Details

analyze682.0ms (11.9%)

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)

sample1.5s (25.6%)

Symmetry

(sort V l)

Results

980.0ms	8256×	body	128	valid
450.0ms	3939×	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 (0.1%)

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

18.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	18.6b	(.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
✓	1.0b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	3.7b	(/.f64 A (*.f64 V l))
✓	17.3b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series91.0ms (1.6%)

Counts

3 → 12

Calls

3 calls:

49.0ms	(.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 (0.9%)

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 (0.2%)

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

prune80.0ms (1.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	84	11	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	11	96

Error

3.5b

Counts

96 → 11

Alt Table

Status	Error	Program
	46.0b	(sqrt.f64 (.f64 (/.f64 (/.f64 A V) l) (.f64 c0 c0)))
	37.0b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	36.3b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	26.2b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	28.7b	(*.f64 c0 (cbrt.f64 (pow.f64 (/.f64 (/.f64 A V) l) 3/2)))
	37.0b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	37.9b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	54.5b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
	18.6b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) l) (/.f64 (cbrt.f64 A) V))))
	20.0b	(*.f64 c0 (/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V)))))
▶	17.8b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))

Compiler

Compiled 1509 to 666 computations (55.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
✓	3.1b	(*.f64 (/.f64 1 V) (/.f64 A l))
✓	17.3b	(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))

series90.0ms (1.6%)

Counts

3 → 48

Calls

3 calls:

48.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
26.0ms	(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))
17.0ms	(*.f64 (/.f64 1 V) (/.f64 A l))

rewrite52.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

589×	`log-prod_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
184×	`log-pow_binary64`
137×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	228	28
2	2991	28

Stop Event

1×	node limit

Counts

3 → 104

Calls

3 calls:

50.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
50.0ms	(*.f64 (/.f64 1 V) (/.f64 A l))
50.0ms	(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	396
1	13	396
2	15	396

Stop Event

1×

saturated

Counts

152 → 105

prune86.0ms (1.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	103	13	116

Error

3.3b

Counts

116 → 13

Alt Table

Status	Error	Program
	46.0b	(sqrt.f64 (.f64 (/.f64 (/.f64 A V) l) (.f64 c0 c0)))
	37.0b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
▶	17.7b	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))
	36.3b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	26.2b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	45.3b	(sqrt.f64 (.f64 (/.f64 A (.f64 V l)) (*.f64 c0 c0)))
✓	17.8b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	19.2b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)) 3)
	50.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 A l)) (pow.f64 V -1/2)))
	37.9b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	54.5b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
	18.6b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 A) 2) l) (/.f64 (cbrt.f64 A) V))))
	20.0b	(*.f64 c0 (/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V)))))

Compiler

Compiled 1631 to 723 computations (55.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 V (/.f64 l A)))
✓	1.0b	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))
✓	2.9b	(*.f64 V (/.f64 l A))
✓	17.3b	(sqrt.f64 (/.f64 1 (*.f64 V (/.f64 l A))))

series102.0ms (1.8%)

Counts

4 → 84

Calls

4 calls:

46.0ms	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))
24.0ms	(sqrt.f64 (/.f64 1 (*.f64 V (/.f64 l A))))
19.0ms	(/.f64 1 (*.f64 V (/.f64 l A)))
12.0ms	(*.f64 V (/.f64 l A))

rewrite52.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`log-prod_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
186×	`log-pow_binary64`
124×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	226	35
2	2901	35

Stop Event

1×	node limit

Counts

4 → 122

Calls

4 calls:

50.0ms	(/.f64 1 (*.f64 V (/.f64 l A)))
50.0ms	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))
50.0ms	(*.f64 V (/.f64 l A))
50.0ms	(sqrt.f64 (/.f64 1 (*.f64 V (/.f64 l A))))

simplify596.0ms (10.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	648
1	16	648
2	20	648
3	23	648
4	24	648

