Details

analyze366.0ms (4.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 37 to 28 computations (24.3% saved)

sample76.0ms (0.9%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true

Compiler

Compiled 54 to 42 computations (22.2% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`sub-neg_binary32`
7×	`+-commutative_binary32`
6×	`fma-def_binary32`
4×	`*-commutative_binary32`
4×	`div-sub_binary32`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.5b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2)))

Compiler

Compiled 42 to 33 computations (21.4% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f32 u1 (-.f32 1 u1))
✓	0.2b	(sin.f32 (*.f32 314159265359/50000000000 u2))
✓	0.3b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2)))
✓	0.4b	(*.f32 314159265359/50000000000 u2)

series32.0ms (0.4%)

Counts

4 → 28

Calls

4 calls:

26.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2)))
2.0ms	(/.f32 u1 (-.f32 1 u1))
2.0ms	(sin.f32 (*.f32 314159265359/50000000000 u2))
2.0ms	(*.f32 314159265359/50000000000 u2)

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary32`
50×	`*-un-lft-identity_binary32`
37×	`times-frac_binary32`
30×	`associate-l_binary32`
29×	`add-cube-cbrt_binary32`

Counts

4 → 119

Calls

4 calls:

10.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2)))
4.0ms	(/.f32 u1 (-.f32 1 u1))
3.0ms	(*.f32 314159265359/50000000000 u2)
1.0ms	(sin.f32 (*.f32 314159265359/50000000000 u2))

simplify109.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-def_binary32`
448×	`associate-r_binary32`
378×	`associate-/r*_binary32`
357×	`times-frac_binary32`
261×	`fma-neg_binary32`

Counts

147 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	2754
1	569	2577
2	1673	2467
3	4686	2467
4	5037	2467

prune228.0ms (2.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	177	12	189
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	178	12	190

Error

0.1b

Counts

190 → 12

Alt Table

Status	Error	Program
	0.7b	(.f32 (sqrt.f32 (/.f32 1 (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (/.f32 u1 (cbrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 314159265359/50000000000 u2))))
	2.7b	(exp.f32 (log.f32 (.f32 (sin.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	0.7b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) (cbrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (sqrt.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sin.f32 (.f32 314159265359/50000000000 u2))))
	2.0b	(-.f32 (+.f32 (.f32 314159265359/50000000000 (.f32 u2 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 3060196847853821555298148281676017575122444629042460390799/37500000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 5) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))) (+.f32 (.f32 302029322777818351566783844332719832329455959975176141755859165754785028165295919/3937500000000000000000000000000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 7) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 31006276680305942139213528068663279/750000000000000000000000000000000 (.f32 (pow.f32 u2 3) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sin.f32 (.f32 314159265359/50000000000 u2))))
	0.9b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 314159265359/50000000000 u2)) (cbrt.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (.f32 314159265359/50000000000 u2)))))
	0.7b	(/.f32 (.f32 (sqrt.f32 u1) (sin.f32 (.f32 314159265359/50000000000 u2))) (sqrt.f32 (-.f32 1 u1)))
	0.8b	(.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
	11.6b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (log.f32 (exp.f32 (sin.f32 (.f32 314159265359/50000000000 u2)))))
	0.6b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
	0.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 (.f32 (sin.f32 (.f32 314159265359/50000000000 u2)) (sin.f32 (.f32 314159265359/50000000000 u2))) (sin.f32 (.f32 314159265359/50000000000 u2)))))
▶	0.5b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))

Compiler

Compiled 4408 to 3240 computations (26.5% saved)

localize41.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 u1 (-.f32 1 u1))
✓	0.2b	(sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))
✓	0.3b	(.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))
✓	0.3b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))

series63.0ms (0.7%)

Counts

3 → 44

Calls

3 calls:

31.0ms

(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))

27.0ms

(*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))

4.0ms

(sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary32`
28×	`associate-l_binary32`
26×	`sqrt-prod_binary32`
24×	`*-un-lft-identity_binary32`
19×	`times-frac_binary32`

Counts

3 → 80

Calls

3 calls:

10.0ms

(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))

10.0ms

(*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))

2.0ms

(sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))

simplify95.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-neg_binary32`
426×	`fma-def_binary32`
352×	`*-commutative_binary32`
299×	`associate-/r*_binary32`
265×	`sub-neg_binary32`

Counts

124 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	2264
1	463	2106
2	1404	1994
3	3743	1994
4	4968	1994

prune259.0ms (3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	203	6	209
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	209	12	221

