Details

analyze108.0ms (2.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.1%	99.9%	0
0%	0.1%	99.9%	1
0%	0.1%	99.9%	2
0.1%	0.1%	99.9%	3
0.1%	0.1%	99.9%	4
0.1%	0%	99.9%	5
0.1%	0%	99.9%	6
0.1%	0%	99.9%	7
0.1%	0%	99.9%	8
0.1%	0%	99.9%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 31 to 25 computations (19.4% saved)

sample1.6s (36.7%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 78 to 64 computations (17.9% saved)

simplify39.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

764×	`fma-def_binary32`
494×	`fma-neg_binary32`
125×	`cancel-sign-sub-inv_binary32`
104×	`distribute-rgt-in_binary32`
87×	`sub-neg_binary32`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	14	20
1	33	19
2	61	17
3	139	15
4	242	15
5	334	15
6	441	13
7	635	13
8	1013	13
9	1273	13
10	1659	13
11	1921	13
12	2358	13
13	2674	13
14	2709	13
15	2710	13
16	2710	13

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.3b	(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
▶	0.6b	(.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))

Compiler

Compiled 79 to 67 computations (15.2% saved)

localize23.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f32 u -4/3 1/3)
✓	0.3b	(log1p.f32 (fma.f32 u -4/3 1/3))
✓	0.4b	(.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))

series254.0ms (5.7%)

Counts

3 → 48

Calls

3 calls:

250.0ms	(.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))
2.0ms	(log1p.f32 (fma.f32 u -4/3 1/3))
2.0ms	(fma.f32 u -4/3 1/3)

rewrite42.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

823×	`expm1-log1p-u_binary32`
822×	`log1p-expm1-u_binary32`
97×	`add-sqr-sqrt_binary32`
91×	`add-log-exp_binary32`
90×	`add-cube-cbrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	202	25
2	2230	25

Stop Event

1×	node limit

Counts

3 → 54

Calls

3 calls:

41.0ms	(fma.f32 u -4/3 1/3)
41.0ms	(log1p.f32 (fma.f32 u -4/3 1/3))
41.0ms	(.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))

simplify35.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-def_binary32`
504×	`fma-neg_binary32`
470×	`cancel-sign-sub-inv_binary32`
391×	`sub-neg_binary32`
220×	`unsub-neg_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	820
1	320	770
2	1022	704
3	3538	704

Stop Event

1×	node limit

Counts

102 → 106

prune74.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	96	10	106
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	97	11	108

Error

0.1b

Counts

108 → 11

Alt Table

Status	Error	Program
	1.3b	(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
	0.8b	(.f32 (log1p.f32 (.f32 (cbrt.f32 (fma.f32 u -4/3 1/3)) (cbrt.f32 (pow.f32 (fma.f32 u -4/3 1/3) 2)))) (*.f32 s -3))
	0.9b	(.f32 -3 (.f32 s (log.f32 (fma.f32 u -4/3 4/3))))
	0.8b	(pow.f32 (sqrt.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))) 2)
	0.9b	(pow.f32 (cbrt.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))) 3)
	1.0b	(.f32 (log1p.f32 (-.f32 1/3 (.f32 4/3 u))) (*.f32 s -3))
	1.0b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (fma.f32 u -4/3 1/3))) 3) (.f32 s -3))
	0.7b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (fma.f32 u -4/3 1/3))) (cbrt.f32 (pow.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) 2))) (*.f32 s -3))
	9.5b	(.f32 (-.f32 (exp.f32 (log1p.f32 (log1p.f32 (fma.f32 u -4/3 1/3)))) 1) (.f32 s -3))
	2.9b	(exp.f32 (log.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))))
▶	0.6b	(expm1.f32 (log1p.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))))

Compiler

Compiled 1901 to 1508 computations (20.7% saved)

localize30.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(expm1.f32 (log1p.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))))
	0.3b	(fma.f32 u -4/3 1/3)
	0.3b	(log1p.f32 (fma.f32 u -4/3 1/3))
	0.4b	(.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))

series245.0ms (5.5%)

Counts

1 → 24

Calls

1 calls:

245.0ms

(expm1.f32 (log1p.f32 (*.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (*.f32 s -3))))

rewrite43.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

899×	`expm1-log1p-u_binary32`
897×	`log1p-expm1-u_binary32`
339×	`prod-diff_binary32`
105×	`add-sqr-sqrt_binary32`
98×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	223	13
2	2438	13

Stop Event

1×	node limit

Counts

1 → 36

Calls

1 calls:

