Details

analyze327.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample71.0ms (0%)

Algorithm

1×

intervals

Results

23.0ms	206×	body	128	valid
11.0ms	256×	pre	128	true
11.0ms	24×	body	1024	valid
5.0ms	16×	body	512	valid
2.0ms	9×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify767.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (250.0ms)

Iter	Nodes	Cost
0	5371	43

prune32.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 22.0b

Counts

2 → 1

Compiler

Compiled 58 to 40 computations (31% saved)

localize57.0ms (0%)

Local error

Found 3 expressions with local error:

0.1b

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

1.8b

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

19.1b

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite377.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_3494`
47×	`*-un-lft-identity_binary64_3488`
25×	`add-sqr-sqrt_binary64_3510` `add-cube-cbrt_binary64_3523`
17×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
14×	`associate-/r/_binary64_3434`
11×	`distribute-lft-out_binary64_3439` `flip-+_binary64_3462` `flip3-+_binary64_3491`
10×	`associate-/l*_binary64_3433`
9×	`associate-/l/_binary64_3435`
7×	`associate-/r*_binary64_3432` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485`
5×	`add-log-exp_binary64_3527`
4×	`frac-times_binary64_3498`
3×	`flip3--_binary64_3492` `flip--_binary64_3463` `pow1_binary64_3549`
2×	`associate-l/_binary64_3431` `clear-num_binary64_3487` `cbrt-unprod_binary64_3521` `associate-r/_binary64_3430` `frac-2neg_binary64_3499` `prod-exp_binary64_3537`
1×	`+-commutative_binary64_3418` `sum-log_binary64_3579`

Counts

3 → 111

Calls

3 calls:

157.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

94.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

56.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series3.5s (1.1%)

Counts

3 → 9

Calls

3 calls:

1.9s

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

1.4s

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

230.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify497.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (309.0ms)

Iter	Nodes	Cost
0	4941	5261
1	4941	5261

prune3.8s (1.2%)

Pruning

63 alts after pruning (62 fresh and 1 done)

	Pruned	Kept	Total
New	58	62	120
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	63	121

Merged error: 5.1b

Counts

121 → 63

Compiler

Compiled 8018 to 4493 computations (44% saved)

localize62.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha))
0.1b	(/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 2))
0.1b	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha)))
1.8b	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 2)) 1)

rewrite1.2s (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

1250×	`times-frac_binary64_3494`
1055×	`*-un-lft-identity_binary64_3488`
619×	`add-sqr-sqrt_binary64_3510`
461×	`add-cube-cbrt_binary64_3523`
218×	`distribute-lft-out_binary64_3439`
96×	`associate-/l*_binary64_3433`
79×	`difference-of-squares_binary64_3457` `distribute-lft-out--_binary64_3440`
60×	`associate-/r/_binary64_3434`
33×	`div-inv_binary64_3485`
30×	`associate-/r*_binary64_3432`
26×	`flip3--_binary64_3492` `flip--_binary64_3463`
20×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
10×	`div-exp_binary64_3539` `cbrt-undiv_binary64_3522`
6×	`add-log-exp_binary64_3527`
5×	`associate-/l/_binary64_3435`
4×	`flip-+_binary64_3462` `flip3-+_binary64_3491` `pow1_binary64_3549`
3×	`clear-num_binary64_3487` `frac-2neg_binary64_3499`
1×	`+-commutative_binary64_3418` `sum-log_binary64_3579`

Counts

4 → 645

Calls

4 calls:

580.0ms	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 2)) 1)
199.0ms	(/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 2))
70.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha)))
25.0ms	(/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha))

series3.4s (1.1%)

Counts

4 → 12

Calls

4 calls:

1.4s	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 2)) 1)
1.3s	(/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 2))
422.0ms	(/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha))
286.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha)))

simplify1.5s (0.5%)

Algorithm

1×	egg-herbie

Counts

657 → 657

Iterations

Useful iterations: 0 (147.0ms)

