Details

analyze123.0ms (1.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.9%	99.1%	0
0%	0.9%	99.1%	1
0%	0.9%	99.1%	2
0.4%	0.4%	99.1%	3
0.4%	0.4%	99.1%	4
0.6%	0.2%	99.1%	5
0.6%	0.2%	99.1%	6
0.7%	0.1%	99.1%	7
0.7%	0.1%	99.1%	8
0.8%	0.1%	99.1%	9
0.8%	0.1%	99.1%	10
0.8%	0%	99.1%	11
0.8%	0%	99.1%	12
0.8%	0%	99.1%	13
0.8%	0%	99.1%	14

Compiler

Compiled 32 to 24 computations (25% saved)

sample2.1s (26.5%)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 81 to 61 computations (24.7% saved)

simplify155.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

2879×	`fma-def_binary32`
2626×	`associate-+l+_binary32`
362×	`distribute-rgt-in_binary32`
324×	`associate-+r+_binary32`
323×	`distribute-rgt-out_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	21	19
2	35	19
3	54	19
4	110	19
5	173	19
6	247	19
7	405	19
8	505	19
9	563	19
10	613	19
11	636	19
12	672	19
13	781	19
14	959	19
15	1218	19
16	1550	19
17	1556	19
18	1548	19
19	1896	19
20	2113	19
21	2208	19
22	2307	19
23	2275	19
24	2275	19
25	2275	19
26	4265	19
27	4265	19
28	4265	19
29	4265	19
30	5619	19

prune4.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(fma.f32 v (log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u)) 1)
	0.2b	(+.f32 1 (.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))))

Compiler

Compiled 94 to 70 computations (25.5% saved)

localize37.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u)
✓	0.1b	(log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u))
✓	0.1b	(fma.f32 v (log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u)) 1)
✓	0.1b	(exp.f32 (/.f32 -2 v))

series279.0ms (3.5%)

Counts

4 → 80

Calls

4 calls:

202.0ms	(log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u))
66.0ms	(fma.f32 v (log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u)) 1)
8.0ms	(fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u)
2.0ms	(exp.f32 (/.f32 -2 v))

rewrite93.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

106× egg-rr

Counts

4 → 106

Calls

2 calls:

90.0ms

((exp.f32 (/.f32 -2 v)) (fma.f32 v (log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u)) 1) (log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u)) (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	53
1	224	53
2	2618	53
3	4872	53
4	4988	53
0	0	0
1	0	0

simplify77.0ms (1%)

Algorithm

1×	egg-herbie

Rules

629×	`cancel-sign-sub-inv_binary32`
438×	`sub-neg_binary32`
254×	`fma-def_binary32`
231×	`+-commutative_binary32`
225×	`fma-neg_binary32`

Counts

186 → 192

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	3048
1	912	2982
2	3630	2942
3	5157	2942

prune343.0ms (4.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	185	7	192
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	187	7	194

