Details

analyze738.0ms (14.4%)

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)

sample1.7s (32.4%)

Symmetry

(sort V l)

Results

1.1s	8256×	body	128	valid
496.0ms	3914×	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

20.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	20.6b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.5b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	6.2b	(/.f64 A (*.f64 V l))
✓	15.0b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series85.0ms (1.7%)

Counts

3 → 12

Calls

3 calls:

45.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
25.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
14.0ms	(/.f64 A (*.f64 V l))

rewrite58.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

914×	`log1p-expm1-u_binary64`
914×	`expm1-log1p-u_binary64`
97×	`egg-rr`
93×	`add-sqr-sqrt_binary64`
86×	`add-log-exp_binary64`

Counts

3 → 97

Calls

3 calls:

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

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 (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

109 → 97

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	144
1	13	144
2	15	144
3	15	144

prune87.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	85	12	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	12	98

Error

5.7b

Counts

98 → 12

Alt Table

Status	Error	Program
	20.7b	(.f64 c0 (pow.f64 (pow.f64 (/.f64 A (.f64 V l)) 1/4) 2))
	50.5b	(cbrt.f64 (.f64 (pow.f64 (/.f64 A (.f64 V l)) 3/2) (pow.f64 c0 3)))
	38.2b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (neg.f64 (.f64 V l)))))
	40.4b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	39.7b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	32.6b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (cbrt.f64 (*.f64 A A)) V) (/.f64 (cbrt.f64 A) l))))
	19.2b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
▶	18.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
	29.0b	(.f64 c0 (cbrt.f64 (pow.f64 (/.f64 A (.f64 V l)) 3/2)))
	50.9b	(sqrt.f64 (.f64 (/.f64 A (.f64 V l)) (*.f64 c0 c0)))
	21.2b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)) 3)
	26.1b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))

Compiler

Compiled 1563 to 678 computations (56.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.5b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
✓	4.5b	(*.f64 (/.f64 A V) (/.f64 1 l))
✓	15.0b	(sqrt.f64 (*.f64 (/.f64 A V) (/.f64 1 l)))

series117.0ms (2.3%)

Counts

3 → 48

Calls

3 calls:

48.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
34.0ms	(*.f64 (/.f64 A V) (/.f64 1 l))
34.0ms	(sqrt.f64 (*.f64 (/.f64 A V) (/.f64 1 l)))

rewrite66.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

595×	`log-prod_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
184×	`log-pow_binary64`
138×	`log-div_binary64`

Counts

3 → 106

Calls

3 calls:

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

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

simplify15.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

154 → 107

Iterations

Useful iterations: 0 (0.0ms)

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

prune138.0ms (2.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	106	13	119

Error

5.2b

Counts

119 → 13

Alt Table

Status	Error	Program
	39.7b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
▶	18.9b	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 l (/.f64 A V)))))
	20.7b	(.f64 c0 (pow.f64 (pow.f64 (/.f64 A (.f64 V l)) 1/4) 2))
	50.2b	(sqrt.f64 (.f64 (/.f64 (/.f64 A V) l) (.f64 c0 c0)))
	50.5b	(cbrt.f64 (.f64 (pow.f64 (/.f64 A (.f64 V l)) 3/2) (pow.f64 c0 3)))
	38.2b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (neg.f64 (.f64 V l)))))
	40.4b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	52.4b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A l)) (sqrt.f64 V)))
	26.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 A V)) (pow.f64 l -1/2)))
	19.2b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
✓	18.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
	21.2b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)) 3)
	26.1b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))

Compiler

Compiled 1641 to 729 computations (55.6% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(/.f64 1 (/.f64 l (/.f64 A V)))
✓	1.5b	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 l (/.f64 A V)))))
✓	4.5b	(/.f64 l (/.f64 A V))
✓	15.0b	(sqrt.f64 (/.f64 1 (/.f64 l (/.f64 A V))))

series115.0ms (2.3%)

Counts

4 → 84

Calls

4 calls:

50.0ms	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 l (/.f64 A V)))))
25.0ms	(sqrt.f64 (/.f64 1 (/.f64 l (/.f64 A V))))
24.0ms	(/.f64 l (/.f64 A V))
17.0ms	(/.f64 1 (/.f64 l (/.f64 A V)))

rewrite73.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

621×	`log-prod_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
190×	`log-pow_binary64`
155×	`log-div_binary64`

Counts

4 → 153

Calls

4 calls:

