Details

analyze100.0ms (1.6%)

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)

sample1.4s (23.4%)

Results

1.4s

8256×

body

128

valid

Compiler

Compiled 54 to 42 computations (22.2% saved)

preprocess117.0ms (1.9%)

Algorithm

2×	egg-herbie

Rules

870×	`fma-neg_binary32`
458×	`fma-def_binary32`
424×	`distribute-rgt-in_binary32`
319×	`unsub-neg_binary32`
236×	`distribute-lft-in_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	38	22
2	71	22
3	124	22
4	168	22
5	229	22
6	300	22
7	411	22
8	688	22
9	961	22
10	1098	22
11	1295	22
12	1509	22
13	1759	22
14	1826	22
15	1856	22
16	1935	22
17	2367	22
18	3640	22
19	3914	22
20	4066	22
21	4096	22
22	4116	22
23	4116	22
24	4525	22
25	4742	22
26	4782	22
27	4806	22
28	4822	22
29	4822	22
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify17.0ms (0.3%)

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

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.2b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 37 to 29 computations (21.6% saved)

localize17.0ms (0.3%)

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))

series236.0ms (3.9%)

Counts

2 → 36

Calls

9 calls:

93.0ms	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))	s	0
69.0ms	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))	s	inf
66.0ms	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))	s	-inf
2.0ms	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))	u	0
1.0ms	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))	u	inf

rewrite39.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

641×	`pow1_binary32`
592×	`add-log-exp_binary32`
591×	`expm1-log1p-u_binary32`
590×	`log1p-expm1-u_binary32`
80×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	162	15
2	1938	15
0	8	17

Stop Event

1×	saturated
1×	node limit

Counts

2 → 31

simplify37.0ms (0.6%)

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

67 → 80

prune53.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	7	81

Error

0.1b

Counts

81 → 7

Alt Table

Status	Error	Program
▶	0.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))
	11.4b	(.f32 (log.f32 (+.f32 (.f32 u -4) 1)) (neg.f32 s))
	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
	2.4b	(.f32 (fma.f32 u (-.f32 -4 (.f32 u 8)) (fma.f32 (pow.f32 u 4) -64 (*.f32 (pow.f32 u 3) -64/3))) (neg.f32 s))
	2.4b	(.f32 (neg.f32 (+.f32 (.f32 64 (pow.f32 u 4)) (+.f32 (.f32 64/3 (pow.f32 u 3)) (+.f32 (.f32 8 (pow.f32 u 2)) (*.f32 4 u))))) (neg.f32 s))
	2.3b	(+.f32 (.f32 s (fma.f32 4 u (.f32 64 (pow.f32 u 4)))) (.f32 s (.f32 (.f32 u u) (+.f32 8 (.f32 u 64/3)))))
	2.4b	(+.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)))))

Compiler

Compiled 1423 to 1019 computations (28.4% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (*.f32 u -4))
✓	0.1b	(cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 3))
✓	0.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))
✓	0.6b	(pow.f32 (log1p.f32 (*.f32 u -4)) 3)

series238.0ms (3.9%)

Counts

3 → 48

Calls

12 calls:

87.0ms	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))	s	0
67.0ms	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))	s	inf
65.0ms	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))	s	-inf
6.0ms	(pow.f32 (log1p.f32 (*.f32 u -4)) 3)	u	-inf
5.0ms	(pow.f32 (log1p.f32 (*.f32 u -4)) 3)	u	inf

rewrite42.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

758×	`expm1-log1p-u_binary32`
757×	`log1p-expm1-u_binary32`
101×	`add-sqr-sqrt_binary32`
96×	`add-log-exp_binary32`
95×	`add-exp-log_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	231	24
2	2442	24
0	11	36

Stop Event

1×	saturated
1×	node limit

Counts

3 → 59

simplify53.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

441×	`fma-def_binary32`
434×	`times-frac_binary32`
339×	`associate-+r+_binary32`
272×	`sub-neg_binary32`
252×	`+-commutative_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	1975
1	999	1880
2	3830	1866