Error

0.0b

Counts

221 → 12

Alt Table

Status	Error	Program
	1.0b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	11.6b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (log.f32 (exp.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	0.6b	(/.f32 (.f32 (sqrt.f32 u1) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))) (sqrt.f32 (-.f32 1 u1)))
	0.7b	(.f32 (sqrt.f32 (/.f32 1 (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (/.f32 u1 (cbrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 314159265359/50000000000 u2))))
	0.8b	(.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
	2.7b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	0.6b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
	0.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 (.f32 (sin.f32 (.f32 314159265359/50000000000 u2)) (sin.f32 (.f32 314159265359/50000000000 u2))) (sin.f32 (.f32 314159265359/50000000000 u2)))))
	0.8b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (sin.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (sin.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
▶	0.5b	(.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))
	2.0b	(-.f32 (+.f32 (.f32 314159265359/50000000000 (.f32 u2 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 3060196847853821555298148281676017575122444629042460390799/37500000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 5) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))) (+.f32 (.f32 302029322777818351566783844332719832329455959975176141755859165754785028165295919/3937500000000000000000000000000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 7) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 31006276680305942139213528068663279/750000000000000000000000000000000 (.f32 (pow.f32 u2 3) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))))
	0.9b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 314159265359/50000000000 u2)) (cbrt.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (.f32 314159265359/50000000000 u2)))))

Compiler

Compiled 5905 to 4669 computations (20.9% saved)

localize50.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(log1p.f32 (/.f32 u1 (-.f32 1 u1)))
	0.3b	(.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))
✓	0.3b	(expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))
✓	0.3b	(.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))

series41.0ms (0.5%)

Counts

3 → 44

Calls

3 calls:

35.0ms

(*.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))

3.0ms

(log1p.f32 (/.f32 u1 (-.f32 1 u1)))

2.0ms

(expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary32`
6×	`associate-l_binary32`
6×	`*-un-lft-identity_binary32`
6×	`add-cube-cbrt_binary32`
5×	`add-cbrt-cube_binary32`

Counts

3 → 46

Calls

3 calls:

7.0ms

(*.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))

0.0ms

(log1p.f32 (/.f32 u1 (-.f32 1 u1)))

0.0ms

(expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))

simplify85.0ms (1%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-neg_binary32`
509×	`fma-def_binary32`
380×	`associate-l_binary32`
323×	`associate-r_binary32`
255×	`associate-+l+_binary32`

Counts

90 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	2307
1	439	1811
2	1338	1693
3	4614	1693
4	5252	1693

prune221.0ms (2.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	144	13	157

Error

0.0b

Counts

157 → 13

Alt Table

Status	Error	Program
	0.9b	(.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 314159265359/50000000000 u2)) (cbrt.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (.f32 314159265359/50000000000 u2)))))
	0.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 (.f32 (sin.f32 (.f32 314159265359/50000000000 u2)) (sin.f32 (.f32 314159265359/50000000000 u2))) (sin.f32 (.f32 314159265359/50000000000 u2)))))
	0.8b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (sin.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (sin.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
▶	0.5b	(.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (.f32 314159265359/50000000000 (.f32 (.f32 u2 u2) u2))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))))) (cbrt.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))))) (.f32 (sin.f32 (.f32 314159265359/50000000000 u2)) (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	11.6b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (log.f32 (exp.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	0.6b	(/.f32 (.f32 (sqrt.f32 u1) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))) (sqrt.f32 (-.f32 1 u1)))
	0.7b	(.f32 (sqrt.f32 (/.f32 1 (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (/.f32 u1 (cbrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 314159265359/50000000000 u2))))
	0.8b	(.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
	2.7b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	0.6b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
✓	0.5b	(.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))
	2.0b	(-.f32 (+.f32 (.f32 314159265359/50000000000 (.f32 u2 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 3060196847853821555298148281676017575122444629042460390799/37500000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 5) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))) (+.f32 (.f32 302029322777818351566783844332719832329455959975176141755859165754785028165295919/3937500000000000000000000000000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 7) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 31006276680305942139213528068663279/750000000000000000000000000000000 (.f32 (pow.f32 u2 3) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))))

Compiler

Compiled 4543 to 3778 computations (16.8% saved)

localize82.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))
✓	0.3b	(.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (.f32 314159265359/50000000000 (.f32 (.f32 u2 u2) u2))))))
✓	0.4b	(.f32 (.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (.f32 314159265359/50000000000 (.f32 (*.f32 u2 u2) u2)))
✓	0.4b	(.f32 314159265359/50000000000 (.f32 (*.f32 u2 u2) u2))

series69.0ms (0.8%)

Counts

3 → 44

Calls

3 calls:

44.0ms

(*.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (*.f32 314159265359/50000000000 (*.f32 (*.f32 u2 u2) u2))))))