Error

0.0b

Counts

194 → 7

Alt Table

Status	Error	Program
▶	0.2b	(log1p.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))
	29.9b	(-.f32 (+.f32 (/.f32 (.f32 v u) (exp.f32 (/.f32 -2 v))) (/.f32 (.f32 v (.f32 u u)) (exp.f32 (/.f32 -2 v)))) (fma.f32 (.f32 v (.f32 u u)) 1/2 (+.f32 1 (fma.f32 v u (.f32 1/2 (/.f32 (.f32 v (.f32 u u)) (pow.f32 (exp.f32 (/.f32 -2 v)) 2)))))))
	2.8b	(exp.f32 (log1p.f32 (*.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)))))
	29.9b	(-.f32 (+.f32 (.f32 1/3 (/.f32 (.f32 v (pow.f32 u 3)) (pow.f32 (exp.f32 (/.f32 -2 v)) 3))) (+.f32 (/.f32 (.f32 v u) (exp.f32 (/.f32 -2 v))) (+.f32 (/.f32 (.f32 v (pow.f32 u 2)) (exp.f32 (/.f32 -2 v))) (/.f32 (.f32 v (pow.f32 u 3)) (exp.f32 (/.f32 -2 v)))))) (+.f32 (.f32 1/2 (.f32 v (pow.f32 u 2))) (+.f32 1 (+.f32 (.f32 1/3 (.f32 v (pow.f32 u 3))) (+.f32 (.f32 v u) (+.f32 (/.f32 (.f32 v (pow.f32 u 3)) (pow.f32 (exp.f32 (/.f32 -2 v)) 2)) (.f32 1/2 (/.f32 (*.f32 v (pow.f32 u 2)) (pow.f32 (exp.f32 (/.f32 -2 v)) 2)))))))))
	28.8b	(-.f32 (fma.f32 2/3 (/.f32 u (pow.f32 v 3)) (fma.f32 2 (+.f32 u (/.f32 u v)) (fma.f32 4/3 (/.f32 u (.f32 v v)) (fma.f32 8/3 (/.f32 (pow.f32 u 3) (.f32 v v)) (.f32 8 (pow.f32 (/.f32 u v) 3)))))) (fma.f32 4 (/.f32 (pow.f32 u 4) (pow.f32 v 3)) (+.f32 1 (fma.f32 2 (/.f32 (.f32 u u) v) (fma.f32 4 (.f32 (/.f32 u v) (/.f32 u v)) (.f32 14/3 (/.f32 (*.f32 u u) (pow.f32 v 3))))))))
	29.9b	(fma.f32 v (-.f32 (+.f32 (/.f32 (pow.f32 u 3) (exp.f32 (/.f32 -2 v))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 u 3) (pow.f32 (exp.f32 (/.f32 -2 v)) 3))) (+.f32 (/.f32 (pow.f32 u 2) (exp.f32 (/.f32 -2 v))) (/.f32 u (exp.f32 (/.f32 -2 v)))))) (+.f32 (.f32 1/2 (/.f32 (pow.f32 u 2) (pow.f32 (exp.f32 (/.f32 -2 v)) 2))) (+.f32 (.f32 1/3 (pow.f32 u 3)) (+.f32 (.f32 1/2 (pow.f32 u 2)) (+.f32 (/.f32 (pow.f32 u 3) (pow.f32 (exp.f32 (/.f32 -2 v)) 2)) (+.f32 u (*.f32 2 (/.f32 1 v)))))))) 1)
	0.3b	(*.f32 (cbrt.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)) (pow.f32 (cbrt.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)) 2))

Compiler

Compiled 5964 to 4329 computations (27.4% saved)

localize45.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)
✓	0.1b	(log1p.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))
	0.1b	(exp.f32 (/.f32 -2 v))
✓	0.8b	(expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1))

series213.0ms (2.7%)

Counts

3 → 72

Calls

3 calls:

88.0ms

(expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1))

63.0ms

(log1p.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))

62.0ms

(fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)

rewrite69.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

91× egg-rr

Counts

3 → 91

Calls

2 calls:

66.0ms

((expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)) (log1p.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1))) (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	59
1	243	59
2	2812	59
3	5157	59
0	0	0
1	0	0

simplify124.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

565×	`times-frac_binary32`
364×	`associate-/l*_binary32`
360×	`fma-def_binary32`
334×	`associate-/r*_binary32`
289×	`associate-r_binary32`

Counts

163 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	386	5788
1	1381	5563
2	4945	5552
3	4994	5552

