Details

analyze657.0ms (8.3%)

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)

sample1.4s (17.4%)

Symmetry

(sort V l)

Results

932.0ms	8256×	body	128	valid
414.0ms	3797×	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`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 1

prune3.0ms (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

19.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	19.1b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.5b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	4.9b	(/.f64 A (*.f64 V l))
✓	15.3b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series112.0ms (1.4%)

Counts

3 → 12

Calls

3 calls:

62.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
30.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
20.0ms	(/.f64 A (*.f64 V l))

rewrite51.0ms (0.6%)

Algorithm

1×	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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	185	28
2	2473	28

Stop Event

1×	node limit

Counts

3 → 94

Calls

3 calls:

49.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
49.0ms	(/.f64 A (*.f64 V l))
49.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

106 → 95

prune86.0ms (1.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	81	14	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	14	96

Error

3.9b

Counts

96 → 14

Alt Table

Status	Error	Program
	21.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (/.f64 A V) l) 1)))
	40.0b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	26.2b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	55.9b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
	35.4b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	38.8b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 2)
	33.8b	(.f64 c0 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (/.f64 A V) l) 2))) (sqrt.f64 (cbrt.f64 (/.f64 (/.f64 A V) l)))))
	19.1b	(.f64 c0 (sqrt.f64 (neg.f64 (/.f64 A (.f64 l (neg.f64 V))))))
	21.6b	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
	38.4b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0) 3))
	47.9b	(sqrt.f64 (.f64 (/.f64 (/.f64 A V) l) (.f64 c0 c0)))
	40.4b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	29.0b	(*.f64 c0 (cbrt.f64 (pow.f64 (/.f64 (/.f64 A V) l) 3/2)))
▶	18.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))))

Compiler

Compiled 1619 to 742 computations (54.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 A)
✓	1.5b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))))
✓	3.1b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))
✓	15.3b	(sqrt.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l)))

series135.0ms (1.7%)

Counts

4 → 60

Calls

4 calls:

47.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))))
33.0ms	(cbrt.f64 A)
28.0ms	(sqrt.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l)))
27.0ms	(*.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))

rewrite56.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
219×	`log-pow_binary64`
169×	`log-div_binary64`
134×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
1	276	31
2	3670	31

Stop Event

1×	node limit

Counts

4 → 122

Calls

4 calls:

54.0ms	(cbrt.f64 A)
54.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))))
54.0ms	(*.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))
54.0ms	(sqrt.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l)))

simplify81.0ms (1%)

Algorithm

1×	egg-herbie

Rules

724×	`unswap-sqr_binary64`
584×	`associate-l_binary64`
488×	`sqr-pow_binary64`
345×	`associate-r_binary64`
236×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	464
1	31	460
2	45	460
3	72	460
4	149	460
5	439	460
6	1644	460
7	2980	460
8	3151	460
9	3446	460
10	3765	460
11	4206	460
12	4819	460

Stop Event

1×	node limit

Counts

182 → 127

prune128.0ms (1.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	147	6	153
Fresh	4	9	13
Picked	0	1	1
Done	0	0	0
Total	151	16	167

Error

3.8b

Counts

167 → 16

Alt Table

Status	Error	Program
	50.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 (cbrt.f64 A) l)) (/.f64 (cbrt.f64 A) (sqrt.f64 V))))
	40.0b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	21.6b	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
▶	19.7b	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A l) V) 1/4) 2))
	26.2b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	52.0b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A l)) (sqrt.f64 V)))
	55.9b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
	46.4b	(sqrt.f64 (.f64 (/.f64 (/.f64 A l) V) (.f64 c0 c0)))
	19.9b	(.f64 c0 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 A l) V))) (cbrt.f64 (/.f64 (/.f64 A l) V))))
	35.4b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	38.8b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 2)
	27.2b	(*.f64 c0 (cbrt.f64 (pow.f64 (/.f64 (/.f64 A l) V) 3/2)))
	33.8b	(.f64 c0 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (/.f64 A V) l) 2))) (sqrt.f64 (cbrt.f64 (/.f64 (/.f64 A V) l)))))
	38.4b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0) 3))
	40.4b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
✓	18.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))))

Compiler

Compiled 2651 to 1316 computations (50.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (pow.f64 (/.f64 (/.f64 A l) V) 1/4) 2)
✓	1.5b	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A l) V) 1/4) 2))
✓	4.6b	(/.f64 (/.f64 A l) V)
✓	17.8b	(pow.f64 (/.f64 (/.f64 A l) V) 1/4)

series1.3s (15.9%)

Counts

4 → 120

Calls

4 calls:

599.0ms	(pow.f64 (pow.f64 (/.f64 (/.f64 A l) V) 1/4) 2)
598.0ms	(pow.f64 (/.f64 (/.f64 A l) V) 1/4)
46.0ms	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A l) V) 1/4) 2))
17.0ms	(/.f64 (/.f64 A l) V)

rewrite53.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

618×	`log-prod_binary64`
217×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`
198×	`log-pow_binary64`
125×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	262	38
2	3297	38

Stop Event

1×	node limit

Counts

4 → 122

Calls

4 calls:

51.0ms	(pow.f64 (pow.f64 (/.f64 (/.f64 A l) V) 1/4) 2)
51.0ms	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A l) V) 1/4) 2))
51.0ms	(/.f64 (/.f64 A l) V)
51.0ms	(pow.f64 (/.f64 (/.f64 A l) V) 1/4)

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

312×	`fma-def_binary64`
233×	`associate-+l+_binary64`
211×	`associate-+r+_binary64`
210×	`distribute-rgt-in_binary64`
199×	`exp-sum_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1880
1	194	1784
2	458	1652
3	1382	1208