68.0ms	(/.f64 1 (/.f64 l (/.f64 A V)))
68.0ms	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 l (/.f64 A V)))))
68.0ms	(/.f64 l (/.f64 A V))
68.0ms	(sqrt.f64 (/.f64 1 (/.f64 l (/.f64 A V))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	231	35
2	2931	35
3	5184	35
0	0	0
1	0	0

simplify24.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

237 → 156

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	648
1	16	648
2	20	648
3	23	648
4	24	648
5	24	648

prune103.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	4	7	11
Picked	1	0	1
Done	0	1	1
Total	159	10	169

Error

5.2b

Counts

169 → 10

Alt Table

Status	Error	Program
	38.2b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (neg.f64 (.f64 V l)))))
	40.4b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	52.4b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A l)) (sqrt.f64 V)))
	39.7b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
▶	18.7b	(/.f64 c0 (sqrt.f64 (/.f64 l (/.f64 A V))))
✓	18.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
	19.6b	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))
	50.2b	(sqrt.f64 (.f64 (/.f64 (/.f64 A V) l) (.f64 c0 c0)))
	21.2b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)) 3)
	26.1b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))

Compiler

Compiled 2423 to 1019 computations (57.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.6b	(/.f64 c0 (sqrt.f64 (/.f64 l (/.f64 A V))))
	4.5b	(/.f64 l (/.f64 A V))
✓	15.4b	(sqrt.f64 (/.f64 l (/.f64 A V)))

series124.0ms (2.4%)

Counts

2 → 12

Calls

2 calls:

97.0ms	(/.f64 c0 (sqrt.f64 (/.f64 l (/.f64 A V))))
27.0ms	(sqrt.f64 (/.f64 l (/.f64 A V)))

rewrite55.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

575×	`log-prod_binary64`
182×	`expm1-udef_binary64`
182×	`log1p-udef_binary64`
171×	`log-div_binary64`
171×	`log-pow_binary64`

Counts

2 → 75

Calls

2 calls:

53.0ms	(/.f64 c0 (sqrt.f64 (/.f64 l (/.f64 A V))))
53.0ms	(sqrt.f64 (/.f64 l (/.f64 A V)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	196	21
2	2740	21
3	4992	21
0	0	0
1	0	0

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

87 → 76

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	144
1	13	144
2	15	144
3	15	144

prune84.0ms (1.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	121	13	134

Error

3.7b

Counts

134 → 13

Alt Table

Status	Error	Program
	52.4b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A l)) (sqrt.f64 V)))
	49.4b	(/.f64 c0 (/.f64 (sqrt.f64 (neg.f64 l)) (sqrt.f64 (/.f64 (neg.f64 A) V))))
	19.0b	(pow.f64 (/.f64 (sqrt.f64 (/.f64 l (/.f64 A V))) c0) -1)
	21.2b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)) 3)
	38.2b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (neg.f64 (.f64 V l)))))
	27.3b	(*.f64 (/.f64 c0 (sqrt.f64 l)) (sqrt.f64 (/.f64 A V)))
	40.4b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	25.9b	(/.f64 c0 (*.f64 (sqrt.f64 l) (sqrt.f64 (/.f64 V A))))
	39.7b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
✓	18.7b	(/.f64 c0 (sqrt.f64 (/.f64 l (/.f64 A V))))
✓	18.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
	19.6b	(.f64 c0 (sqrt.f64 (/.f64 1 (.f64 V (/.f64 l A)))))
	26.1b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))

Compiler

Compiled 1779 to 643 computations (63.9% saved)

regimes1.2s (24.2%)

Accuracy

Total 3.7b remaining (59.3%)

Threshold costs 0b (0%)

Counts

82 → 5

Compiler

Compiled 10513 to 7295 computations (30.6% saved)

bsearch2.0ms (0%)

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

simplify7.0ms (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	45	113
1	63	113
2	73	113
3	79	113
4	81	113
5	80	113

end274.0ms (5.4%)

Compiler: Compiled 491 to 303 computations (38.3% saved)

Details

analyze738.0ms (14.4%)

sample1.7s (32.4%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.2%)

series85.0ms (1.7%)

rewrite58.0ms (1.1%)

simplify9.0ms (0.2%)

prune87.0ms (1.7%)

localize7.0ms (0.1%)

series117.0ms (2.3%)

rewrite66.0ms (1.3%)

simplify15.0ms (0.3%)

prune138.0ms (2.7%)

localize7.0ms (0.1%)

series115.0ms (2.3%)

rewrite73.0ms (1.4%)

simplify24.0ms (0.5%)

prune103.0ms (2%)

localize6.0ms (0.1%)

series124.0ms (2.4%)

rewrite55.0ms (1.1%)

simplify9.0ms (0.2%)

prune84.0ms (1.6%)

regimes1.2s (24.2%)

bsearch2.0ms (0%)

simplify7.0ms (0.1%)

end274.0ms (5.4%)

Profiling