Details

analyze663.0ms (9.7%)

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 (21.7%)

Symmetry

(sort V l)

Results

994.0ms	8256×	body	128	valid
451.0ms	3935×	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

22.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	22.7b	(.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
✓	2.1b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	7.2b	(/.f64 A (*.f64 V l))
✓	15.7b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series120.0ms (1.8%)

Counts

3 → 12

Calls

3 calls:

66.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
37.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
17.0ms	(/.f64 A (*.f64 V l))

rewrite56.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

94× egg-rr

Counts

3 → 94

Calls

2 calls:

54.0ms	((sqrt.f64 (/.f64 A (.f64 V l))) (/.f64 A (.f64 V l)) (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l)))))
0.0ms	()

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

prune153.0ms (2.2%)

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

6.1b

Counts

96 → 14

Alt Table

Status	Error	Program
	48.0b	(sqrt.f64 (.f64 (/.f64 A (.f64 V l)) (*.f64 c0 c0)))
	40.7b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (neg.f64 (.f64 V l)))))
	39.5b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	38.8b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	22.0b	(.f64 c0 (/.f64 1 (sqrt.f64 (/.f64 (.f64 V l) A))))
	38.5b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (cbrt.f64 (*.f64 A A)) V) (/.f64 (cbrt.f64 A) l))))
	20.8b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
▶	20.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
	38.9b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	31.3b	(.f64 c0 (cbrt.f64 (pow.f64 (/.f64 A (.f64 V l)) 3/2)))
	23.4b	(.f64 c0 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) 3))
	28.0b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	40.0b	(pow.f64 (sqrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)) 2)
	38.8b	(.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (.f64 V l)) (sqrt.f64 A))))

Compiler

Compiled 1599 to 713 computations (55.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	2.1b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
✓	4.9b	(*.f64 (/.f64 A V) (/.f64 1 l))
✓	15.7b	(sqrt.f64 (*.f64 (/.f64 A V) (/.f64 1 l)))

series118.0ms (1.7%)

Counts

3 → 48

Calls

3 calls:

64.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
37.0ms	(sqrt.f64 (*.f64 (/.f64 A V) (/.f64 1 l)))
16.0ms	(*.f64 (/.f64 A V) (/.f64 1 l))

rewrite65.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

104× egg-rr

Counts

3 → 104

Calls

2 calls:

63.0ms	((sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))) (.f64 (/.f64 A V) (/.f64 1 l)) (.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	229	28
2	2836	28
3	4964	28
0	0	0
1	0	0

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

152 → 105

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	396
1	13	396
2	15	396
3	15	396

prune93.0ms (1.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	99	6	105
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	105	14	119

Error

5.2b

Counts

119 → 14

Alt Table

Status	Error	Program
	38.1b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 2)
	38.9b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	39.5b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	38.8b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	52.0b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A l)) (sqrt.f64 V)))
	38.8b	(.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (.f64 V l)) (sqrt.f64 A))))
	22.0b	(.f64 c0 (/.f64 1 (sqrt.f64 (/.f64 (.f64 V l) A))))
	28.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 A V)) (pow.f64 l -1/2)))
	47.1b	(sqrt.f64 (.f64 (/.f64 (/.f64 A V) l) (.f64 c0 c0)))
	20.8b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
	23.4b	(.f64 c0 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) 3))
	28.0b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	40.7b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (neg.f64 (.f64 V l)))))
▶	20.5b	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))

Compiler

Compiled 1661 to 753 computations (54.7% 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)
✓	2.1b	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
✓	4.8b	(/.f64 (/.f64 A V) l)
✓	18.7b	(pow.f64 (/.f64 (/.f64 A V) l) 1/4)

series1.7s (24.5%)

Counts

4 → 120

Calls

4 calls:

813.0ms	(pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2)
782.0ms	(pow.f64 (/.f64 (/.f64 A V) l) 1/4)
66.0ms	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
18.0ms	(/.f64 (/.f64 A V) l)

rewrite68.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

122× egg-rr

Counts

4 → 122

Calls

2 calls:

66.0ms	((pow.f64 (/.f64 (/.f64 A V) l) 1/4) (/.f64 (/.f64 A V) l) (*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2)) (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	262	38
2	3064	38
3	5275	38
0	0	0
1	0	0

simplify85.0ms (1.2%)

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

242 → 144

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1800
1	179	1656
2	336	1548
3	1138	1080
4	3677	1080
5	5035	1080

prune120.0ms (1.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	139	5	144
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	141	17	158

