Details

analyze652.0ms (12.7%)

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 (29%)

Results

1.0s	8256×	body	128	valid
430.0ms	3939×	body	128	invalid

Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess26.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

12×	`*-commutative_binary64`
12×	`associate-/r*_binary64`
1×	`swap-V-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	84
1	56	84
2	64	84
0	4	4
1	4	4

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort V l)

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify8.0ms (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	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

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)))

series88.0ms (1.7%)

Counts

3 → 12

Calls

30 calls:

5.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))	l	-inf
5.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))	V	inf
4.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))	A	0
4.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))	c0	-inf
4.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))	V	-inf

rewrite55.0ms (1.1%)

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

simplify10.0ms (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

prune82.0ms (1.6%)

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

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)))

series93.0ms (1.8%)

Counts

3 → 48

Calls

30 calls:

7.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))	c0	-inf
6.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))	A	-inf
5.0ms	(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))	V	0
4.0ms	(*.f64 (/.f64 1 V) (/.f64 A l))	V	inf
4.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))	l	-inf

rewrite74.0ms (1.4%)

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

simplify23.0ms (0.4%)

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

prune93.0ms (1.8%)

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

Compiler

Compiled 1631 to 723 computations (55.7% saved)

localize8.0ms (0.2%)

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))))

series105.0ms (2%)

Counts

4 → 84

Calls

39 calls:

7.0ms	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))	l	-inf
5.0ms	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))	c0	inf
4.0ms	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))	A	-inf
4.0ms	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))	V	inf
4.0ms	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))	c0	-inf

rewrite57.0ms (1.1%)

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

simplify24.0ms (0.5%)

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

prune95.0ms (1.9%)

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
	36.3b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	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))))
	18.0b	(.f64 c0 (sqrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 (.f64 V (/.f64 l A))) 3))))
✓	17.8b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	20.0b	(*.f64 c0 (/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V)))))
	54.5b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
✓	17.7b	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))
	37.9b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
▶	17.6b	(/.f64 c0 (sqrt.f64 (*.f64 V (/.f64 l A))))
	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)

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)))

series125.0ms (2.4%)

Counts

2 → 12

Calls

21 calls:

21.0ms	(/.f64 c0 (sqrt.f64 (*.f64 V (/.f64 l A))))	V	-inf
21.0ms	(/.f64 c0 (sqrt.f64 (*.f64 V (/.f64 l A))))	l	-inf
19.0ms	(/.f64 c0 (sqrt.f64 (*.f64 V (/.f64 l A))))	A	-inf
6.0ms	(/.f64 c0 (sqrt.f64 (*.f64 V (/.f64 l A))))	V	0
5.0ms	(/.f64 c0 (sqrt.f64 (*.f64 V (/.f64 l A))))	l	0

rewrite51.0ms (1%)

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

simplify11.0ms (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 (1.5%)

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
	36.3b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	50.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 A l)) (pow.f64 V -1/2)))
	18.9b	(/.f64 c0 (pow.f64 (pow.f64 (/.f64 (*.f64 V l) A) 1/4) 2))
	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))))
✓	17.7b	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))
	26.2b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	37.0b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
✓	17.8b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	37.0b	(/.f64 c0 (/.f64 (sqrt.f64 (*.f64 V l)) (sqrt.f64 A)))
	17.8b	(/.f64 c0 (sqrt.f64 (/.f64 V (/.f64 A l))))
	19.2b	(pow.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 V l) A)) c0) -1)

Compiler

Compiled 1518 to 561 computations (63% saved)

regimes1.6s (30.4%)

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 (0.1%)

Algorithm

4×	left-value

Calls

4 calls:

0.0ms	(*.f64 V l)
0.0ms	(*.f64 V l)
0.0ms	(*.f64 V l)
0.0ms	(*.f64 V l)

Steps

Iters	Point		Range
4.879326628049021e+306	∈ [	4.879326628049021e+306	,	#hash((type . real) (value . +inf))	]
0.0	∈ [	0.0	,	7.331950921926823e-306	]
-9.476766494841006e-290	∈ [	-9.476766494841006e-290	,	-3.1453609444199197e-292	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-7.738922769045099e+294	]

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

end303.0ms (5.9%)

Stop Event

1×

fuel

Compiler

Compiled 462 to 262 computations (43.3% saved)

Details

analyze652.0ms (12.7%)

sample1.5s (29%)

preprocess26.0ms (0.5%)

simplify8.0ms (0.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series88.0ms (1.7%)

rewrite55.0ms (1.1%)

simplify10.0ms (0.2%)

prune82.0ms (1.6%)

localize7.0ms (0.1%)

series93.0ms (1.8%)

rewrite74.0ms (1.4%)

simplify23.0ms (0.4%)

prune93.0ms (1.8%)

localize8.0ms (0.2%)

series105.0ms (2%)

rewrite57.0ms (1.1%)

simplify24.0ms (0.5%)

prune95.0ms (1.9%)

localize6.0ms (0.1%)

series125.0ms (2.4%)

rewrite51.0ms (1%)

simplify11.0ms (0.2%)

prune77.0ms (1.5%)

regimes1.6s (30.4%)

bsearch3.0ms (0.1%)

simplify5.0ms (0.1%)

end303.0ms (5.9%)

Profiling