Details

analyze1.3s (15.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
15.6%	84.3%	0.1%	7
18.7%	81.1%	0.1%	8
25.7%	73.3%	0.9%	9
28.5%	60.8%	10.7%	10
30.2%	58.7%	11.1%	11
32.7%	52.2%	15.2%	12
33.5%	39.2%	27.4%	13
34.3%	37.8%	27.9%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.7s (20.5%)

Results

1.2s	8256×	body	128	valid
522.0ms	3750×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

preprocess40.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

1844×	`pow-sqr_binary64`
1096×	`sqr-pow_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	88
1	44	88
2	62	88
3	91	88
4	145	88
5	239	88
6	419	88
7	744	88
8	1374	88
9	2536	88
10	2536	88
11	4804	88
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify33.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1715×	`pow-sqr_binary64`
988×	`sqr-pow_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	19	22
2	24	22
3	32	22
4	47	22
5	73	22
6	123	22
7	213	22
8	388	22
9	710	22
10	1340	22
11	2516	22
12	4826	22
13	4826	22

Stop Event

1×	node limit

Counts

1 → 1

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

1.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.9b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

Compiler

Compiled 54 to 36 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (*.f64 10 k))
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	0.0b	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
✓	1.9b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

series444.0ms (5.3%)

Counts

4 → 96

Calls

24 calls:

86.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))	a	0
63.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))	a	-inf
63.0ms	(*.f64 a (pow.f64 k m))	a	0
62.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))	a	inf
50.0ms	(*.f64 a (pow.f64 k m))	a	inf

rewrite43.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

333×	`pow2_binary64`
321×	`log-prod_binary64`
241×	`log-pow_binary64`
232×	`pow1/3_binary64`
231×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	49
1	253	49
2	2706	49

Stop Event

1×	node limit

Counts

4 → 79

simplify93.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

794×	`pow-sqr_binary64`
592×	`sqr-pow_binary64`
290×	`fma-def_binary64`
234×	`log-pow_binary64`
225×	`cube-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	1833
1	179	1833
2	215	1749
3	271	1749
4	369	1749
5	517	1749
6	752	1749
7	1180	1749
8	1942	1749
9	3522	1749

Stop Event

1×	node limit

Counts

175 → 136

prune115.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	4	137

Error

1.4b

Counts

137 → 4

Alt Table

Status	Error	Program
▶	9.5b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 10 k 1))
	23.1b	(pow.f64 (/.f64 (sqrt.f64 (.f64 a (pow.f64 k m))) (hypot.f64 (sqrt.f64 (+.f64 1 (.f64 k 10))) k)) 2)
	30.3b	(/.f64 (fma.f64 a (.f64 (log.f64 k) m) a) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
	29.9b	(-.f64 (.f64 a (exp.f64 (.f64 (log.f64 k) m))) (.f64 10 (.f64 k (.f64 a (exp.f64 (.f64 (log.f64 k) m))))))

Compiler

Compiled 3404 to 1852 computations (45.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.1b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 10 k 1))
✓	0.1b	(fma.f64 10 k 1)

series200.0ms (2.4%)

Counts

2 → 48

Calls

12 calls:

68.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 10 k 1))	a	0
58.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 10 k 1))	a	-inf
53.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 10 k 1))	a	inf
5.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 10 k 1))	m	-inf
5.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 10 k 1))	m	inf

rewrite34.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

729×	`log1p-expm1-u_binary64`
729×	`expm1-log1p-u_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`
97×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	186	19
2	1893	19

Stop Event

1×	node limit

Counts

2 → 33

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

795×	`pow-sqr_binary64`
583×	`sqr-pow_binary64`
284×	`fma-def_binary64`
233×	`log-pow_binary64`
225×	`cube-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	1138
1	160	1138
2	193	1078
3	244	1078
4	337	1078
5	480	1078
6	710	1078
7	1133	1078
8	1890	1078
9	3465	1078

Stop Event

1×	node limit

Counts

81 → 72

prune92.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	99	5	104

Error

1.4b

Counts

104 → 5

Alt Table

Status	Error	Program
	23.1b	(pow.f64 (/.f64 (sqrt.f64 (.f64 a (pow.f64 k m))) (hypot.f64 (sqrt.f64 (+.f64 1 (.f64 k 10))) k)) 2)
	30.3b	(/.f64 (fma.f64 a (.f64 (log.f64 k) m) a) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
▶	9.5b	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (cbrt.f64 (fma.f64 10 k 1)) 3))
	16.3b	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 10 k 1))))
	29.9b	(-.f64 (.f64 a (exp.f64 (.f64 (log.f64 k) m))) (.f64 10 (.f64 k (.f64 a (exp.f64 (.f64 (log.f64 k) m))))))

Compiler

Compiled 2273 to 1319 computations (42% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (cbrt.f64 (fma.f64 10 k 1)) 3))
	0.1b	(fma.f64 10 k 1)
✓	0.2b	(cbrt.f64 (fma.f64 10 k 1))
✓	0.4b	(pow.f64 (cbrt.f64 (fma.f64 10 k 1)) 3)

series212.0ms (2.5%)

Counts

3 → 44

Calls

15 calls:

72.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (cbrt.f64 (fma.f64 10 k 1)) 3))	a	0
55.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (cbrt.f64 (fma.f64 10 k 1)) 3))	a	-inf
51.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (cbrt.f64 (fma.f64 10 k 1)) 3))	a	inf
6.0ms	(pow.f64 (cbrt.f64 (fma.f64 10 k 1)) 3)	k	inf
5.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (cbrt.f64 (fma.f64 10 k 1)) 3))	m	-inf

rewrite38.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

877×	`log1p-expm1-u_binary64`
877×	`expm1-log1p-u_binary64`
115×	`add-sqr-sqrt_binary64`
108×	`add-cbrt-cube_binary64`
107×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	245	26
2	2331	26

Stop Event

1×	node limit

Counts

3 → 52

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

796×	`pow-sqr_binary64`
583×	`sqr-pow_binary64`
286×	`fma-def_binary64`
233×	`log-pow_binary64`
225×	`cube-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	1143
1	173	1143
2	206	1083
3	257	1083
4	350	1083
5	493	1083
6	723	1083
7	1146	1083
8	1903	1083
9	3478	1083

Stop Event

1×	node limit

Counts

96 → 95

prune114.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	114	6	120

Error

1.4b

Counts

120 → 6

Alt Table

Status	Error	Program
	23.1b	(pow.f64 (/.f64 (sqrt.f64 (.f64 a (pow.f64 k m))) (hypot.f64 (sqrt.f64 (+.f64 1 (.f64 k 10))) k)) 2)
	30.3b	(/.f64 (fma.f64 a (.f64 (log.f64 k) m) a) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
✓	9.5b	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (cbrt.f64 (fma.f64 10 k 1)) 3))
▶	16.3b	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 10 k 1))))
	29.9b	(-.f64 (.f64 a (exp.f64 (.f64 (log.f64 k) m))) (.f64 10 (.f64 k (.f64 a (exp.f64 (.f64 (log.f64 k) m))))))
	16.3b	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (fma.f64 10 k 1)))) 3))

Compiler

Compiled 2614 to 1588 computations (39.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (fma.f64 10 k 1))
✓	0.0b	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 10 k 1))))
	0.1b	(fma.f64 10 k 1)
✓	2.1b	(expm1.f64 (log1p.f64 (fma.f64 10 k 1)))

series400.0ms (4.8%)

Counts

3 → 60

Calls

15 calls:

200.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 10 k 1))))	k	inf
69.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 10 k 1))))	a	0
57.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 10 k 1))))	a	inf
53.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 10 k 1))))	a	-inf
4.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 10 k 1))))	m	-inf

rewrite36.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

794×	`expm1-log1p-u_binary64`
793×	`log1p-expm1-u_binary64`
185×	`log1p-udef_binary64`
105×	`add-sqr-sqrt_binary64`
96×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	206	26
2	2063	26

Stop Event

1×	node limit

Counts

3 → 47

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

795×	`pow-sqr_binary64`
583×	`sqr-pow_binary64`
291×	`fma-def_binary64`
233×	`log-pow_binary64`
225×	`cube-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	1383
1	204	1383
2	237	1323
3	288	1323
4	383	1323
5	530	1323
6	760	1323
7	1183	1323
8	1948	1323
9	3523	1323

Stop Event

1×	node limit

Counts

107 → 107

prune102.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	128	5	133

Error

1.4b

Counts

133 → 5

Alt Table

Status	Error	Program
	23.1b	(pow.f64 (/.f64 (sqrt.f64 (.f64 a (pow.f64 k m))) (hypot.f64 (sqrt.f64 (+.f64 1 (.f64 k 10))) k)) 2)
	17.0b	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (pow.f64 (cbrt.f64 (log1p.f64 (fma.f64 10 k 1))) 3)))
	30.3b	(/.f64 (fma.f64 a (.f64 (log.f64 k) m) a) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
✓	9.5b	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (cbrt.f64 (fma.f64 10 k 1)) 3))
	29.9b	(-.f64 (.f64 a (exp.f64 (.f64 (log.f64 k) m))) (.f64 10 (.f64 k (.f64 a (exp.f64 (.f64 (log.f64 k) m))))))

Compiler

Compiled 2749 to 1651 computations (39.9% saved)

regimes449.0ms (5.4%)

Accuracy

Total 0.9b remaining (46.6%)

Threshold costs 0.9b (46.6%)

Counts

117 → 1

Compiler

Compiled 7984 to 5862 computations (26.6% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	28
1	18	28

Stop Event

1×

saturated

end2.7s (31.8%)

Stop Event

1×

fuel

Compiler

Compiled 140 to 97 computations (30.7% saved)

Details

analyze1.3s (15.5%)

sample1.7s (20.5%)

preprocess40.0ms (0.5%)

simplify33.0ms (0.4%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series444.0ms (5.3%)

rewrite43.0ms (0.5%)

simplify93.0ms (1.1%)

prune115.0ms (1.4%)

localize6.0ms (0.1%)

series200.0ms (2.4%)

rewrite34.0ms (0.4%)

simplify62.0ms (0.7%)

prune92.0ms (1.1%)

localize9.0ms (0.1%)

series212.0ms (2.5%)

rewrite38.0ms (0.5%)

simplify62.0ms (0.7%)

prune114.0ms (1.4%)

localize9.0ms (0.1%)

series400.0ms (4.8%)

rewrite36.0ms (0.4%)

simplify71.0ms (0.8%)

prune102.0ms (1.2%)

regimes449.0ms (5.4%)

simplify1.0ms (0%)

end2.7s (31.8%)

Profiling