Details

analyze651.0ms (7.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	93.6%	6.4%	7
3.1%	84.2%	12.7%	8
12.5%	67.1%	20.5%	9
16%	63.5%	20.5%	10
17.9%	57.7%	24.4%	11
22.6%	48.7%	28.7%	12
28.7%	37.8%	33.6%	13
30.4%	35.9%	33.7%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.3s (14.8%)

Symmetry

(sort V l)

Results

897.0ms	8256×	body	128	valid
398.0ms	3859×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-/r*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	15	12
3	15	12

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

20.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	20.0b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.7b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	4.4b	(/.f64 A (*.f64 V l))
✓	18.4b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series108.0ms (1.2%)

Counts

3 → 12

Calls

3 calls:

59.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
34.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
15.0ms	(/.f64 A (*.f64 V l))

rewrite60.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

914×	`log1p-expm1-u_binary64`
914×	`expm1-log1p-u_binary64`
94×	`egg-rr`
93×	`add-sqr-sqrt_binary64`
86×	`add-log-exp_binary64`

Counts

3 → 94

Calls

3 calls:

58.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
58.0ms	(/.f64 A (*.f64 V l))
58.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	184	28
2	2372	28
3	5709	28
0	0	0
1	0	0

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-/r*_binary64`

Counts

106 → 95

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	144
1	13	144
2	15	144
3	15	144

prune72.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	84	11	95
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	12	96

Error

2.8b

Counts

96 → 12

Alt Table

Status	Error	Program
	20.8b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
	38.0b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
✓	20.0b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
▶	20.2b	(.f64 c0 (pow.f64 (pow.f64 (/.f64 A (.f64 V l)) 1/4) 2))
	38.1b	(pow.f64 (sqrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)) 2)
	37.9b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	20.6b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)) 3)
	39.1b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	41.2b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (sqrt.f64 A) V) (/.f64 (sqrt.f64 A) l))))
	20.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 (.f64 V l)) 2)) (/.f64 A (cbrt.f64 (.f64 V l))))))
	23.3b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	36.9b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (neg.f64 (.f64 V l)))))

Compiler

Compiled 1539 to 667 computations (56.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (/.f64 A (*.f64 V l)) 1/4) 2)
✓	0.7b	(.f64 c0 (pow.f64 (pow.f64 (/.f64 A (.f64 V l)) 1/4) 2))
	4.4b	(/.f64 A (*.f64 V l))
✓	20.1b	(pow.f64 (/.f64 A (*.f64 V l)) 1/4)

series1.5s (16.9%)

Counts

3 → 84

Calls

3 calls:

746.0ms	(pow.f64 (/.f64 A (*.f64 V l)) 1/4)
714.0ms	(pow.f64 (pow.f64 (/.f64 A (*.f64 V l)) 1/4) 2)
60.0ms	(.f64 c0 (pow.f64 (pow.f64 (/.f64 A (.f64 V l)) 1/4) 2))

rewrite58.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

596×	`log-prod_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`
192×	`log-pow_binary64`
118×	`add-sqr-sqrt_binary64`

Counts

3 → 73

Calls

3 calls:

56.0ms	(pow.f64 (pow.f64 (/.f64 A (*.f64 V l)) 1/4) 2)
56.0ms	(.f64 c0 (pow.f64 (pow.f64 (/.f64 A (.f64 V l)) 1/4) 2))
56.0ms	(pow.f64 (/.f64 A (*.f64 V l)) 1/4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	256	31
2	2875	31
3	4881	31
0	0	0
1	0	0

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

675×	`fma-neg_binary64`
601×	`exp-sum_binary64`
371×	`exp-diff_binary64`
312×	`fma-def_binary64`
229×	`associate-+l+_binary64`

Counts

157 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1548
1	179	1404
2	336	1296
3	1138	828
4	3677	828
5	5035	828

prune104.0ms (1.2%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	133	5	138
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	134	16	150

Error

1.3b

Counts

150 → 16

Alt Table

Status	Error	Program
	28.7b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (*.f64 -1 (/.f64 A l))) (log.f64 (/.f64 -1 V))))) 2))
	41.2b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (sqrt.f64 A) V) (/.f64 (sqrt.f64 A) l))))
	20.8b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
	38.0b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
✓	20.0b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	20.2b	(.f64 c0 (pow.f64 (pow.f64 (/.f64 A (.f64 V l)) 1/4) 2))
	20.9b	(.f64 c0 (pow.f64 (pow.f64 (.f64 (/.f64 1 l) (/.f64 A V)) 1/4) 2))
	23.3b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	55.6b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	38.1b	(pow.f64 (sqrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)) 2)
	37.9b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
▶	20.6b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)) 3)
	39.1b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	53.3b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 -1 l)) (log.f64 (*.f64 -1 (/.f64 A V)))))) 2))
	50.9b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (/.f64 A l)) (log.f64 V)))) 2))
	36.9b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (neg.f64 (.f64 V l)))))

Compiler

Compiled 2630 to 1320 computations (49.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)
	4.4b	(/.f64 A (*.f64 V l))
✓	7.0b	(cbrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0))
	18.4b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series1.2s (13.3%)

Counts

2 → 36

Calls

2 calls:

1.1s	(cbrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0))
65.0ms	(.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)

rewrite56.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

553×	`log-prod_binary64`
261×	`pow2_binary64`
185×	`pow1/3_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`

Counts

2 → 46

Calls

2 calls:

54.0ms	(.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)
54.0ms	(cbrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	202	26
2	2567	26
3	5043	26
0	0	0
1	0	0

simplify81.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

685×	`unswap-sqr_binary64`
561×	`div-sub_binary64`
437×	`fma-neg_binary64`
388×	`associate-l_binary64`
334×	`associate-r_binary64`