Stop Event

1×

saturated

Counts

206 → 127

prune93.0ms (1.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	128	12	140

Error

3.2b

Counts

140 → 12

Alt Table

Status	Error	Program
	54.5b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
▶	17.6b	(/.f64 c0 (sqrt.f64 (*.f64 V (/.f64 l A))))
	37.0b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
✓	17.7b	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))
	36.3b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	26.2b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	19.2b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)) 3)
	50.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 A l)) (pow.f64 V -1/2)))
	37.9b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	18.0b	(.f64 c0 (sqrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 (.f64 V (/.f64 l A))) 3))))
	20.0b	(*.f64 c0 (/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V)))))
✓	17.8b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))

Compiler

Compiled 1985 to 859 computations (56.7% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.1b	(/.f64 c0 (sqrt.f64 (*.f64 V (/.f64 l A))))
	2.9b	(*.f64 V (/.f64 l A))
✓	17.4b	(sqrt.f64 (*.f64 V (/.f64 l A)))

series126.0ms (2.2%)

Counts

2 → 12

Calls

2 calls:

100.0ms	(/.f64 c0 (sqrt.f64 (*.f64 V (/.f64 l A))))
26.0ms	(sqrt.f64 (*.f64 V (/.f64 l A)))

rewrite45.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

538×	`log-prod_binary64`
182×	`pow1/3_binary64`
176×	`expm1-udef_binary64`
176×	`log1p-udef_binary64`
166×	`pow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	191	21
2	2629	21

Stop Event

1×	node limit

Counts

2 → 70

Calls

2 calls:

44.0ms	(/.f64 c0 (sqrt.f64 (*.f64 V (/.f64 l A))))
44.0ms	(sqrt.f64 (*.f64 V (/.f64 l A)))

simplify9.0ms (0.2%)

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

82 → 71

prune77.0ms (1.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	3	6	9
Picked	1	0	1
Done	0	2	2
Total	105	12	117

Error

3.2b

Counts

117 → 12

Alt Table

Status	Error	Program
	17.8b	(/.f64 c0 (sqrt.f64 (/.f64 V (/.f64 A l))))
	50.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 A l)) (pow.f64 V -1/2)))
	37.0b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
✓	17.7b	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))
	36.3b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	26.2b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	37.0b	(/.f64 c0 (/.f64 (sqrt.f64 (*.f64 V l)) (sqrt.f64 A)))
✓	17.8b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	19.2b	(pow.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 V l) A)) c0) -1)
	19.2b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)) 3)
	54.5b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
	18.9b	(/.f64 c0 (pow.f64 (pow.f64 (/.f64 (*.f64 V l) A) 1/4) 2))

Compiler

Compiled 1518 to 561 computations (63% saved)

regimes1.7s (29.5%)

Accuracy

Total 1.8b remaining (33.5%)

Threshold costs 0b (0%)

Counts

99 → 5

Compiler

Compiled 12974 to 9066 computations (30.1% saved)

bsearch3.0ms (0%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	108
1	49	108
2	58	108
3	64	108
4	67	108
5	68	108

Stop Event

1×

saturated

end284.0ms (4.9%)

Compiler: Compiled 462 to 262 computations (43.3% saved)

Details

analyze682.0ms (11.9%)

sample1.5s (25.6%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series91.0ms (1.6%)

rewrite50.0ms (0.9%)

simplify9.0ms (0.2%)

prune80.0ms (1.4%)

localize7.0ms (0.1%)

series90.0ms (1.6%)

rewrite52.0ms (0.9%)

simplify14.0ms (0.3%)

prune86.0ms (1.5%)

localize8.0ms (0.1%)

series102.0ms (1.8%)

rewrite52.0ms (0.9%)

simplify596.0ms (10.4%)

prune93.0ms (1.6%)

localize6.0ms (0.1%)

series126.0ms (2.2%)

rewrite45.0ms (0.8%)

simplify9.0ms (0.2%)

prune77.0ms (1.3%)

regimes1.7s (29.5%)

bsearch3.0ms (0%)

simplify5.0ms (0.1%)

end284.0ms (4.9%)

Profiling