42.0ms

(expm1.f32 (log1p.f32 (*.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (*.f32 s -3))))

simplify25.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

475×	`fma-def_binary32`
282×	`associate-+l+_binary32`
270×	`fma-neg_binary32`
246×	`associate-l_binary32`
239×	`associate-+r+_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	532
1	218	490
2	659	442
3	2105	432

Stop Event

1×	node limit

Counts

60 → 62

prune109.0ms (2.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	164	4	168
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	166	13	179

Error

0.0b

Counts

179 → 13

Alt Table

Status	Error	Program
	1.3b	(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
	0.8b	(.f32 (log1p.f32 (.f32 (cbrt.f32 (fma.f32 u -4/3 1/3)) (cbrt.f32 (pow.f32 (fma.f32 u -4/3 1/3) 2)))) (*.f32 s -3))
	0.9b	(.f32 -3 (.f32 s (log.f32 (fma.f32 u -4/3 4/3))))
	1.0b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (fma.f32 u -4/3 1/3))) 3) (.f32 s -3))
▶	0.6b	(.f32 -3 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) s))
	0.8b	(pow.f32 (sqrt.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))) 2)
	0.9b	(pow.f32 (cbrt.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))) 3)
	1.0b	(.f32 (log1p.f32 (-.f32 1/3 (.f32 4/3 u))) (*.f32 s -3))
	0.7b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) 2)) (.f32 (cbrt.f32 (log1p.f32 (fma.f32 u -4/3 1/3))) (*.f32 s -3)))
	0.6b	(.f32 s (.f32 -3 (log1p.f32 (fma.f32 u -4/3 1/3))))
	1.0b	(.f32 (log.f32 (fma.f32 u -4/3 4/3)) (.f32 -3 s))
	2.9b	(exp.f32 (log.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))))
✓	0.6b	(expm1.f32 (log1p.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))))

Compiler

Compiled 3151 to 2525 computations (19.9% saved)

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) s)
	0.3b	(fma.f32 u -4/3 1/3)
✓	0.3b	(.f32 -3 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) s))
	0.3b	(log1p.f32 (fma.f32 u -4/3 1/3))

series495.0ms (11.1%)

Counts

2 → 48

Calls

2 calls:

249.0ms	(.f32 -3 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) s))
246.0ms	(*.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) s)

rewrite41.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

821×	`expm1-log1p-u_binary32`
820×	`log1p-expm1-u_binary32`
97×	`add-sqr-sqrt_binary32`
91×	`add-log-exp_binary32`
90×	`add-cube-cbrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	202	23
2	2225	23

Stop Event

1×	node limit

Counts

2 → 28

Calls

2 calls:

40.0ms	(*.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) s)
40.0ms	(.f32 -3 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) s))

simplify41.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

630×	`fma-def_binary32`
618×	`fma-neg_binary32`
319×	`sub-neg_binary32`
218×	`cancel-sign-sub-inv_binary32`
194×	`unsub-neg_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	101	961
1	331	913
2	1032	815
3	3553	809

Stop Event

1×	node limit

Counts

76 → 77

prune83.0ms (1.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	142	13	155

Error

0.0b

Counts

155 → 13

Alt Table

Status	Error	Program
	1.3b	(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
	0.8b	(.f32 (log1p.f32 (.f32 (cbrt.f32 (fma.f32 u -4/3 1/3)) (cbrt.f32 (pow.f32 (fma.f32 u -4/3 1/3) 2)))) (*.f32 s -3))
	0.9b	(.f32 -3 (.f32 s (log.f32 (fma.f32 u -4/3 4/3))))
	1.0b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (fma.f32 u -4/3 1/3))) 3) (.f32 s -3))
✓	0.6b	(.f32 -3 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) s))
	0.8b	(pow.f32 (sqrt.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))) 2)
	0.9b	(pow.f32 (cbrt.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))) 3)
	1.0b	(.f32 (log1p.f32 (-.f32 1/3 (.f32 4/3 u))) (*.f32 s -3))
	0.7b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) 2)) (.f32 (cbrt.f32 (log1p.f32 (fma.f32 u -4/3 1/3))) (*.f32 s -3)))
▶	0.6b	(.f32 s (.f32 -3 (log1p.f32 (fma.f32 u -4/3 1/3))))
	1.0b	(.f32 (log.f32 (fma.f32 u -4/3 4/3)) (.f32 -3 s))
	2.9b	(exp.f32 (log.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))))
✓	0.6b	(expm1.f32 (log1p.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))))

Compiler

Compiled 2478 to 1920 computations (22.5% saved)

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 s (.f32 -3 (log1p.f32 (fma.f32 u -4/3 1/3))))
✓	0.3b	(*.f32 -3 (log1p.f32 (fma.f32 u -4/3 1/3)))
	0.3b	(fma.f32 u -4/3 1/3)
	0.3b	(log1p.f32 (fma.f32 u -4/3 1/3))

series240.0ms (5.4%)