prune277.0ms (3.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	167	9	176

Error

Counts

176 → 9

Alt Table

Status	Error	Program
	0.3b	(log1p.f32 (fma.f32 (exp.f32 (*.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)))) (E.f32) -1))
	0.3b	(log1p.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1))))) (log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))))))
	29.9b	(-.f32 (fma.f32 1/3 (/.f32 (.f32 v (pow.f32 u 3)) (pow.f32 (exp.f32 (/.f32 -2 v)) 3)) (+.f32 (/.f32 (.f32 v u) (exp.f32 (/.f32 -2 v))) (+.f32 (/.f32 (.f32 v (.f32 u u)) (exp.f32 (/.f32 -2 v))) (/.f32 (.f32 v (pow.f32 u 3)) (exp.f32 (/.f32 -2 v)))))) (fma.f32 1/2 (.f32 v (.f32 u u)) (+.f32 1 (fma.f32 1/3 (.f32 v (pow.f32 u 3)) (fma.f32 v u (fma.f32 1/2 (/.f32 (.f32 v (.f32 u u)) (pow.f32 (exp.f32 (/.f32 -2 v)) 2)) (/.f32 (*.f32 v (pow.f32 u 3)) (pow.f32 (exp.f32 (/.f32 -2 v)) 2))))))))
	29.9b	(-.f32 (+.f32 (/.f32 (.f32 v u) (exp.f32 (/.f32 -2 v))) (/.f32 (.f32 v (.f32 u u)) (exp.f32 (/.f32 -2 v)))) (fma.f32 (.f32 v (.f32 u u)) 1/2 (+.f32 1 (fma.f32 v u (.f32 1/2 (/.f32 (.f32 v (.f32 u u)) (pow.f32 (exp.f32 (/.f32 -2 v)) 2)))))))
	28.8b	(-.f32 (fma.f32 2/3 (/.f32 u (pow.f32 v 3)) (fma.f32 2 (+.f32 u (/.f32 u v)) (fma.f32 4/3 (/.f32 u (.f32 v v)) (fma.f32 8/3 (/.f32 (pow.f32 u 3) (.f32 v v)) (.f32 8 (pow.f32 (/.f32 u v) 3)))))) (fma.f32 4 (/.f32 (pow.f32 u 4) (pow.f32 v 3)) (+.f32 1 (fma.f32 2 (/.f32 (.f32 u u) v) (fma.f32 4 (.f32 (/.f32 u v) (/.f32 u v)) (.f32 14/3 (/.f32 (*.f32 u u) (pow.f32 v 3))))))))
▶	0.2b	(fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)
	29.9b	(fma.f32 v (-.f32 (+.f32 (/.f32 (pow.f32 u 3) (exp.f32 (/.f32 -2 v))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 u 3) (pow.f32 (exp.f32 (/.f32 -2 v)) 3))) (+.f32 (/.f32 (pow.f32 u 2) (exp.f32 (/.f32 -2 v))) (/.f32 u (exp.f32 (/.f32 -2 v)))))) (+.f32 (.f32 1/2 (/.f32 (pow.f32 u 2) (pow.f32 (exp.f32 (/.f32 -2 v)) 2))) (+.f32 (.f32 1/3 (pow.f32 u 3)) (+.f32 (.f32 1/2 (pow.f32 u 2)) (+.f32 (/.f32 (pow.f32 u 3) (pow.f32 (exp.f32 (/.f32 -2 v)) 2)) (+.f32 u (*.f32 2 (/.f32 1 v)))))))) 1)
	0.3b	(*.f32 (cbrt.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)) (pow.f32 (cbrt.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)) 2))
	0.3b	(log1p.f32 (+.f32 (log.f32 (*.f32 (cbrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))) (cbrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))))) (log.f32 (cbrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))))))

Compiler

Compiled 8215 to 6115 computations (25.6% saved)

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)
✓	0.1b	(log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u))
	0.1b	(fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)
	0.1b	(exp.f32 (/.f32 -2 v))

series164.0ms (2.1%)

Counts

2 → 48

Calls

2 calls:

156.0ms	(log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u))
8.0ms	(fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)

rewrite81.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

57× egg-rr

Counts

2 → 57

Calls

2 calls:

79.0ms	((log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	203	28
2	2359	28
3	4963	28
4	5070	28
0	0	0
1	0	0

simplify51.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-def_binary32`
627×	`associate-/l*_binary32`
279×	`cancel-sign-sub-inv_binary32`
235×	`sub-neg_binary32`
163×	`distribute-rgt-in_binary32`

Counts

105 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	1694
1	510	1670
2	1968	1545
3	5260	1545

