Details

analyze103.0ms (2.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	1.5%	98.5%	0
0%	1.5%	98.5%	1
0%	1.5%	98.5%	2
0.8%	0.8%	98.5%	3
0.8%	0.8%	98.5%	4
1.2%	0.4%	98.5%	5
1.2%	0.4%	98.5%	6
1.4%	0.2%	98.5%	7
1.4%	0.2%	98.5%	8
1.4%	0.1%	98.5%	9
1.4%	0.1%	98.5%	10
1.5%	0%	98.5%	11
1.5%	0%	98.5%	12
1.5%	0%	98.5%	13
1.5%	0%	98.5%	14

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample1.6s (39.7%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 66 to 52 computations (21.2% saved)

simplify16.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

175×	`fma-neg_binary32`
152×	`fma-def_binary32`
46×	`cancel-sign-sub-inv_binary32`
46×	`sub-neg_binary32`
30×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	24	11
2	41	11
3	70	11
4	97	11
5	127	11
6	167	11
7	241	11
8	359	11
9	435	11
10	511	11
11	603	11
12	741	11
13	853	11
14	866	11

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	11.8b	(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))
▶	0.2b	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))

Compiler

Compiled 61 to 49 computations (19.7% saved)

localize19.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (*.f32 u -4))
✓	0.2b	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))

series233.0ms (5.7%)

Counts

2 → 36

Calls

2 calls:

230.0ms	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))
2.0ms	(log1p.f32 (*.f32 u -4))

rewrite34.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

591×	`expm1-log1p-u_binary32`
590×	`log1p-expm1-u_binary32`
334×	`log-prod_binary32`
143×	`prod-diff_binary32`
125×	`expm1-udef_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	162	15
2	1949	15

Stop Event

1×	node limit

Counts

2 → 42

Calls

2 calls:

33.0ms	(log1p.f32 (*.f32 u -4))
33.0ms	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))

simplify35.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-neg_binary32`
526×	`fma-def_binary32`
364×	`sub-neg_binary32`
212×	`associate-+l+_binary32`
186×	`unsub-neg_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	726
1	336	675
2	1065	632
3	3590	624

Stop Event

1×	node limit

Counts

78 → 91

prune57.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	84	7	91
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Error

0.1b

Counts

93 → 9

Alt Table

Status	Error	Program
	11.8b	(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))
	2.6b	(+.f32 (.f32 8 (.f32 s (pow.f32 u 2))) (+.f32 (.f32 64/3 (.f32 s (pow.f32 u 3))) (+.f32 (.f32 64 (.f32 s (pow.f32 u 4))) (.f32 4 (.f32 s u)))))
	3.3b	(fma.f32 4 (.f32 s u) (.f32 s (.f32 (.f32 u u) (+.f32 8 (*.f32 u 64/3)))))
▶	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
	0.7b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2)) (neg.f32 s))
	12.0b	(.f32 (-.f32 (log.f32 (-.f32 1 (.f32 (.f32 u u) 16))) (log.f32 (-.f32 1 (.f32 u -4)))) (neg.f32 s))
	11.8b	(.f32 (-.f32 (log1p.f32 (pow.f32 (.f32 u -4) 3)) (log.f32 (+.f32 1 (-.f32 (.f32 (.f32 u u) 16) (*.f32 u -4))))) (neg.f32 s))
✓	0.2b	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))
	3.3b	(.f32 (fma.f32 u (-.f32 -4 (.f32 u 8)) (*.f32 (pow.f32 u 3) -64/3)) (neg.f32 s))

Compiler

Compiled 1629 to 1173 computations (28% saved)

localize30.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (*.f32 u -4))
✓	0.1b	(cbrt.f32 (log1p.f32 (*.f32 u -4)))
✓	0.2b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
✓	0.7b	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)

series260.0ms (6.3%)

Counts

3 → 40

Calls

3 calls:

228.0ms	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
19.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)
13.0ms	(cbrt.f32 (log1p.f32 (*.f32 u -4)))

rewrite38.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

760×	`expm1-log1p-u_binary32`
759×	`log1p-expm1-u_binary32`
143×	`prod-diff_binary32`
99×	`add-sqr-sqrt_binary32`
93×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	224	23
2	2461	23

Stop Event

1×	node limit

Counts

3 → 59

Calls

3 calls:

37.0ms	(cbrt.f32 (log1p.f32 (*.f32 u -4)))
37.0ms	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
37.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)

simplify40.0ms (1%)

Algorithm

1×	egg-herbie

Rules

310×	`times-frac_binary32`
242×	`cancel-sign-sub-inv_binary32`
217×	`associate-*l/_binary32`
198×	`fma-def_binary32`
194×	`associate-*r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	1869
1	601	1682
2	2015	1645