Stop Event

1×	node limit

Counts

242 → 149

prune130.0ms (1.6%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	1	13	14
Picked	0	1	1
Done	0	1	1
Total	148	17	165

Error

2.4b

Counts

165 → 17

Alt Table

Status	Error	Program
	50.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 (cbrt.f64 A) l)) (/.f64 (cbrt.f64 A) (sqrt.f64 V))))
	40.0b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	21.6b	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
✓	19.7b	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A l) V) 1/4) 2))
	26.2b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	52.0b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A l)) (sqrt.f64 V)))
	53.8b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 -1 l)) (log.f64 (*.f64 -1 (/.f64 A V)))))) 2))
	55.9b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
	46.4b	(sqrt.f64 (.f64 (/.f64 (/.f64 A l) V) (.f64 c0 c0)))
▶	19.9b	(.f64 c0 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 A l) V))) (cbrt.f64 (/.f64 (/.f64 A l) V))))
	35.4b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	38.8b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 2)
	22.7b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 (neg.f64 A) l)) (sqrt.f64 (neg.f64 V))))
	40.4b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	38.4b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0) 3))
	27.2b	(*.f64 c0 (cbrt.f64 (pow.f64 (/.f64 (/.f64 A l) V) 3/2)))
✓	18.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))))

Compiler

Compiled 2814 to 1430 computations (49.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.6b	(cbrt.f64 (sqrt.f64 (/.f64 (/.f64 A l) V)))
	4.6b	(/.f64 (/.f64 A l) V)
✓	15.3b	(sqrt.f64 (/.f64 (/.f64 A l) V))
✓	18.1b	(cbrt.f64 (/.f64 (/.f64 A l) V))

series1.1s (13.5%)

Counts

3 → 60

Calls

3 calls:

630.0ms	(cbrt.f64 (/.f64 (/.f64 A l) V))
414.0ms	(cbrt.f64 (sqrt.f64 (/.f64 (/.f64 A l) V)))
24.0ms	(sqrt.f64 (/.f64 (/.f64 A l) V))

rewrite45.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

484×	`log-prod_binary64`
236×	`pow2_binary64`
164×	`pow1/3_binary64`
161×	`expm1-udef_binary64`
161×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	188	28
2	2545	28

Stop Event

1×	node limit

Counts

3 → 103

Calls

3 calls:

44.0ms	(cbrt.f64 (sqrt.f64 (/.f64 (/.f64 A l) V)))
44.0ms	(sqrt.f64 (/.f64 (/.f64 A l) V))
44.0ms	(cbrt.f64 (/.f64 (/.f64 A l) V))

simplify43.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

646×	`fma-def_binary64`
371×	`exp-sum_binary64`
345×	`fma-neg_binary64`
300×	`div-sub_binary64`
230×	`exp-diff_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	73	1176
1	179	1080
2	419	1044
3	1091	696
4	2955	648

Stop Event

1×	node limit

Counts

163 → 121

prune137.0ms (1.7%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	14	14
Picked	0	1	1
Done	0	2	2
Total	223	17	240

Error

2.4b

Counts

240 → 17

Alt Table

Status	Error	Program
	50.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 (cbrt.f64 A) l)) (/.f64 (cbrt.f64 A) (sqrt.f64 V))))
	40.0b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	21.6b	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
✓	19.7b	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A l) V) 1/4) 2))
	26.2b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	52.0b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A l)) (sqrt.f64 V)))
	53.8b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 -1 l)) (log.f64 (*.f64 -1 (/.f64 A V)))))) 2))
	55.9b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
	46.4b	(sqrt.f64 (.f64 (/.f64 (/.f64 A l) V) (.f64 c0 c0)))
✓	19.9b	(.f64 c0 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 A l) V))) (cbrt.f64 (/.f64 (/.f64 A l) V))))
	35.4b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	38.8b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 2)
	22.7b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 (neg.f64 A) l)) (sqrt.f64 (neg.f64 V))))
	40.4b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	38.4b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0) 3))
	27.2b	(*.f64 c0 (cbrt.f64 (pow.f64 (/.f64 (/.f64 A l) V) 3/2)))
✓	18.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))))

Compiler

Compiled 5023 to 1666 computations (66.8% saved)

regimes2.1s (26.3%)

Accuracy

Total 4.4b remaining (68.5%)

Threshold costs 0b (0%)

Counts

127 → 5

Compiler

Compiled 16727 to 11729 computations (29.9% saved)

bsearch3.0ms (0%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	118
1	56	118
2	67	118
3	75	118
4	79	118
5	80	118

Stop Event

1×

saturated

end307.0ms (3.9%)

Compiler: Compiled 579 to 337 computations (41.8% saved)

Details

analyze657.0ms (8.3%)

sample1.4s (17.4%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series112.0ms (1.4%)

rewrite51.0ms (0.6%)

simplify9.0ms (0.1%)

prune86.0ms (1.1%)

localize10.0ms (0.1%)

series135.0ms (1.7%)

rewrite56.0ms (0.7%)

simplify81.0ms (1%)

prune128.0ms (1.6%)

localize11.0ms (0.1%)

series1.3s (15.9%)

rewrite53.0ms (0.7%)

simplify48.0ms (0.6%)

prune130.0ms (1.6%)

localize9.0ms (0.1%)

series1.1s (13.5%)

rewrite45.0ms (0.6%)

simplify43.0ms (0.5%)

prune137.0ms (1.7%)

regimes2.1s (26.3%)

bsearch3.0ms (0%)

simplify5.0ms (0.1%)

end307.0ms (3.9%)

Profiling