Stop Event

1×	node limit

Counts

107 → 130

prune135.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	167	8	175

Error

0.1b

Counts

175 → 8

Alt Table

Status	Error	Program
	2.4b	(.f32 (fma.f32 -64 (pow.f32 u 4) (fma.f32 (pow.f32 u 3) -64/3 (fma.f32 u -4 (.f32 (*.f32 u u) -8)))) (neg.f32 s))
✓	0.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))
	11.4b	(.f32 (log.f32 (+.f32 (.f32 u -4) 1)) (neg.f32 s))
▶	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
	1.5b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2) 1/3)) (neg.f32 s))
	2.4b	(.f32 (fma.f32 u (-.f32 -4 (.f32 u 8)) (fma.f32 (pow.f32 u 4) -64 (*.f32 (pow.f32 u 3) -64/3))) (neg.f32 s))
	2.3b	(+.f32 (.f32 s (fma.f32 4 u (.f32 64 (pow.f32 u 4)))) (.f32 s (.f32 (.f32 u u) (+.f32 8 (.f32 u 64/3)))))
	2.4b	(+.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)))))

Compiler

Compiled 4333 to 3246 computations (25.1% saved)

localize26.0ms (0.4%)

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)

series256.0ms (4.2%)

Counts

3 → 40

Calls

12 calls:

86.0ms	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))	s	0
67.0ms	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))	s	-inf
66.0ms	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))	s	inf
7.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)	u	-inf
7.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)	u	inf

rewrite42.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

760×	`expm1-log1p-u_binary32`
759×	`log1p-expm1-u_binary32`
101×	`add-sqr-sqrt_binary32`
96×	`add-log-exp_binary32`
95×	`add-exp-log_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	231	23
2	2449	23
0	11	35

Stop Event

1×	saturated
1×	node limit

Counts

3 → 59

simplify43.0ms (0.7%)

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

prune110.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	152	10	162

Error

0.1b

Counts

162 → 10

Alt Table

Status	Error	Program
▶	0.9b	(.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2) (cbrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2))) (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) (neg.f32 s))
✓	0.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))
	3.0b	(fma.f32 8 (.f32 u (.f32 u s)) (.f32 s (+.f32 (.f32 u 4) (*.f32 64/3 (pow.f32 u 3)))))
	2.4b	(.f32 (fma.f32 u (-.f32 -4 (.f32 u 8)) (fma.f32 (pow.f32 u 4) -64 (*.f32 (pow.f32 u 3) -64/3))) (neg.f32 s))
	2.4b	(.f32 (fma.f32 -64 (pow.f32 u 4) (fma.f32 (pow.f32 u 3) -64/3 (fma.f32 u -4 (.f32 (*.f32 u u) -8)))) (neg.f32 s))
	11.4b	(.f32 (log.f32 (+.f32 (.f32 u -4) 1)) (neg.f32 s))
✓	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
	1.5b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2) 1/3)) (neg.f32 s))
	2.3b	(+.f32 (.f32 s (fma.f32 4 u (.f32 64 (pow.f32 u 4)))) (.f32 s (.f32 (.f32 u u) (+.f32 8 (.f32 u 64/3)))))
	2.4b	(+.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)))))

Compiler

Compiled 3891 to 3033 computations (22.1% saved)

localize41.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2) (cbrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2))) (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) (neg.f32 s))
✓	0.3b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2) (cbrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)))
✓	0.3b	(.f32 (.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2) (cbrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2))) (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))))
✓	0.5b	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)

series1.2s (20.1%)

Counts

4 → 56

Calls

15 calls:

