	Program
	0.9b	(/.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	3.1b	(exp.f32 (neg.f32 (log1p.f32 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32)))))))
	1.0b	(fma.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (-.f32 -1 c) (.f32 (PI.f32) (.f32 cosTheta cosTheta))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))
	0.6b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (cbrt.f32 (PI.f32))))) (sqrt.f32 (cbrt.f32 (cbrt.f32 (PI.f32)))))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.7b	(/.f32 (/.f32 1 (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
▶	0.4b	(.f32 (/.f32 1 (+.f32 (.f32 (+.f32 (pow.f32 1 3) (pow.f32 c 3)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (sqrt.f32 (fma.f32 cosTheta -2 1))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))))

Compiler

Compiled 10223 to 5028 computations (50.8% saved)

localize118.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f32 1 (+.f32 (.f32 (+.f32 (pow.f32 1 3) (pow.f32 c 3)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (sqrt.f32 (fma.f32 cosTheta -2 1)))))
✓	0.1b	(.f32 (/.f32 1 (+.f32 (.f32 (+.f32 (pow.f32 1 3) (pow.f32 c 3)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (sqrt.f32 (fma.f32 cosTheta -2 1))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))))
	0.3b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))
	0.5b	(.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))

series2.7s (19.3%)

Counts

2 → 36

Calls

2 calls:

2.0s

(*.f32 (/.f32 1 (+.f32 (*.f32 (+.f32 (pow.f32 1 3) (pow.f32 c 3)) (*.f32 (sqrt.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (*.f32 (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))) (*.f32 (+.f32 (*.f32 1 1) (-.f32 (*.f32 c c) (*.f32 1 c))) (sqrt.f32 (fma.f32 cosTheta -2 1))))) (*.f32 (+.f32 (*.f32 1 1) (-.f32 (*.f32 c c) (*.f32 1 c))) (*.f32 (sqrt.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (*.f32 (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))))

614.0ms

(/.f32 1 (+.f32 (*.f32 (+.f32 (pow.f32 1 3) (pow.f32 c 3)) (*.f32 (sqrt.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (*.f32 (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))) (*.f32 (+.f32 (*.f32 1 1) (-.f32 (*.f32 c c) (*.f32 1 c))) (sqrt.f32 (fma.f32 cosTheta -2 1)))))

rewrite111.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`add-exp-log_binary32`
60×	`prod-exp_binary32`
49×	`add-cbrt-cube_binary32`
30×	`cbrt-unprod_binary32`
23×	`pow1_binary32`

Counts

2 → 109

Calls

2 calls:

47.0ms

(*.f32 (/.f32 1 (+.f32 (*.f32 (+.f32 (pow.f32 1 3) (pow.f32 c 3)) (*.f32 (sqrt.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (*.f32 (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))) (*.f32 (+.f32 (*.f32 1 1) (-.f32 (*.f32 c c) (*.f32 1 c))) (sqrt.f32 (fma.f32 cosTheta -2 1))))) (*.f32 (+.f32 (*.f32 1 1) (-.f32 (*.f32 c c) (*.f32 1 c))) (*.f32 (sqrt.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (*.f32 (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))))

23.0ms

(/.f32 1 (+.f32 (*.f32 (+.f32 (pow.f32 1 3) (pow.f32 c 3)) (*.f32 (sqrt.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (*.f32 (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))) (*.f32 (+.f32 (*.f32 1 1) (-.f32 (*.f32 c c) (*.f32 1 c))) (sqrt.f32 (fma.f32 cosTheta -2 1)))))

simplify331.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

430×	`*-commutative_binary32`
342×	`+-commutative_binary32`
299×	`associate-+r+_binary32`
257×	`fma-def_binary32`
234×	`distribute-rgt-in_binary32`

Counts

145 → 215

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1138	24101
1	3976	21503
2	5193	21503

prune1.0s (7.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	373	2	375
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	376	8	384

Error

Counts

384 → 8

Alt Table

Status	Error	Program
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))
	0.5b	(.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (exp.f32 (pow.f32 cosTheta 2)) cosTheta) (+.f32 (sqrt.f32 (-.f32 1 (.f32 2 cosTheta))) (.f32 (sqrt.f32 (PI.f32)) (*.f32 (exp.f32 (pow.f32 cosTheta 2)) cosTheta)))))
▶	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32)))))))
	0.6b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (cbrt.f32 (PI.f32))))) (sqrt.f32 (cbrt.f32 (cbrt.f32 (PI.f32)))))))))
	0.7b	(.f32 (log.f32 (exp.f32 (/.f32 1 (+.f32 (.f32 (+.f32 (pow.f32 1 3) (pow.f32 c 3)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (sqrt.f32 (fma.f32 cosTheta -2 1))))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.9b	(/.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
✓	0.4b	(.f32 (/.f32 1 (+.f32 (.f32 (+.f32 (pow.f32 1 3) (pow.f32 c 3)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (sqrt.f32 (fma.f32 cosTheta -2 1))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))))