21.0ms

(*.f32 (*.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (*.f32 314159265359/50000000000 (*.f32 (*.f32 u2 u2) u2)))

3.0ms

(*.f32 314159265359/50000000000 (*.f32 (*.f32 u2 u2) u2))

rewrite148.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

292×	`add-exp-log_binary32`
292×	`pow1_binary32`
241×	`cbrt-unprod_binary32`
241×	`prod-exp_binary32`
241×	`pow-prod-down_binary32`

Counts

3 → 191

Calls

3 calls:

81.0ms

(*.f32 (*.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (*.f32 314159265359/50000000000 (*.f32 (*.f32 u2 u2) u2)))

8.0ms

(*.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (*.f32 314159265359/50000000000 (*.f32 (*.f32 u2 u2) u2))))))

7.0ms

(*.f32 314159265359/50000000000 (*.f32 (*.f32 u2 u2) u2))

simplify222.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

587×	`*-commutative_binary32`
478×	`fma-neg_binary32`
378×	`associate-l_binary32`
378×	`fma-def_binary32`
311×	`associate-r_binary32`

Counts

235 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	8981
1	527	3074
2	1717	2957
3	4620	2957
4	4894	2957

prune371.0ms (4.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	0	11	11
Picked	0	1	1
Done	1	0	1
Total	215	13	228

Error

0.0b

Counts

228 → 13

Alt Table

Status	Error	Program
	0.7b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (cbrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))))) (.f32 (sqrt.f32 (cbrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (.f32 314159265359/50000000000 (.f32 (.f32 u2 u2) u2)))))))
	0.6b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
	0.9b	(.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 314159265359/50000000000 u2)) (cbrt.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (.f32 314159265359/50000000000 u2)))))
	0.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 (.f32 (sin.f32 (.f32 314159265359/50000000000 u2)) (sin.f32 (.f32 314159265359/50000000000 u2))) (sin.f32 (.f32 314159265359/50000000000 u2)))))
	0.8b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (sin.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (sin.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
✓	0.5b	(.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000))) (.f32 314159265359/50000000000 (.f32 (.f32 u2 u2) u2))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))))) (cbrt.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))))) (.f32 (sin.f32 (.f32 314159265359/50000000000 u2)) (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	11.6b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (log.f32 (exp.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	0.6b	(/.f32 (.f32 (sqrt.f32 u1) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))) (sqrt.f32 (-.f32 1 u1)))
	0.7b	(.f32 (sqrt.f32 (/.f32 1 (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (/.f32 u1 (cbrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 314159265359/50000000000 u2))))
	0.8b	(.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
	2.7b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	2.0b	(-.f32 (+.f32 (.f32 314159265359/50000000000 (.f32 u2 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 3060196847853821555298148281676017575122444629042460390799/37500000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 5) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))) (+.f32 (.f32 302029322777818351566783844332719832329455959975176141755859165754785028165295919/3937500000000000000000000000000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 7) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 31006276680305942139213528068663279/750000000000000000000000000000000 (.f32 (pow.f32 u2 3) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))))

Compiler

Compiled 9948 to 7924 computations (20.3% saved)

regimes4.0s (46.5%)

Accuracy

Total 0.4b remaining (89.4%)

Threshold costs 0.4b (89.4%)

Counts

311 → 1

Compiler

Compiled 72711 to 58678 computations (19.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	56
1	29	56
2	33	56
3	35	56
4	36	56
5	35	56

end1.0ms (0%)

Compiler: Compiled 37 to 34 computations (8.1% saved)

sample1.9s (22.6%)

Algorithm

1×

intervals

Results

809.0ms	8000×	body	128	valid
282.0ms	8000×	pre	128	true
0.0ms	2×	pre	128	false

Compiler

Compiled 506 to 417 computations (17.6% saved)

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

Details

analyze366.0ms (4.3%)

sample76.0ms (0.9%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize28.0ms (0.3%)

series32.0ms (0.4%)

rewrite26.0ms (0.3%)

simplify109.0ms (1.3%)

prune228.0ms (2.6%)

localize41.0ms (0.5%)

series63.0ms (0.7%)

rewrite29.0ms (0.3%)

simplify95.0ms (1.1%)

prune259.0ms (3%)

localize50.0ms (0.6%)

series41.0ms (0.5%)

rewrite10.0ms (0.1%)

simplify85.0ms (1%)

prune221.0ms (2.6%)

localize82.0ms (1%)

series69.0ms (0.8%)

rewrite148.0ms (1.7%)

simplify222.0ms (2.6%)

prune371.0ms (4.3%)

regimes4.0s (46.5%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.9s (22.6%)

Profiling

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17