Iter	Nodes	Cost
0	4997	38851
1	4997	38851

prune31.6s (10.2%)

Pruning

259 alts after pruning (257 fresh and 2 done)

	Pruned	Kept	Total
New	434	223	657
Fresh	27	34	61
Picked	0	1	1
Done	0	1	1
Total	461	259	720

Merged error: 5.1b

Counts

720 → 259

Compiler

Compiled 47285 to 24945 computations (47.2% saved)

localize55.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha))
0.1b	(.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
1.8b	(+.f64 (/.f64 (+.f64 alpha beta) (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
2.5b	(/.f64 (+.f64 alpha beta) (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

rewrite375.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64_3488`
45×	`add-sqr-sqrt_binary64_3510`
35×	`times-frac_binary64_3494`
26×	`add-cube-cbrt_binary64_3523`
21×	`associate-l_binary64_3429`
20×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
9×	`associate-/r/_binary64_3434`
7×	`difference-of-squares_binary64_3457` `distribute-lft-out--_binary64_3440` `flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/l*_binary64_3433`
6×	`associate-/r*_binary64_3432` `add-log-exp_binary64_3527` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `pow1_binary64_3549`
4×	`distribute-lft-out_binary64_3439` `associate-/l/_binary64_3435` `cbrt-unprod_binary64_3521` `frac-times_binary64_3498` `associate-r/_binary64_3430` `associate-r*_binary64_3428` `prod-exp_binary64_3537`
3×	`div-inv_binary64_3485`
2×	`associate-*l/_binary64_3431` `clear-num_binary64_3487` `unswap-sqr_binary64_3456` `flip3--_binary64_3492` `frac-2neg_binary64_3499` `flip--_binary64_3463`
1×	`distribute-lft-in_binary64_3437` `distribute-rgt-in_binary64_3438` `+-commutative_binary64_3418` `pow-prod-down_binary64_3559` `*-commutative_binary64_3419` `sum-log_binary64_3579`

Counts

4 → 130

Calls

4 calls:

106.0ms	(.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
75.0ms	(/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha))
65.0ms	(+.f64 (/.f64 (+.f64 alpha beta) (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
57.0ms	(/.f64 (+.f64 alpha beta) (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

series3.4s (1.1%)

Counts

4 → 12

Calls

4 calls:

1.2s	(+.f64 (/.f64 (+.f64 alpha beta) (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
1.2s	(/.f64 (+.f64 alpha beta) (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
581.0ms	(.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
449.0ms	(/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha))

simplify270.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (154.0ms)

Iter	Nodes	Cost
0	4950	4764
1	4950	4764

prune12.5s (4%)

Pruning

278 alts after pruning (275 fresh and 3 done)

	Pruned	Kept	Total
New	106	36	142
Fresh	17	239	256
Picked	0	1	1
Done	0	2	2
Total	123	278	401

Merged error: 5.1b

Counts

401 → 278

Compiler

Compiled 20733 to 12218 computations (41.1% saved)

localize34.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha))
0.1b	(.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (-.f64 -2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
1.8b	(+.f64 (/.f64 (neg.f64 (+.f64 alpha beta)) (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (-.f64 -2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
2.5b	(/.f64 (neg.f64 (+.f64 alpha beta)) (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (-.f64 -2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

