Details

analyze627.0ms (8.9%)

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 (19.6%)

Symmetry

(sort V l)

Results

939.0ms	8256×	body	128	valid
407.0ms	3965×	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

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

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)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	4.8b	(/.f64 A (*.f64 V l))
✓	16.8b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series87.0ms (1.2%)

Counts

3 → 12

Calls

3 calls:

46.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
25.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
16.0ms	(/.f64 A (*.f64 V l))

rewrite50.0ms (0.7%)

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:

48.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
48.0ms	(/.f64 A (*.f64 V l))
48.0ms	(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

prune77.0ms (1.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	83	12	95
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	13	96

Error

2.7b

Counts

96 → 13

Alt Table

Status	Error	Program
	35.2b	(.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (.f64 V l)) (sqrt.f64 A))))
✓	19.1b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
	39.1b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (sqrt.f64 A) V) (/.f64 (sqrt.f64 A) l))))
▶	17.9b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))))
	39.5b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	24.5b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	27.5b	(*.f64 c0 (cbrt.f64 (pow.f64 (/.f64 (/.f64 A V) l) 3/2)))
	18.9b	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
	48.0b	(cbrt.f64 (*.f64 (pow.f64 (/.f64 (/.f64 A V) l) 3/2) (pow.f64 c0 3)))
	41.1b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0) 3))
	57.0b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
	37.2b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 2)
	36.3b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))

Compiler

Compiled 1565 to 708 computations (54.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 A)
✓	1.0b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))))
✓	2.9b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))
✓	16.8b	(sqrt.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l)))

series145.0ms (2.1%)

Counts

4 → 60

Calls

4 calls:

50.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))))
40.0ms	(cbrt.f64 A)
27.0ms	(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))

rewrite58.0ms (0.8%)

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:

56.0ms	(cbrt.f64 A)
56.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))))
56.0ms	(*.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))
56.0ms	(sqrt.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l)))

simplify76.0ms (1.1%)

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

prune112.0ms (1.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	148	5	153
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	151	15	166

Error

2.7b

Counts

166 → 15

Alt Table

Status	Error	Program
	41.6b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A l) V)) c0) 3))
	39.5b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	47.4b	(sqrt.f64 (.f64 (/.f64 (/.f64 A l) V) (.f64 c0 c0)))
	24.5b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	37.0b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A l) V)) c0)) 2)
	28.4b	(*.f64 c0 (cbrt.f64 (pow.f64 (/.f64 (/.f64 A l) V) 3/2)))
	35.2b	(.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (.f64 V l)) (sqrt.f64 A))))
✓	19.1b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
	50.6b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A l)) (sqrt.f64 V)))
	41.1b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0) 3))
	39.1b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (sqrt.f64 A) V) (/.f64 (sqrt.f64 A) l))))
✓	17.9b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))))
▶	18.9b	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
	57.0b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
	36.3b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))

Compiler

Compiled 2575 to 1272 computations (50.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2)
✓	1.0b	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
✓	4.5b	(/.f64 (/.f64 A V) l)
✓	18.2b	(pow.f64 (/.f64 (/.f64 A V) l) 1/4)

series1.4s (20.2%)

Counts

4 → 120

Calls

4 calls:

694.0ms	(pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2)
670.0ms	(pow.f64 (/.f64 (/.f64 A V) l) 1/4)
49.0ms	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
16.0ms	(/.f64 (/.f64 A V) l)

rewrite54.0ms (0.8%)

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

simplify47.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

312×	`fma-def_binary64`
231×	`associate-+l+_binary64`
210×	`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	1377	1208

Stop Event

1×	node limit

Counts

242 → 150

prune120.0ms (1.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	144	6	150
Fresh	1	11	12
Picked	1	0	1
Done	1	1	2
Total	147	18	165

Error

1.8b

Counts

165 → 18

Alt Table

Status	Error	Program
	41.6b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A l) V)) c0) 3))
	39.5b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	50.2b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 (neg.f64 A) V)) (sqrt.f64 (neg.f64 l))))
	47.4b	(sqrt.f64 (.f64 (/.f64 (/.f64 A l) V) (.f64 c0 c0)))
	24.5b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	38.2b	(pow.f64 (sqrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))) 2)
	50.6b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A l)) (sqrt.f64 V)))
	41.1b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0) 3))
	26.8b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (*.f64 -1 (/.f64 A l))) (log.f64 (/.f64 -1 V))))) 2))
	57.0b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
	24.6b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 (/.f64 1 l))))
	36.3b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	39.1b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (sqrt.f64 A) V) (/.f64 (sqrt.f64 A) l))))
✓	17.9b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))))
	37.0b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A l) V)) c0)) 2)
	35.2b	(.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (.f64 V l)) (sqrt.f64 A))))
	24.7b	(.f64 c0 (pow.f64 (.f64 (pow.f64 (/.f64 A V) 1/4) (pow.f64 (/.f64 1 l) 1/4)) 2))
▶	18.9b	(.f64 c0 (sqrt.f64 (.f64 -1 (/.f64 (/.f64 (neg.f64 A) l) V))))

