Details

analyze516.0ms (13.1%)

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%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample21.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify98.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

prune2.0ms (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

28.6b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.5b	(+.f64 (.f64 a c) (.f64 b d))
28.2b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_3510` `add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
9×	`times-frac_binary64_3494`
4×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `add-log-exp_binary64_3527`
3×	`associate-/r_binary64_3432` `flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/l_binary64_3433`
2×	`associate-/l/_binary64_3435` `associate-/r/_binary64_3434` `pow1_binary64_3549`
1×	`clear-num_binary64_3487` `+-commutative_binary64_3418` `frac-2neg_binary64_3499` `div-exp_binary64_3539` `sum-log_binary64_3579` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485`

Counts

2 → 42

Calls

2 calls:

9.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

series138.0ms (3.5%)

Counts

2 → 6

Calls

2 calls:

100.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
37.0ms	(+.f64 (.f64 a c) (.f64 b d))

simplify61.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5447	1227

prune68.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	40	8	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	9	49

Error

27.9b

Counts

49 → 9

Compiler

Compiled 1317 to 258 computations (80.4% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (.f64 a c) (.f64 b d))
17.5b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
30.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_3510`
21×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
18×	`times-frac_binary64_3494` `sqrt-prod_binary64_3504`
6×	`associate-/r*_binary64_3432` `sqrt-div_binary64_3505` `add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `add-log-exp_binary64_3527` `pow1_binary64_3549`
5×	`flip-+_binary64_3462` `flip3-+_binary64_3491`
3×	`associate-/l*_binary64_3433`
2×	`associate-/l/_binary64_3435` `associate-/r/_binary64_3434` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501`
1×	`clear-num_binary64_3487` `+-commutative_binary64_3418` `frac-2neg_binary64_3499` `div-exp_binary64_3539` `sum-log_binary64_3579` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485`

Counts

4 → 84

Calls

4 calls:

10.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series211.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
36.0ms	(+.f64 (.f64 a c) (.f64 b d))
25.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
25.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify70.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5230	2326

prune97.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	5	2	7
Picked	0	1	1
Done	0	1	1
Total	95	10	105

Error

26.6b

Counts

105 → 10

Compiler

Compiled 3309 to 454 computations (86.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (.f64 a c) (.f64 b d))
17.6b	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
30.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite40.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_3510`
24×	`associate-r_binary64_3428`
22×	`times-frac_binary64_3494` `*-un-lft-identity_binary64_3488`
20×	`add-cube-cbrt_binary64_3523`
17×	`sqrt-prod_binary64_3504`
13×	`add-exp-log_binary64_3526`
9×	`add-cbrt-cube_binary64_3524`
8×	`pow1_binary64_3549`
6×	`sqrt-div_binary64_3505` `flip-+_binary64_3462` `flip3-+_binary64_3491` `add-log-exp_binary64_3527`
5×	`unswap-sqr_binary64_3456`
4×	`prod-exp_binary64_3537`
3×	`associate-l_binary64_3429`
2×	`associate-*l/_binary64_3431` `associate-/r/_binary64_3434` `cbrt-unprod_binary64_3521` `frac-times_binary64_3498` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `div-exp_binary64_3539` `rem-sqrt-square_binary64_3501`
1×	`1-exp_binary64_3532` `+-commutative_binary64_3418` `rec-exp_binary64_3538` `associate-r/_binary64_3430` `pow-prod-down_binary64_3559` `-commutative_binary64_3419` `sum-log_binary64_3579` `cbrt-undiv_binary64_3522` `un-div-inv_binary64_3486` `div-inv_binary64_3485`

Counts

4 → 94

Calls

4 calls:

17.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series213.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
37.0ms	(+.f64 (.f64 a c) (.f64 b d))
24.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
24.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify92.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4966	2273
1	4966	2273

prune114.0ms (2.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	105	11	116

Error

26.6b

Counts

116 → 11

Compiler

Compiled 3707 to 710 computations (80.8% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

10.2b	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (+.f64 (.f64 c a) (.f64 d b)) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d))))))
30.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite81.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

137×	`add-sqr-sqrt_binary64_3510`
108×	`sqrt-prod_binary64_3504`
99×	`times-frac_binary64_3494`
57×	`*-un-lft-identity_binary64_3488`
45×	`add-cube-cbrt_binary64_3523`
33×	`associate-l_binary64_3429` `associate-r_binary64_3428`
28×	`unswap-sqr_binary64_3456`
26×	`add-exp-log_binary64_3526`
16×	`add-cbrt-cube_binary64_3524`
14×	`sqrt-div_binary64_3505`
9×	`pow1_binary64_3549`
8×	`div-exp_binary64_3539` `prod-exp_binary64_3537`
5×	`flip-+_binary64_3462` `flip3-+_binary64_3491`
4×	`associate-/r/_binary64_3434` `cbrt-unprod_binary64_3521` `add-log-exp_binary64_3527` `cbrt-undiv_binary64_3522`
3×	`pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501`
2×	`1-exp_binary64_3532` `rec-exp_binary64_3538` `div-inv_binary64_3485`
1×	`associate-l/_binary64_3431` `frac-times_binary64_3498` `associate-r/_binary64_3430` `pow-prod-down_binary64_3559` `*-commutative_binary64_3419`

Counts

4 → 163

Calls

4 calls:

43.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (+.f64 (.f64 c a) (.f64 d b)) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d))))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series178.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (+.f64 (.f64 c a) (.f64 d b)) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d))))))
25.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
23.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
21.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify117.0ms (3%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5054	5807

prune187.0ms (4.7%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	175	11	186

Error

26.6b

Counts

186 → 11

Compiler

Compiled 7889 to 957 computations (87.9% saved)

regimes359.0ms (9.1%)

Accuracy

Total 2.3b remaining (8.8%)

Threshold costs 0b (0%)

Compiler

Compiled 5142 to 2726 computations (47% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	82
1	39	82

end0.0ms (0%)

sample1.2s (29.8%)

Algorithm

1×

intervals

Results

330.0ms	8000×	body	128	valid
21.0ms	459×	body	128	invalid

Compiler

Compiled 1094 to 571 computations (47.8% saved)

Details

analyze516.0ms (13.1%)

sample21.0ms (0.5%)

simplify98.0ms (2.5%)

prune2.0ms (0.1%)

localize9.0ms (0.2%)

rewrite17.0ms (0.4%)

series138.0ms (3.5%)

simplify61.0ms (1.5%)

prune68.0ms (1.7%)

localize14.0ms (0.4%)

rewrite30.0ms (0.7%)

series211.0ms (5.3%)

simplify70.0ms (1.8%)

prune97.0ms (2.5%)

localize13.0ms (0.3%)

rewrite40.0ms (1%)

series213.0ms (5.4%)

simplify92.0ms (2.3%)

prune114.0ms (2.9%)

localize16.0ms (0.4%)

rewrite81.0ms (2.1%)

series178.0ms (4.5%)

simplify117.0ms (3%)

prune187.0ms (4.7%)

regimes359.0ms (9.1%)

bsearch3.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (29.8%)

Profiling