Counts

82 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	824
1	124	760
2	227	760
3	641	568
4	1731	568
5	4050	568
6	4545	568
7	5099	568

prune92.0ms (1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	129	4	133
Fresh	2	11	13
Picked	1	0	1
Done	1	1	2
Total	133	16	149

Error

1.2b

Counts

149 → 16

Alt Table

Status	Error	Program
	20.8b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
	38.0b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
▶	20.7b	(pow.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) (cbrt.f64 c0)) 3)
✓	20.0b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
	20.9b	(.f64 c0 (pow.f64 (pow.f64 (.f64 (/.f64 1 l) (/.f64 A V)) 1/4) 2))
	23.3b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	55.6b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	38.1b	(pow.f64 (sqrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)) 2)
	37.9b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	39.1b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	53.3b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 -1 l)) (log.f64 (*.f64 -1 (/.f64 A V)))))) 2))
	28.7b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (*.f64 -1 (/.f64 A l))) (log.f64 (/.f64 -1 V))))) 2))
	23.9b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)) c0)) 3)
	39.3b	(pow.f64 (cbrt.f64 (/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))) 3)
	57.6b	(pow.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 (/.f64 A l)) (log.f64 V)))) (pow.f64 c0 1/3)) 3)
	36.9b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (neg.f64 (.f64 V l)))))

Compiler

Compiled 2609 to 1338 computations (48.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(pow.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) (cbrt.f64 c0)) 3)
✓	2.0b	(cbrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))
	4.4b	(/.f64 A (*.f64 V l))
	18.4b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series1.7s (19.1%)

Counts

2 → 60

Calls

2 calls:

1.2s	(pow.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) (cbrt.f64 c0)) 3)
481.0ms	(cbrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))

rewrite67.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

665×	`log-prod_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
211×	`log-pow_binary64`
127×	`add-sqr-sqrt_binary64`

Counts

2 → 62

Calls

2 calls:

65.0ms	(pow.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) (cbrt.f64 c0)) 3)
65.0ms	(cbrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	28
1	267	22
2	3158	22
3	5360	22
0	0	0
1	0	0

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

582×	`unswap-sqr_binary64`
414×	`fma-neg_binary64`
329×	`prod-exp_binary64`
270×	`associate-l_binary64`
267×	`unsub-neg_binary64`

Counts

122 → 75

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	57	1296
1	130	1176
2	204	1176
3	604	816
4	2169	708
5	4717	672
6	5216	672

prune106.0ms (1.2%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	146	6	152
Fresh	3	11	14
Picked	0	1	1
Done	0	1	1
Total	149	19	168

Error

1.2b

Counts

168 → 19

Alt Table

Status	Error	Program
	20.8b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
	38.0b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	39.3b	(pow.f64 (cbrt.f64 (/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))) 3)
	24.0b	(pow.f64 (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l))) (cbrt.f64 c0)) 3)
✓	20.7b	(pow.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) (cbrt.f64 c0)) 3)
✓	20.0b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
	42.2b	(.f64 (.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) (sqrt.f64 c0)) (sqrt.f64 c0))
	20.9b	(.f64 c0 (pow.f64 (pow.f64 (.f64 (/.f64 1 l) (/.f64 A V)) 1/4) 2))
	38.5b	(pow.f64 (.f64 (/.f64 (cbrt.f64 (sqrt.f64 A)) (cbrt.f64 (sqrt.f64 (.f64 V l)))) (cbrt.f64 c0)) 3)
	23.3b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	51.0b	(.f64 (pow.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 (/.f64 A l)) (log.f64 V)))) 3) c0)
	36.9b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (neg.f64 (.f64 V l)))))
	55.6b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	37.9b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	39.1b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	53.3b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 -1 l)) (log.f64 (*.f64 -1 (/.f64 A V)))))) 2))
	28.7b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (*.f64 -1 (/.f64 A l))) (log.f64 (/.f64 -1 V))))) 2))
	37.3b	(pow.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (neg.f64 (.f64 V l))))) (cbrt.f64 c0)) 3)
	20.2b	(.f64 (pow.f64 (/.f64 A (.f64 V l)) 1/4) (.f64 (pow.f64 (/.f64 A (.f64 V l)) 1/4) c0))

Compiler

Compiled 2892 to 1270 computations (56.1% saved)

regimes1.2s (13.6%)

Accuracy

Total 3.0b remaining (56.7%)

Threshold costs 0b (0%)

Counts

50 → 5

Compiler

Compiled 8358 to 5665 computations (32.2% saved)

bsearch2.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	111
1	56	111
2	66	111
3	72	111
4	74	111
5	73	111

end351.0ms (3.9%)

Compiler: Compiled 615 to 380 computations (38.2% saved)

Details

analyze651.0ms (7.2%)

sample1.3s (14.8%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series108.0ms (1.2%)

rewrite60.0ms (0.7%)

simplify9.0ms (0.1%)

prune72.0ms (0.8%)

localize9.0ms (0.1%)

series1.5s (16.9%)

rewrite58.0ms (0.6%)

simplify69.0ms (0.8%)

prune104.0ms (1.2%)

localize8.0ms (0.1%)

series1.2s (13.3%)

rewrite56.0ms (0.6%)

simplify81.0ms (0.9%)

prune92.0ms (1%)

localize10.0ms (0.1%)

series1.7s (19.1%)

rewrite67.0ms (0.7%)

simplify78.0ms (0.9%)

prune106.0ms (1.2%)

regimes1.2s (13.6%)

bsearch2.0ms (0%)

simplify5.0ms (0.1%)

end351.0ms (3.9%)

Profiling