Details

analyze653.0ms (9.3%)

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 (20.6%)

Symmetry

(sort V l)

Results

981.0ms	8256×	body	128	valid
433.0ms	3953×	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

prune5.0ms (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

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
✓	1.3b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	5.1b	(/.f64 A (*.f64 V l))
✓	18.8b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series81.0ms (1.1%)

Counts

3 → 12

Calls

3 calls:

41.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
23.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
16.0ms	(/.f64 A (*.f64 V l))

rewrite49.0ms (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:

47.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
47.0ms	(/.f64 A (*.f64 V l))
47.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

simplify8.0ms (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

prune82.0ms (1.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	82	13	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	13	96

Error

5.0b

Counts

96 → 13

Alt Table

Status	Error	Program
	22.7b	(.f64 c0 (sqrt.f64 (neg.f64 (/.f64 A (.f64 l (neg.f64 V))))))
	36.5b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
▶	22.4b	(*.f64 c0 (/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V)))))
	39.0b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 2)
	23.1b	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 3)
	36.8b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	22.9b	(*.f64 c0 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 A V) l)) 3)))
	22.7b	(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
	22.5b	(*.f64 c0 (pow.f64 (/.f64 (/.f64 A V) l) 1/2))
	41.3b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	26.0b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	36.3b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	56.1b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))

Compiler

Compiled 1563 to 710 computations (54.6% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V))))
✓	1.3b	(*.f64 c0 (/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V)))))
✓	5.0b	(/.f64 l (/.f64 A V))
✓	18.5b	(sqrt.f64 (/.f64 l (/.f64 A V)))

series214.0ms (3%)

Counts

4 → 48

Calls

4 calls:

100.0ms	(*.f64 c0 (/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V)))))
74.0ms	(/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V))))
29.0ms	(sqrt.f64 (/.f64 l (/.f64 A V)))
11.0ms	(/.f64 l (/.f64 A V))

rewrite56.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`log-prod_binary64`
198×	`expm1-udef_binary64`
198×	`log1p-udef_binary64`
188×	`log-pow_binary64`
163×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	233	37
2	3169	37

Stop Event

1×	node limit

Counts

4 → 148

Calls

4 calls:

53.0ms	(/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V))))
53.0ms	(*.f64 c0 (/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V)))))
53.0ms	(/.f64 l (/.f64 A V))
53.0ms	(sqrt.f64 (/.f64 l (/.f64 A V)))

simplify15.0ms (0.2%)

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	396
1	16	396
2	20	396
3	23	396
4	24	396

Stop Event

1×

saturated

Counts

196 → 152

prune118.0ms (1.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	143	9	152
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	149	16	165

Error

3.5b

Counts

165 → 16

Alt Table

Status	Error	Program
	22.7b	(.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)
	36.5b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	50.1b	(*.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (neg.f64 l)) (sqrt.f64 (/.f64 (neg.f64 A) V)))))
	36.3b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	56.1b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
	51.3b	(.f64 c0 (/.f64 1 (.f64 (sqrt.f64 (/.f64 l A)) (sqrt.f64 V))))
	25.9b	(.f64 c0 (/.f64 1 (.f64 (sqrt.f64 l) (sqrt.f64 (/.f64 V A)))))
	23.1b	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 3)
	36.8b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	22.8b	(/.f64 (/.f64 c0 (cbrt.f64 (.f64 V (/.f64 l A)))) (cbrt.f64 (sqrt.f64 (.f64 V (/.f64 l A)))))
▶	22.7b	(/.f64 (/.f64 c0 (pow.f64 (.f64 V (/.f64 l A)) 1/4)) (pow.f64 (.f64 V (/.f64 l A)) 1/4))
	42.3b	(/.f64 (sqrt.f64 c0) (/.f64 (sqrt.f64 (*.f64 V (/.f64 l A))) (sqrt.f64 c0)))
	23.0b	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 V (/.f64 l A))) c0))
	26.1b	(.f64 c0 (.f64 (/.f64 1 (sqrt.f64 l)) (sqrt.f64 (/.f64 A V))))
	41.3b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	26.0b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))