Counts

2 → 36

Calls

2 calls:

237.0ms	(.f32 s (.f32 -3 (log1p.f32 (fma.f32 u -4/3 1/3))))
3.0ms	(*.f32 -3 (log1p.f32 (fma.f32 u -4/3 1/3)))

rewrite38.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

821×	`expm1-log1p-u_binary32`
820×	`log1p-expm1-u_binary32`
97×	`add-sqr-sqrt_binary32`
91×	`add-log-exp_binary32`
90×	`add-cube-cbrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	202	23
2	2225	23

Stop Event

1×	node limit

Counts

2 → 28

Calls

2 calls:

37.0ms	(.f32 s (.f32 -3 (log1p.f32 (fma.f32 u -4/3 1/3))))
37.0ms	(*.f32 -3 (log1p.f32 (fma.f32 u -4/3 1/3)))

simplify39.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

688×	`fma-def_binary32`
348×	`fma-neg_binary32`
258×	`cancel-sign-sub-inv_binary32`
252×	`associate-l_binary32`
241×	`unsub-neg_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	799
1	337	739
2	1010	672
3	2959	656

Stop Event

1×	node limit

Counts

64 → 76

prune93.0ms (2.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	136	5	141
Fresh	4	6	10
Picked	1	0	1
Done	0	2	2
Total	141	13	154

Error

0.0b

Counts

154 → 13

Alt Table

Status	Error	Program
	0.9b	(pow.f32 (cbrt.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))) 3)
	0.6b	(.f32 s (sqrt.f32 (.f32 9 (pow.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) 2))))
	1.0b	(.f32 (log1p.f32 (-.f32 1/3 (.f32 4/3 u))) (*.f32 s -3))
	0.9b	(.f32 s (pow.f32 (cbrt.f32 (.f32 -3 (log1p.f32 (fma.f32 u -4/3 1/3)))) 3))
	0.8b	(.f32 (log1p.f32 (.f32 (cbrt.f32 (fma.f32 u -4/3 1/3)) (cbrt.f32 (pow.f32 (fma.f32 u -4/3 1/3) 2)))) (*.f32 s -3))
	0.9b	(.f32 -3 (.f32 s (log.f32 (fma.f32 u -4/3 4/3))))
	0.7b	(.f32 s (pow.f32 (pow.f32 (.f32 -3 (log1p.f32 (fma.f32 u -4/3 1/3))) 3) 1/3))
	0.8b	(pow.f32 (sqrt.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))) 2)
✓	0.6b	(.f32 -3 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) s))
	1.0b	(.f32 (log.f32 (fma.f32 u -4/3 4/3)) (.f32 -3 s))
	9.5b	(.f32 s (.f32 -3 (-.f32 (exp.f32 (log1p.f32 (log1p.f32 (fma.f32 u -4/3 1/3)))) 1)))
	0.6b	(.f32 s (log1p.f32 (expm1.f32 (.f32 -3 (log1p.f32 (fma.f32 u -4/3 1/3))))))
✓	0.6b	(expm1.f32 (log1p.f32 (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) (.f32 s -3))))

Compiler

Compiled 2289 to 1813 computations (20.8% saved)

regimes525.0ms (11.8%)

Accuracy

Total 0.6b remaining (89.4%)

Threshold costs 0.6b (89.4%)

Counts

55 → 1

Compiler

Compiled 6919 to 5882 computations (15% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	12	13

Stop Event

1×

saturated

end134.0ms (3%)

Compiler: Compiled 199 to 168 computations (15.6% saved)

Details

analyze108.0ms (2.4%)

sample1.6s (36.7%)

simplify39.0ms (0.9%)

prune4.0ms (0.1%)

localize23.0ms (0.5%)

series254.0ms (5.7%)

rewrite42.0ms (0.9%)

simplify35.0ms (0.8%)

prune74.0ms (1.7%)

localize30.0ms (0.7%)

series245.0ms (5.5%)

rewrite43.0ms (1%)

simplify25.0ms (0.6%)

prune109.0ms (2.5%)

localize25.0ms (0.6%)

series495.0ms (11.1%)

rewrite41.0ms (0.9%)

simplify41.0ms (0.9%)

prune83.0ms (1.9%)

localize25.0ms (0.6%)

series240.0ms (5.4%)

rewrite38.0ms (0.8%)

simplify39.0ms (0.9%)

prune93.0ms (2.1%)

regimes525.0ms (11.8%)

simplify2.0ms (0%)

end134.0ms (3%)

Profiling