Error

2.8b

Counts

158 → 17

Alt Table

Status	Error	Program
	27.0b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (*.f64 -1 (/.f64 A l))) (log.f64 (/.f64 -1 V))))) 2))
	20.8b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
	49.1b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 (neg.f64 A) V)) (sqrt.f64 (neg.f64 l))))
✓	20.5b	(*.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))))
	39.5b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	38.8b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	52.0b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A l)) (sqrt.f64 V)))
	38.8b	(.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (.f64 V l)) (sqrt.f64 A))))
	28.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 A V)) (pow.f64 l -1/2)))
	30.6b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (/.f64 A V)) (log.f64 l)))) 2))
	47.1b	(sqrt.f64 (.f64 (/.f64 (/.f64 A V) l) (.f64 c0 c0)))
	38.1b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 2)
▶	20.3b	(.f64 c0 (/.f64 1 (sqrt.f64 (.f64 l (/.f64 V A)))))
	23.4b	(.f64 c0 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) 3))
	28.0b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	40.7b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (neg.f64 (.f64 V l)))))

Compiler

Compiled 2743 to 1389 computations (49.4% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (sqrt.f64 (*.f64 l (/.f64 V A))))
✓	2.1b	(.f64 c0 (/.f64 1 (sqrt.f64 (.f64 l (/.f64 V A)))))
✓	5.3b	(*.f64 l (/.f64 V A))
✓	15.1b	(sqrt.f64 (*.f64 l (/.f64 V A)))

series340.0ms (5%)

Counts

4 → 48

Calls

4 calls:

157.0ms	(.f64 c0 (/.f64 1 (sqrt.f64 (.f64 l (/.f64 V A)))))
130.0ms	(/.f64 1 (sqrt.f64 (*.f64 l (/.f64 V A))))
40.0ms	(sqrt.f64 (*.f64 l (/.f64 V A)))
13.0ms	(*.f64 l (/.f64 V A))

rewrite65.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

124× egg-rr

Counts

4 → 124

Calls

2 calls:

63.0ms	((sqrt.f64 (.f64 l (/.f64 V A))) (.f64 l (/.f64 V A)) (.f64 c0 (/.f64 1 (sqrt.f64 (.f64 l (/.f64 V A))))) (/.f64 1 (sqrt.f64 (*.f64 l (/.f64 V A)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	226	38
2	2741	38
3	4961	38
0	0	0
1	0	0

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

172 → 126

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	396
1	16	396
2	20	396
3	23	396
4	24	396
5	24	396

prune90.0ms (1.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	1	14	15
Picked	1	0	1
Done	0	1	1
Total	126	17	143

Error

2.8b

Counts

143 → 17

Alt Table

Status	Error	Program
	27.0b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (*.f64 -1 (/.f64 A l))) (log.f64 (/.f64 -1 V))))) 2))
	20.8b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
	49.1b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 (neg.f64 A) V)) (sqrt.f64 (neg.f64 l))))
	28.1b	(.f64 c0 (/.f64 1 (.f64 (sqrt.f64 l) (sqrt.f64 (/.f64 V A)))))
✓	20.5b	(*.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))))
	39.5b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	38.8b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	20.2b	(/.f64 c0 (sqrt.f64 (*.f64 l (/.f64 V A))))
	52.0b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A l)) (sqrt.f64 V)))
	38.8b	(.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (.f64 V l)) (sqrt.f64 A))))
	28.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 A V)) (pow.f64 l -1/2)))
	30.6b	(.f64 c0 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (/.f64 A V)) (log.f64 l)))) 2))
	47.1b	(sqrt.f64 (.f64 (/.f64 (/.f64 A V) l) (.f64 c0 c0)))
	38.1b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 2)
	23.4b	(.f64 c0 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) 3))
	40.7b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (neg.f64 (.f64 V l)))))

Compiler

Compiled 1971 to 888 computations (54.9% saved)

regimes1.2s (17.9%)

Accuracy

Total 4.0b remaining (65.5%)

Threshold costs 0b (0%)

Counts

68 → 5

Compiler

Compiled 9312 to 6346 computations (31.9% saved)

bsearch2.0ms (0%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	121
1	68	121
2	80	121
3	87	121
4	90	121
5	90	121

end337.0ms (4.9%)

Compiler: Compiled 578 to 373 computations (35.5% saved)

Details

analyze663.0ms (9.7%)

sample1.5s (21.7%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series120.0ms (1.8%)

rewrite56.0ms (0.8%)

simplify9.0ms (0.1%)

prune153.0ms (2.2%)

localize7.0ms (0.1%)

series118.0ms (1.7%)

rewrite65.0ms (0.9%)

simplify14.0ms (0.2%)

prune93.0ms (1.4%)

localize9.0ms (0.1%)

series1.7s (24.5%)

rewrite68.0ms (1%)

simplify85.0ms (1.2%)

prune120.0ms (1.8%)

localize7.0ms (0.1%)

series340.0ms (5%)

rewrite65.0ms (1%)

simplify18.0ms (0.3%)

prune90.0ms (1.3%)

regimes1.2s (17.9%)

bsearch2.0ms (0%)

simplify5.0ms (0.1%)

end337.0ms (4.9%)

Profiling