470.0ms	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2) (cbrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)))	u	inf
454.0ms	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2) (cbrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)))	u	-inf
103.0ms	(.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2) (cbrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2))) (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) (neg.f32 s))	s	0
85.0ms	(.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2) (cbrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2))) (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) (neg.f32 s))	s	inf
73.0ms	(.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2) (cbrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2))) (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) (neg.f32 s))	s	-inf

rewrite56.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

582×	`log-prod_binary32`
203×	`expm1-udef_binary32`
203×	`log1p-udef_binary32`
176×	`log-pow_binary32`
143×	`prod-diff_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	118
1	302	42
2	3487	42
0	15	118

Stop Event

1×	saturated
1×	node limit

Counts

4 → 80

simplify248.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

621×	`*-commutative_binary32`
356×	`+-commutative_binary32`
346×	`fma-def_binary32`
324×	`associate-+r+_binary32`
240×	`associate-r_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1476	22602
1	4979	22566

Stop Event

1×	node limit

Counts

136 → 168

prune786.0ms (13%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	204	3	207
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	207	10	217

Error

0.1b

Counts

217 → 10

Alt Table

Status	Error	Program
	1.5b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2) 1/3)) (neg.f32 s))
	0.8b	(.f32 (.f32 (.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 4)) (cbrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2))) (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) (neg.f32 s))
	3.0b	(fma.f32 8 (.f32 u (.f32 u s)) (.f32 s (+.f32 (.f32 u 4) (*.f32 64/3 (pow.f32 u 3)))))
	2.4b	(.f32 (fma.f32 u (-.f32 -4 (.f32 u 8)) (fma.f32 (pow.f32 u 4) -64 (*.f32 (pow.f32 u 3) -64/3))) (neg.f32 s))
	11.4b	(*.f32 (log.f32 (fma.f32 u -4 1)) (neg.f32 s))
	2.4b	(.f32 (fma.f32 -64 (pow.f32 u 4) (fma.f32 (pow.f32 u 3) -64/3 (fma.f32 u -4 (.f32 (*.f32 u u) -8)))) (neg.f32 s))
✓	0.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))
✓	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
	2.4b	(fma.f32 8 (.f32 (.f32 u u) s) (fma.f32 64/3 (.f32 (pow.f32 u 3) s) (fma.f32 64 (.f32 (pow.f32 u 4) s) (.f32 4 (.f32 u s)))))
	2.3b	(+.f32 (.f32 s (fma.f32 4 u (.f32 64 (pow.f32 u 4)))) (.f32 s (.f32 (.f32 u u) (+.f32 8 (.f32 u 64/3)))))

Compiler

Compiled 29352 to 24665 computations (16% saved)

regimes544.0ms (9%)

Accuracy

Total 0.1b remaining (70.8%)

Threshold costs 0.1b (70.8%)

Counts

81 → 1

Compiler

Compiled 9305 to 7338 computations (21.1% saved)

simplify4.0ms (0.1%)

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	11	16
1	19	16
2	27	16
3	33	16
4	36	16
5	37	16

Stop Event

1×

saturated

end144.0ms (2.4%)

Stop Event

1×

fuel

Compiler

Compiled 223 to 173 computations (22.4% 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

analyze100.0ms (1.6%)

sample1.4s (23.4%)

preprocess117.0ms (1.9%)

simplify17.0ms (0.3%)

prune5.0ms (0.1%)

localize17.0ms (0.3%)

series236.0ms (3.9%)

rewrite39.0ms (0.6%)

simplify37.0ms (0.6%)

prune53.0ms (0.9%)

localize25.0ms (0.4%)

series238.0ms (3.9%)

rewrite42.0ms (0.7%)

simplify53.0ms (0.9%)

prune135.0ms (2.2%)

localize26.0ms (0.4%)

series256.0ms (4.2%)

rewrite42.0ms (0.7%)

simplify43.0ms (0.7%)

prune110.0ms (1.8%)

localize41.0ms (0.7%)

series1.2s (20.1%)

rewrite56.0ms (0.9%)

simplify248.0ms (4.1%)

prune786.0ms (13%)

regimes544.0ms (9%)

simplify4.0ms (0.1%)

end144.0ms (2.4%)

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