Compiler

Compiled 2641 to 1172 computations (55.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 c0 (pow.f64 (*.f64 V (/.f64 l A)) 1/4))
✓	0.3b	(/.f64 (/.f64 c0 (pow.f64 (.f64 V (/.f64 l A)) 1/4)) (pow.f64 (.f64 V (/.f64 l A)) 1/4))
✓	5.0b	(*.f64 V (/.f64 l A))
✓	20.6b	(pow.f64 (*.f64 V (/.f64 l A)) 1/4)

series1.4s (19.9%)

Counts

4 → 132

Calls

4 calls:

795.0ms	(/.f64 c0 (pow.f64 (*.f64 V (/.f64 l A)) 1/4))
548.0ms	(pow.f64 (*.f64 V (/.f64 l A)) 1/4)
45.0ms	(/.f64 (/.f64 c0 (pow.f64 (.f64 V (/.f64 l A)) 1/4)) (pow.f64 (.f64 V (/.f64 l A)) 1/4))
11.0ms	(*.f64 V (/.f64 l A))

rewrite57.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`
201×	`log-pow_binary64`
182×	`log-div_binary64`
122×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	55
1	246	42
2	3456	42

Stop Event

1×	node limit

Counts

4 → 122

Calls

4 calls:

55.0ms	(/.f64 c0 (pow.f64 (*.f64 V (/.f64 l A)) 1/4))
55.0ms	(/.f64 (/.f64 c0 (pow.f64 (.f64 V (/.f64 l A)) 1/4)) (pow.f64 (.f64 V (/.f64 l A)) 1/4))
55.0ms	(*.f64 V (/.f64 l A))
55.0ms	(pow.f64 (*.f64 V (/.f64 l A)) 1/4)

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

351×	`fma-def_binary64`
315×	`exp-sum_binary64`
212×	`distribute-rgt-in_binary64`
184×	`sub-neg_binary64`
183×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	1704
1	293	1704
2	684	1572
3	1838	1440

Stop Event

1×	node limit

Counts

254 → 148

prune137.0ms (1.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	201	2	203
Fresh	3	12	15
Picked	0	1	1
Done	0	0	0
Total	204	15	219

Error

3.5b

Counts

219 → 15

Alt Table

Status	Error	Program
	50.1b	(*.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (neg.f64 l)) (sqrt.f64 (/.f64 (neg.f64 A) V)))))
	36.3b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
▶	22.6b	(.f64 (/.f64 c0 (sqrt.f64 (/.f64 (.f64 V l) A))) 1)
	56.1b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
	51.3b	(.f64 c0 (/.f64 1 (.f64 (sqrt.f64 (/.f64 l A)) (sqrt.f64 V))))
	22.7b	(.f64 (.f64 c0 (pow.f64 (/.f64 (.f64 V l) A) -1/4)) (pow.f64 (/.f64 (.f64 V l) A) -1/4))
	25.9b	(.f64 c0 (/.f64 1 (.f64 (sqrt.f64 l) (sqrt.f64 (/.f64 V A)))))
	36.8b	(/.f64 (.f64 (sqrt.f64 A) c0) (sqrt.f64 (.f64 V l)))
	36.5b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	22.8b	(/.f64 (/.f64 c0 (cbrt.f64 (.f64 V (/.f64 l A)))) (cbrt.f64 (sqrt.f64 (.f64 V (/.f64 l A)))))
✓	22.7b	(/.f64 (/.f64 c0 (pow.f64 (.f64 V (/.f64 l A)) 1/4)) (pow.f64 (.f64 V (/.f64 l A)) 1/4))
	42.3b	(/.f64 (sqrt.f64 c0) (/.f64 (sqrt.f64 (*.f64 V (/.f64 l A))) (sqrt.f64 c0)))
	26.1b	(.f64 c0 (.f64 (/.f64 1 (sqrt.f64 l)) (sqrt.f64 (/.f64 A V))))
	41.3b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))
	26.0b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))

Compiler

Compiled 4635 to 2008 computations (56.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.6b	(/.f64 c0 (sqrt.f64 (/.f64 (*.f64 V l) A)))
✓	5.1b	(/.f64 (*.f64 V l) A)
✓	18.5b	(sqrt.f64 (/.f64 (*.f64 V l) A))

series126.0ms (1.8%)