prune158.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	136	9	145

Error

Counts

145 → 9

Alt Table

Status	Error	Program
	0.3b	(log1p.f32 (fma.f32 (exp.f32 (*.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)))) (E.f32) -1))
▶	0.3b	(log1p.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1))))) (log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))))))
	29.9b	(-.f32 (fma.f32 1/3 (/.f32 (.f32 v (pow.f32 u 3)) (pow.f32 (exp.f32 (/.f32 -2 v)) 3)) (+.f32 (/.f32 (.f32 v u) (exp.f32 (/.f32 -2 v))) (+.f32 (/.f32 (.f32 v (.f32 u u)) (exp.f32 (/.f32 -2 v))) (/.f32 (.f32 v (pow.f32 u 3)) (exp.f32 (/.f32 -2 v)))))) (fma.f32 1/2 (.f32 v (.f32 u u)) (+.f32 1 (fma.f32 1/3 (.f32 v (pow.f32 u 3)) (fma.f32 v u (fma.f32 1/2 (/.f32 (.f32 v (.f32 u u)) (pow.f32 (exp.f32 (/.f32 -2 v)) 2)) (/.f32 (*.f32 v (pow.f32 u 3)) (pow.f32 (exp.f32 (/.f32 -2 v)) 2))))))))
	29.9b	(-.f32 (+.f32 (/.f32 (.f32 v u) (exp.f32 (/.f32 -2 v))) (/.f32 (.f32 v (.f32 u u)) (exp.f32 (/.f32 -2 v)))) (fma.f32 (.f32 v (.f32 u u)) 1/2 (+.f32 1 (fma.f32 v u (.f32 1/2 (/.f32 (.f32 v (.f32 u u)) (pow.f32 (exp.f32 (/.f32 -2 v)) 2)))))))
	28.8b	(-.f32 (fma.f32 2/3 (/.f32 u (pow.f32 v 3)) (fma.f32 2 (+.f32 u (/.f32 u v)) (fma.f32 4/3 (/.f32 u (.f32 v v)) (fma.f32 8/3 (/.f32 (pow.f32 u 3) (.f32 v v)) (.f32 8 (pow.f32 (/.f32 u v) 3)))))) (fma.f32 4 (/.f32 (pow.f32 u 4) (pow.f32 v 3)) (+.f32 1 (fma.f32 2 (/.f32 (.f32 u u) v) (fma.f32 4 (.f32 (/.f32 u v) (/.f32 u v)) (.f32 14/3 (/.f32 (*.f32 u u) (pow.f32 v 3))))))))
✓	0.2b	(fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)
	29.9b	(fma.f32 v (-.f32 (+.f32 (/.f32 (pow.f32 u 3) (exp.f32 (/.f32 -2 v))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 u 3) (pow.f32 (exp.f32 (/.f32 -2 v)) 3))) (+.f32 (/.f32 (pow.f32 u 2) (exp.f32 (/.f32 -2 v))) (/.f32 u (exp.f32 (/.f32 -2 v)))))) (+.f32 (.f32 1/2 (/.f32 (pow.f32 u 2) (pow.f32 (exp.f32 (/.f32 -2 v)) 2))) (+.f32 (.f32 1/3 (pow.f32 u 3)) (+.f32 (.f32 1/2 (pow.f32 u 2)) (+.f32 (/.f32 (pow.f32 u 3) (pow.f32 (exp.f32 (/.f32 -2 v)) 2)) (+.f32 u (*.f32 2 (/.f32 1 v)))))))) 1)
	0.3b	(*.f32 (cbrt.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)) (pow.f32 (cbrt.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)) 2))
	0.3b	(log1p.f32 (+.f32 (log.f32 (*.f32 (cbrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))) (cbrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))))) (log.f32 (cbrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))))))

Compiler

Compiled 4196 to 3090 computations (26.4% saved)

localize64.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(log1p.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1))))) (log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))))))
	0.1b	(exp.f32 (/.f32 -2 v))
✓	0.2b	(log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))))
	0.8b	(expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1))

series967.0ms (12.1%)

Counts

2 → 48

Calls

2 calls:

650.0ms

(log1p.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1))))) (log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))))))

316.0ms

(log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))))

rewrite62.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

42× egg-rr

Counts

2 → 42

Calls

2 calls:

60.0ms

((log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1))))) (log1p.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1))))) (log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1))))))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	46
1	307	13
2	3410	13
3	5002	13
0	0	0
1	0	0

simplify246.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

814×	`fma-def_binary32`
341×	`*-commutative_binary32`
227×	`+-commutative_binary32`
172×	`associate-+r+_binary32`
149×	`associate-/l*_binary32`

Counts

90 → 127

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	867	14917
1	3229	13522
2	4949	13522
3	4975	13522

prune1.1s (13.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	381	0	381
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	381	9	390