Compiler

Compiled 2865 to 1470 computations (48.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 c0 (sqrt.f64 (.f64 -1 (/.f64 (/.f64 (neg.f64 A) l) V))))
✓	4.4b	(/.f64 (/.f64 (neg.f64 A) l) V)
✓	16.8b	(sqrt.f64 (*.f64 -1 (/.f64 (/.f64 (neg.f64 A) l) V)))

series87.0ms (1.2%)

Counts

3 → 48

Calls

3 calls:

46.0ms	(.f64 c0 (sqrt.f64 (.f64 -1 (/.f64 (/.f64 (neg.f64 A) l) V))))
24.0ms	(sqrt.f64 (*.f64 -1 (/.f64 (/.f64 (neg.f64 A) l) V)))
17.0ms	(/.f64 (/.f64 (neg.f64 A) l) V)

rewrite50.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

587×	`log-prod_binary64`
186×	`expm1-udef_binary64`
186×	`log1p-udef_binary64`
170×	`log-pow_binary64`
129×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	38
1	253	28
2	3623	28

Stop Event

1×	node limit

Counts

3 → 117

Calls

3 calls:

48.0ms	(.f64 c0 (sqrt.f64 (.f64 -1 (/.f64 (/.f64 (neg.f64 A) l) V))))
48.0ms	(/.f64 (/.f64 (neg.f64 A) l) V)
48.0ms	(sqrt.f64 (*.f64 -1 (/.f64 (/.f64 (neg.f64 A) l) V)))

simplify26.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

66×	`fma-def_binary64`
24×	`fma-neg_binary64`
20×	`div-sub_binary64`
19×	`sub-neg_binary64`
14×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	468
1	19	468
2	42	468
3	72	468
4	108	468
5	132	468
6	147	468
7	172	468
8	198	468
9	284	468

Stop Event

1×

saturated

Counts

165 → 120

prune650.0ms (9.2%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	16	16
Picked	0	1	1
Done	0	1	1
Total	120	18	138

Error

1.8b

Counts

138 → 18

Alt Table

Status	Error	Program
	41.6b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A l) V)) c0) 3))
	39.5b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	50.2b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 (neg.f64 A) V)) (sqrt.f64 (neg.f64 l))))
	47.4b	(sqrt.f64 (.f64 (/.f64 (/.f64 A l) V) (.f64 c0 c0)))
	24.5b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	38.2b	(pow.f64 (sqrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))) 2)
	50.6b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A l)) (sqrt.f64 V)))
	41.1b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0) 3))
	26.8b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (*.f64 -1 (/.f64 A l))) (log.f64 (/.f64 -1 V))))) 2))
	57.0b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
	24.6b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 (/.f64 1 l))))
	36.3b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	39.1b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (sqrt.f64 A) V) (/.f64 (sqrt.f64 A) l))))
✓	17.9b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) V) (/.f64 (cbrt.f64 A) l))))
	37.0b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A l) V)) c0)) 2)
	35.2b	(.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (.f64 V l)) (sqrt.f64 A))))
	24.7b	(.f64 c0 (pow.f64 (.f64 (pow.f64 (/.f64 A V) 1/4) (pow.f64 (/.f64 1 l) 1/4)) 2))
✓	18.9b	(.f64 c0 (sqrt.f64 (.f64 -1 (/.f64 (/.f64 (neg.f64 A) l) V))))

Compiler

Compiled 2041 to 916 computations (55.1% saved)

regimes1.6s (22.2%)

Accuracy

Total 4.4b remaining (65.2%)

Threshold costs 0b (0%)

Counts

96 → 4

Compiler

Compiled 12363 to 8885 computations (28.1% saved)

bsearch2.0ms (0%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-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	38	90
1	53	90
2	62	90
3	68	90
4	71	90
5	72	90

Stop Event

1×

saturated

end349.0ms (4.9%)

Compiler: Compiled 525 to 340 computations (35.2% saved)

Iter	Nodes	Cost
0	11	468
1	19	468
2	42	468
3	72	468
4	108	468
5	132	468
6	147	468
7	172	468
8	198	468
9	284	468

Iter	Nodes	Cost
0	11	468
1	19	468
2	42	468
3	72	468
4	108	468
5	132	468
6	147	468
7	172	468
8	198	468
9	284	468

Details

analyze627.0ms (8.9%)

sample1.4s (19.6%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series87.0ms (1.2%)

rewrite50.0ms (0.7%)

simplify9.0ms (0.1%)

prune77.0ms (1.1%)

localize10.0ms (0.1%)

series145.0ms (2.1%)

rewrite58.0ms (0.8%)

simplify76.0ms (1.1%)

prune112.0ms (1.6%)

localize9.0ms (0.1%)

series1.4s (20.2%)

rewrite54.0ms (0.8%)

simplify47.0ms (0.7%)

prune120.0ms (1.7%)

localize8.0ms (0.1%)

series87.0ms (1.2%)

rewrite50.0ms (0.7%)

simplify26.0ms (0.4%)

prune650.0ms (9.2%)

regimes1.6s (22.2%)

bsearch2.0ms (0%)

simplify6.0ms (0.1%)

end349.0ms (4.9%)

Profiling

Iter	Nodes	Cost
0	11	468
1	19	468
2	42	468
3	72	468
4	108	468
5	132	468
6	147	468
7	172	468
8	198	468
9	284	468