Stop Event

1×	node limit

Counts

99 → 116

prune129.0ms (3.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	158	11	169

Error

0.1b

Counts

169 → 11

Alt Table

Status	Error	Program
	11.8b	(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))
	2.6b	(+.f32 (.f32 8 (.f32 s (pow.f32 u 2))) (+.f32 (.f32 64/3 (.f32 s (pow.f32 u 3))) (+.f32 (.f32 64 (.f32 s (pow.f32 u 4))) (.f32 4 (.f32 s u)))))
	3.6b	(.f32 (pow.f32 (log.f32 (exp.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) 3) (neg.f32 s))
	3.3b	(.f32 (fma.f32 u (-.f32 -4 (.f32 u 8)) (*.f32 (pow.f32 u 3) -64/3)) (neg.f32 s))
	3.3b	(fma.f32 4 (.f32 s u) (.f32 s (.f32 (.f32 u u) (+.f32 8 (*.f32 u 64/3)))))
	3.2b	(fma.f32 8 (.f32 u (.f32 u s)) (.f32 s (+.f32 (.f32 u 4) (*.f32 64/3 (pow.f32 u 3)))))
✓	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
▶	0.7b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2)) (neg.f32 s))
	12.0b	(.f32 (-.f32 (log.f32 (-.f32 1 (.f32 (.f32 u u) 16))) (log.f32 (-.f32 1 (.f32 u -4)))) (neg.f32 s))
	11.8b	(.f32 (-.f32 (log1p.f32 (pow.f32 (.f32 u -4) 3)) (log.f32 (+.f32 1 (-.f32 (.f32 (.f32 u u) 16) (*.f32 u -4))))) (neg.f32 s))
✓	0.2b	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))

Compiler

Compiled 3995 to 3111 computations (22.1% saved)

localize35.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(cbrt.f32 (log1p.f32 (*.f32 u -4)))
✓	0.2b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2)) (neg.f32 s))
✓	0.4b	(.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2))
✓	0.5b	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)

series248.0ms (6%)

Counts

3 → 44

Calls

3 calls:

227.0ms

(*.f32 (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)) (neg.f32 s))

18.0ms

(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)

3.0ms

(*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2))

rewrite39.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

800×	`expm1-log1p-u_binary32`
799×	`log1p-expm1-u_binary32`
143×	`prod-diff_binary32`
107×	`add-sqr-sqrt_binary32`
100×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	248	26
2	2643	26

Stop Event

1×	node limit

Counts

3 → 47

Calls

3 calls:

38.0ms

(*.f32 (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)) (neg.f32 s))

38.0ms

(*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2))

38.0ms

(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)

simplify39.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

234×	`times-frac_binary32`
229×	`cancel-sign-sub-inv_binary32`
206×	`associate-/r*_binary32`
197×	`fma-def_binary32`
173×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	1616
1	589	1468
2	2065	1416

Stop Event

1×	node limit

Counts

91 → 111

prune173.0ms (4.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	183	4	187
Fresh	4	4	8
Picked	1	0	1
Done	0	2	2
Total	188	10	198

Error

0.0b

Counts

198 → 10

Alt Table

Status	Error	Program
▶	0.4b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2))) (neg.f32 s))
	2.6b	(+.f32 (.f32 8 (.f32 s (pow.f32 u 2))) (+.f32 (.f32 64/3 (.f32 s (pow.f32 u 3))) (+.f32 (.f32 64 (.f32 s (pow.f32 u 4))) (.f32 4 (.f32 s u)))))
	2.5b	(+.f32 (.f32 s (fma.f32 64 (pow.f32 u 4) (.f32 (pow.f32 u 3) 64/3))) (.f32 s (.f32 u (+.f32 (*.f32 8 u) 4))))
	3.2b	(fma.f32 8 (.f32 u (.f32 u s)) (.f32 s (+.f32 (.f32 u 4) (*.f32 64/3 (pow.f32 u 3)))))
✓	0.2b	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))
	0.9b	(.f32 (.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 3) (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2)) (neg.f32 s))
	3.2b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (log.f32 (exp.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) 2)) (neg.f32 s))
✓	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
	12.0b	(.f32 (-.f32 (log.f32 (-.f32 1 (.f32 (.f32 u u) 16))) (log.f32 (-.f32 1 (.f32 u -4)))) (neg.f32 s))
	3.6b	(.f32 (pow.f32 (log.f32 (exp.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) 3) (neg.f32 s))

Compiler

Compiled 6297 to 5066 computations (19.5% saved)

localize35.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(cbrt.f32 (log1p.f32 (*.f32 u -4)))
✓	0.2b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2))) (neg.f32 s))
✓	0.4b	(.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)))
✓	0.5b	(pow.f32 (log1p.f32 (*.f32 u -4)) 2)

series239.0ms (5.8%)