rewrite240.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_3488`
53×	`add-sqr-sqrt_binary64_3510`
43×	`times-frac_binary64_3494`
32×	`add-cube-cbrt_binary64_3523`
21×	`associate-l_binary64_3429`
20×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
15×	`associate-/l*_binary64_3433`
9×	`associate-/r/_binary64_3434`
8×	`difference-of-squares_binary64_3457` `distribute-lft-neg-in_binary64_3445` `distribute-lft-out--_binary64_3440` `distribute-rgt-neg-in_binary64_3446`
6×	`associate-/r*_binary64_3432` `flip3--_binary64_3492` `cancel-sign-sub-inv_binary64_3454` `add-log-exp_binary64_3527` `flip--_binary64_3463` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `pow1_binary64_3549`
5×	`distribute-lft-out_binary64_3439` `associate-r_binary64_3428`
4×	`distribute-lft-in_binary64_3437` `distribute-rgt-in_binary64_3438` `associate-/l/_binary64_3435` `cbrt-unprod_binary64_3521` `frac-times_binary64_3498` `associate-*r/_binary64_3430` `prod-exp_binary64_3537`
3×	`flip-+_binary64_3462` `flip3-+_binary64_3491` `div-inv_binary64_3485`
2×	`associate-*l/_binary64_3431` `clear-num_binary64_3487` `unswap-sqr_binary64_3456` `distribute-neg-frac_binary64_3452` `frac-2neg_binary64_3499` `neg-mul-1_binary64_3484` `neg-sub0_binary64_3483` `div-sub_binary64_3493` `sub-neg_binary64_3481`
1×	`associate-+l-_binary64_3423` `+-commutative_binary64_3418` `pow-prod-down_binary64_3559` `*-commutative_binary64_3419` `distribute-frac-neg_binary64_3451` `sum-log_binary64_3579`

Counts

4 → 156

Calls

4 calls:

70.0ms	(+.f64 (/.f64 (neg.f64 (+.f64 alpha beta)) (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (-.f64 -2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
56.0ms	(.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (-.f64 -2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
50.0ms	(/.f64 (neg.f64 (+.f64 alpha beta)) (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (-.f64 -2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
27.0ms	(/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha))

series3.2s (1%)

Counts

4 → 12

Calls

4 calls:

1.3s	(+.f64 (/.f64 (neg.f64 (+.f64 alpha beta)) (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (-.f64 -2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
1.0s	(/.f64 (neg.f64 (+.f64 alpha beta)) (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (-.f64 -2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
528.0ms	(.f64 (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha)) (-.f64 -2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
428.0ms	(/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha))

simplify906.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (619.0ms)

Iter	Nodes	Cost
0	4981	5946
1	4981	5946

prune14.0s (4.5%)

Pruning

310 alts after pruning (306 fresh and 4 done)

	Pruned	Kept	Total
New	111	57	168
Fresh	25	249	274
Picked	0	1	1
Done	0	3	3
Total	136	310	446

Merged error: 5.1b

Counts

446 → 310

Compiler

Compiled 6572 to 3363 computations (48.8% saved)

regimes1.0min (19.5%)

Compiler: Compiled 227096 to 142160 computations (37.4% saved)

bsearch1.7min (33%)

Compiler: Compiled 25 to 16 computations (36% saved)

simplify56.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	119	113
1	119	113

end7.0ms (0%)

sample1.1min (20.9%)

Algorithm

1×

intervals

Results

982.0ms	6487×	body	128	valid
399.0ms	8000×	pre	128	true
341.0ms	684×	body	1024	valid
200.0ms	483×	body	512	valid
69.0ms	285×	body	256	valid
32.0ms	61×	body	2048	valid

Compiler

Compiled 33308 to 20822 computations (37.5% saved)

Pareto

0.3869718749894158

Details

analyze327.0ms (0.1%)

sample71.0ms (0%)

simplify767.0ms (0.2%)

prune32.0ms (0%)

localize57.0ms (0%)

rewrite377.0ms (0.1%)

series3.5s (1.1%)

simplify497.0ms (0.2%)

prune3.8s (1.2%)

localize62.0ms (0%)

rewrite1.2s (0.4%)

series3.4s (1.1%)

simplify1.5s (0.5%)

prune31.6s (10.2%)

localize55.0ms (0%)

rewrite375.0ms (0.1%)

series3.4s (1.1%)

simplify270.0ms (0.1%)

prune12.5s (4%)

localize34.0ms (0%)

rewrite240.0ms (0.1%)

series3.2s (1%)

simplify906.0ms (0.3%)

prune14.0s (4.5%)

regimes1.0min (19.5%)

bsearch1.7min (33%)

simplify56.0ms (0%)

end7.0ms (0%)

sample1.1min (20.9%)

Profiling