Counts

3 → 12

Calls

3 calls:

91.0ms	(/.f64 c0 (sqrt.f64 (/.f64 (*.f64 V l) A)))
23.0ms	(sqrt.f64 (/.f64 (*.f64 V l) A))
12.0ms	(/.f64 (*.f64 V l) A)

rewrite48.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

546×	`log-prod_binary64`
176×	`expm1-udef_binary64`
176×	`log1p-udef_binary64`
166×	`pow3_binary64`
166×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	191	28
2	2683	28

Stop Event

1×	node limit

Counts

3 → 127

Calls

3 calls:

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

simplify10.0ms (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

139 → 128

prune115.0ms (1.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	128	15	143

Error

3.4b

Counts

143 → 15

Alt Table

Status	Error	Program
	26.0b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	36.3b	(.f64 (/.f64 c0 (.f64 (sqrt.f64 (*.f64 V l)) (sqrt.f64 (/.f64 1 A)))) 1)
	50.1b	(*.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (neg.f64 l)) (sqrt.f64 (/.f64 (neg.f64 A) V)))))
	36.3b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	56.1b	(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
	22.7b	(.f64 (.f64 c0 (pow.f64 (/.f64 (.f64 V l) A) -1/4)) (pow.f64 (/.f64 (.f64 V l) A) -1/4))
	25.9b	(.f64 c0 (/.f64 1 (.f64 (sqrt.f64 l) (sqrt.f64 (/.f64 V A)))))
	36.5b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	22.8b	(/.f64 (/.f64 c0 (cbrt.f64 (.f64 V (/.f64 l A)))) (cbrt.f64 (sqrt.f64 (.f64 V (/.f64 l A)))))
✓	22.7b	(/.f64 (/.f64 c0 (pow.f64 (.f64 V (/.f64 l A)) 1/4)) (pow.f64 (.f64 V (/.f64 l A)) 1/4))
	42.3b	(/.f64 (sqrt.f64 c0) (/.f64 (sqrt.f64 (*.f64 V (/.f64 l A))) (sqrt.f64 c0)))
	41.2b	(.f64 (/.f64 c0 (/.f64 (sqrt.f64 (.f64 V (neg.f64 l))) (sqrt.f64 (neg.f64 A)))) 1)
	51.2b	(*.f64 (/.f64 c0 (/.f64 (sqrt.f64 V) (sqrt.f64 (/.f64 A l)))) 1)
	26.1b	(.f64 c0 (.f64 (/.f64 1 (sqrt.f64 l)) (sqrt.f64 (/.f64 A V))))
	41.3b	(.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (.f64 l (neg.f64 V)))))

Compiler

Compiled 2220 to 1003 computations (54.8% saved)

regimes2.0s (28.4%)

Accuracy

Total 2.8b remaining (50.6%)

Threshold costs 0b (0%)

Counts

126 → 5

Compiler

Compiled 16504 to 11910 computations (27.8% saved)

bsearch3.0ms (0%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-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	49	114
1	70	114
2	79	114
3	86	114
4	89	114
5	90	114

Stop Event

1×

saturated

end318.0ms (4.5%)

Compiler: Compiled 556 to 347 computations (37.6% saved)

Details

analyze653.0ms (9.3%)

sample1.5s (20.6%)

simplify6.0ms (0.1%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series81.0ms (1.1%)

rewrite49.0ms (0.7%)

simplify8.0ms (0.1%)

prune82.0ms (1.2%)

localize7.0ms (0.1%)

series214.0ms (3%)

rewrite56.0ms (0.8%)

simplify15.0ms (0.2%)

prune118.0ms (1.7%)

localize9.0ms (0.1%)

series1.4s (19.9%)

rewrite57.0ms (0.8%)

simplify51.0ms (0.7%)

prune137.0ms (1.9%)

localize7.0ms (0.1%)

series126.0ms (1.8%)

rewrite48.0ms (0.7%)

simplify10.0ms (0.1%)

prune115.0ms (1.6%)

regimes2.0s (28.4%)

bsearch3.0ms (0%)

simplify6.0ms (0.1%)

end318.0ms (4.5%)

Profiling