Counts

3 → 48

Calls

3 calls:

232.0ms

(*.f32 (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2))) (neg.f32 s))

5.0ms

(pow.f32 (log1p.f32 (*.f32 u -4)) 2)

3.0ms

(*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)))

rewrite45.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

863×	`expm1-log1p-u_binary32`
862×	`log1p-expm1-u_binary32`
143×	`prod-diff_binary32`
116×	`add-sqr-sqrt_binary32`
112×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	264	24
2	2955	24

Stop Event

1×	node limit

Counts

3 → 52

Calls

3 calls:

44.0ms

(*.f32 (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2))) (neg.f32 s))

44.0ms

(*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)))

44.0ms

(pow.f32 (log1p.f32 (*.f32 u -4)) 2)

simplify36.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

286×	`cancel-sign-sub-inv_binary32`
282×	`fma-def_binary32`
243×	`sub-neg_binary32`
196×	`associate-l_binary32`
173×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	205	1385
1	671	1304
2	2372	1214

Stop Event

1×	node limit

Counts

100 → 124

prune131.0ms (3.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	162	10	172

Error

0.0b

Counts

172 → 10

Alt Table

Status	Error	Program
✓	0.4b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2))) (neg.f32 s))
	2.6b	(+.f32 (.f32 8 (.f32 s (pow.f32 u 2))) (+.f32 (.f32 64/3 (.f32 s (pow.f32 u 3))) (+.f32 (.f32 64 (.f32 s (pow.f32 u 4))) (.f32 4 (.f32 s u)))))
	2.5b	(+.f32 (.f32 s (fma.f32 64 (pow.f32 u 4) (.f32 (pow.f32 u 3) 64/3))) (.f32 s (.f32 u (+.f32 (*.f32 8 u) 4))))
	3.2b	(fma.f32 8 (.f32 u (.f32 u s)) (.f32 s (+.f32 (.f32 u 4) (*.f32 64/3 (pow.f32 u 3)))))
✓	0.2b	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))
	0.9b	(.f32 (.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 3) (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2)) (neg.f32 s))
	3.2b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (log.f32 (exp.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) 2)) (neg.f32 s))
✓	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
	12.0b	(.f32 (-.f32 (log.f32 (-.f32 1 (.f32 (.f32 u u) 16))) (log.f32 (-.f32 1 (.f32 u -4)))) (neg.f32 s))
	3.6b	(.f32 (pow.f32 (log.f32 (exp.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) 3) (neg.f32 s))

Compiler

Compiled 4549 to 3546 computations (22% saved)

regimes338.0ms (8.2%)

Accuracy

Total 0.2b remaining (72.6%)

Threshold costs 0.2b (72.6%)

Counts

52 → 1

Compiler

Compiled 6351 to 5070 computations (20.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary32`
3×	`+-commutative_binary32`
3×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	24	11
3	30	11
4	33	11
5	34	11

Stop Event

1×

saturated

end125.0ms (3%)

Compiler: Compiled 207 to 164 computations (20.8% saved)

Iter	Nodes	Cost
0	10	14
1	24	11
2	41	11
3	70	11
4	97	11
5	127	11
6	167	11
7	241	11
8	359	11
9	435	11
10	511	11
11	603	11
12	741	11
13	853	11
14	866	11

Iter	Nodes	Cost
0	10	14
1	24	11
2	41	11
3	70	11
4	97	11
5	127	11
6	167	11
7	241	11
8	359	11
9	435	11
10	511	11
11	603	11
12	741	11
13	853	11
14	866	11

Details

analyze103.0ms (2.5%)

sample1.6s (39.7%)

simplify16.0ms (0.4%)

prune4.0ms (0.1%)

localize19.0ms (0.5%)

series233.0ms (5.7%)

rewrite34.0ms (0.8%)

simplify35.0ms (0.8%)

prune57.0ms (1.4%)

localize30.0ms (0.7%)

series260.0ms (6.3%)

rewrite38.0ms (0.9%)

simplify40.0ms (1%)

prune129.0ms (3.1%)

localize35.0ms (0.8%)

series248.0ms (6%)

rewrite39.0ms (0.9%)

simplify39.0ms (0.9%)

prune173.0ms (4.2%)

localize35.0ms (0.9%)

series239.0ms (5.8%)

rewrite45.0ms (1.1%)

simplify36.0ms (0.9%)

prune131.0ms (3.2%)

regimes338.0ms (8.2%)

simplify2.0ms (0%)

end125.0ms (3%)

Profiling

Iter	Nodes	Cost
0	10	14
1	24	11
2	41	11
3	70	11
4	97	11
5	127	11
6	167	11
7	241	11
8	359	11
9	435	11
10	511	11
11	603	11
12	741	11
13	853	11
14	866	11