Error

Counts

390 → 9

Alt Table

Status	Error	Program
	0.3b	(log1p.f32 (fma.f32 (exp.f32 (*.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)))) (E.f32) -1))
✓	0.3b	(log1p.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1))))) (log.f32 (sqrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))))))
	29.9b	(-.f32 (fma.f32 1/3 (/.f32 (.f32 v (pow.f32 u 3)) (pow.f32 (exp.f32 (/.f32 -2 v)) 3)) (+.f32 (/.f32 (.f32 v u) (exp.f32 (/.f32 -2 v))) (+.f32 (/.f32 (.f32 v (.f32 u u)) (exp.f32 (/.f32 -2 v))) (/.f32 (.f32 v (pow.f32 u 3)) (exp.f32 (/.f32 -2 v)))))) (fma.f32 1/2 (.f32 v (.f32 u u)) (+.f32 1 (fma.f32 1/3 (.f32 v (pow.f32 u 3)) (fma.f32 v u (fma.f32 1/2 (/.f32 (.f32 v (.f32 u u)) (pow.f32 (exp.f32 (/.f32 -2 v)) 2)) (/.f32 (*.f32 v (pow.f32 u 3)) (pow.f32 (exp.f32 (/.f32 -2 v)) 2))))))))
	29.9b	(-.f32 (+.f32 (/.f32 (.f32 v u) (exp.f32 (/.f32 -2 v))) (/.f32 (.f32 v (.f32 u u)) (exp.f32 (/.f32 -2 v)))) (fma.f32 (.f32 v (.f32 u u)) 1/2 (+.f32 1 (fma.f32 v u (.f32 1/2 (/.f32 (.f32 v (.f32 u u)) (pow.f32 (exp.f32 (/.f32 -2 v)) 2)))))))
	28.8b	(-.f32 (fma.f32 2/3 (/.f32 u (pow.f32 v 3)) (fma.f32 2 (+.f32 u (/.f32 u v)) (fma.f32 4/3 (/.f32 u (.f32 v v)) (fma.f32 8/3 (/.f32 (pow.f32 u 3) (.f32 v v)) (.f32 8 (pow.f32 (/.f32 u v) 3)))))) (fma.f32 4 (/.f32 (pow.f32 u 4) (pow.f32 v 3)) (+.f32 1 (fma.f32 2 (/.f32 (.f32 u u) v) (fma.f32 4 (.f32 (/.f32 u v) (/.f32 u v)) (.f32 14/3 (/.f32 (*.f32 u u) (pow.f32 v 3))))))))
✓	0.2b	(fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)
	29.9b	(fma.f32 v (-.f32 (+.f32 (/.f32 (pow.f32 u 3) (exp.f32 (/.f32 -2 v))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 u 3) (pow.f32 (exp.f32 (/.f32 -2 v)) 3))) (+.f32 (/.f32 (pow.f32 u 2) (exp.f32 (/.f32 -2 v))) (/.f32 u (exp.f32 (/.f32 -2 v)))))) (+.f32 (.f32 1/2 (/.f32 (pow.f32 u 2) (pow.f32 (exp.f32 (/.f32 -2 v)) 2))) (+.f32 (.f32 1/3 (pow.f32 u 3)) (+.f32 (.f32 1/2 (pow.f32 u 2)) (+.f32 (/.f32 (pow.f32 u 3) (pow.f32 (exp.f32 (/.f32 -2 v)) 2)) (+.f32 u (*.f32 2 (/.f32 1 v)))))))) 1)
	0.3b	(*.f32 (cbrt.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)) (pow.f32 (cbrt.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)) 2))
	0.3b	(log1p.f32 (+.f32 (log.f32 (*.f32 (cbrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))) (cbrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))))) (log.f32 (cbrt.f32 (exp.f32 (expm1.f32 (fma.f32 v (log.f32 (fma.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 u) u)) 1)))))))

Compiler

Compiled 40909 to 32761 computations (19.9% saved)

regimes850.0ms (10.6%)

Accuracy

Total 0.1b remaining (79.2%)

Threshold costs 0.1b (79.2%)

Counts

166 → 1

Compiler

Compiled 18584 to 13960 computations (24.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-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	15	25
1	21	25
2	25	25
3	27	25
4	28	25
5	27	25

end265.0ms (3.3%)

Compiler: Compiled 500 to 358 computations (28.4% saved)

Details

analyze123.0ms (1.5%)

sample2.1s (26.5%)

simplify155.0ms (1.9%)

prune4.0ms (0%)

localize37.0ms (0.5%)

series279.0ms (3.5%)

rewrite93.0ms (1.2%)

simplify77.0ms (1%)

prune343.0ms (4.3%)

localize45.0ms (0.6%)

series213.0ms (2.7%)

rewrite69.0ms (0.9%)

simplify124.0ms (1.6%)

prune277.0ms (3.5%)

localize35.0ms (0.4%)

series164.0ms (2.1%)

rewrite81.0ms (1%)

simplify51.0ms (0.6%)

prune158.0ms (2%)

localize64.0ms (0.8%)

series967.0ms (12.1%)

rewrite62.0ms (0.8%)

simplify246.0ms (3.1%)

prune1.1s (13.7%)

regimes850.0ms (10.6%)

simplify3.0ms (0%)

end265.0ms (3.3%)

Profiling