Compiler

Compiled 47736 to 24479 computations (48.7% saved)

localize63.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32)))
✓	0.3b	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32)))))
✓	0.3b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32)))))))
✓	0.5b	(.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32))))

series266.0ms (1.9%)

Counts

4 → 46

Calls

4 calls:

147.0ms	(.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32)))
82.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32)))))))
27.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32)))))
11.0ms	(.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32))))

rewrite50.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary32`
33×	`add-exp-log_binary32`
28×	`add-cbrt-cube_binary32`
23×	`add-sqr-sqrt_binary32`
23×	`add-cube-cbrt_binary32`

Counts

4 → 130

Calls

4 calls:

12.0ms	(.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32))))
11.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32)))))
10.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32)))))))
5.0ms	(.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32)))

simplify177.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

470×	`associate-r_binary32`
418×	`associate-l_binary32`
302×	`fma-def_binary32`
243×	`*-commutative_binary32`
224×	`associate-/r*_binary32`

Counts

176 → 228

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	392	7349
1	1135	6400
2	4474	6259
3	4983	6259
4	4916	6259

prune350.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	228	8	236

Error

Counts

236 → 8

Alt Table

Status	Error	Program
✓	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32)))))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (/.f32 (.f32 (cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1))) (cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)))) (sqrt.f32 (cbrt.f32 (PI.f32)))) (/.f32 (cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1))) (.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32)))))))
	0.5b	(.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (exp.f32 (pow.f32 cosTheta 2)) cosTheta) (+.f32 (sqrt.f32 (-.f32 1 (.f32 2 cosTheta))) (.f32 (sqrt.f32 (PI.f32)) (*.f32 (exp.f32 (pow.f32 cosTheta 2)) cosTheta)))))
	0.6b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (cbrt.f32 (PI.f32))))) (sqrt.f32 (cbrt.f32 (cbrt.f32 (PI.f32)))))))))
	0.7b	(.f32 (log.f32 (exp.f32 (/.f32 1 (+.f32 (.f32 (+.f32 (pow.f32 1 3) (pow.f32 c 3)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (sqrt.f32 (fma.f32 cosTheta -2 1))))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.9b	(/.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
✓	0.4b	(.f32 (/.f32 1 (+.f32 (.f32 (+.f32 (pow.f32 1 3) (pow.f32 c 3)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (sqrt.f32 (fma.f32 cosTheta -2 1))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))))

Compiler

Compiled 9474 to 5077 computations (46.4% saved)

regimes4.5s (32.4%)

Accuracy

Total 0.4b remaining (95.1%)

Threshold costs 0.4b (95.1%)

Counts

451 → 1

Compiler

Compiled 119458 to 83450 computations (30.1% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary32`
4×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`*-lft-identity_binary32`
1×	`neg-sub0_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	88
1	39	88
2	43	88
3	45	88
4	46	88
5	44	88

end245.0ms (1.8%)

Compiler: Compiled 538 to 329 computations (38.8% saved)

Details

analyze105.0ms (0.8%)

sample2.2s (15.9%)

simplify44.0ms (0.3%)

prune5.0ms (0%)

localize64.0ms (0.5%)

series125.0ms (0.9%)

rewrite31.0ms (0.2%)

simplify122.0ms (0.9%)

prune320.0ms (2.3%)

localize74.0ms (0.5%)

series272.0ms (2%)

rewrite55.0ms (0.4%)

simplify213.0ms (1.5%)

prune282.0ms (2%)

localize118.0ms (0.9%)

series2.7s (19.3%)

rewrite111.0ms (0.8%)

simplify331.0ms (2.4%)

prune1.0s (7.5%)

localize63.0ms (0.5%)

series266.0ms (1.9%)

rewrite50.0ms (0.4%)

simplify177.0ms (1.3%)

prune350.0ms (2.5%)

regimes4.5s (32.4%)

simplify4.0ms (0%)

end245.0ms (1.8%)

Profiling