Details

analyze24.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample62.0ms (0%)

Algorithm

1×

intervals

Results

38.0ms

256×

body

128

valid

Compiler

Compiled 39 to 27 computations (30.8% saved)

simplify801.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (421.0ms)

Iter	Nodes	Cost
0	4787	28
1	4787	28

prune22.0ms (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: 30.9b

Counts

2 → 1

Compiler

Compiled 38 to 24 computations (36.8% saved)

localize42.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
4.4b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
30.3b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

rewrite115.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_18151` `add-sqr-sqrt_binary64_18173` `add-cube-cbrt_binary64_18186`
9×	`times-frac_binary64_18157`
7×	`add-log-exp_binary64_18190`
5×	`add-cbrt-cube_binary64_18187` `add-exp-log_binary64_18189`
3×	`pow1_binary64_18212` `associate-/l_binary64_18096` `associate-/r_binary64_18095`
2×	`flip3--_binary64_18155` `associate-/l/_binary64_18098` `flip-+_binary64_18125` `flip--_binary64_18126` `associate-/r/_binary64_18097` `flip3-+_binary64_18154`
1×	`div-exp_binary64_18202` `div-inv_binary64_18148` `diff-log_binary64_18243` `cancel-sign-sub-inv_binary64_18117` `+-commutative_binary64_18081` `sub-neg_binary64_18144` `clear-num_binary64_18150` `sum-log_binary64_18242` `frac-2neg_binary64_18162` `div-sub_binary64_18156` `cbrt-undiv_binary64_18185`

Counts

3 → 55

Calls

3 calls:

47.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
24.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
22.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

series357.0ms (0.2%)

Counts

3 → 9

Calls

3 calls:

212.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
78.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
66.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

simplify315.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (218.0ms)

Iter	Nodes	Cost
0	4917	1786
1	4917	1786

prune1.6s (0.8%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	37	27	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	28	65

Merged error: 0.9b

Counts

65 → 28

Compiler

Compiled 2762 to 1545 computations (44.1% saved)

localize50.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
0.0b	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (-.f64 (.f64 x x) (.f64 y (.f64 y 4)))))
4.4b	(-.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
30.3b	(/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (-.f64 (.f64 x x) (.f64 y (.f64 y 4))))

rewrite252.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64_18157`
56×	`*-un-lft-identity_binary64_18151` `add-sqr-sqrt_binary64_18173` `add-cube-cbrt_binary64_18186`
18×	`associate-/r*_binary64_18095`
17×	`add-exp-log_binary64_18189`
11×	`add-cbrt-cube_binary64_18187` `associate-/r/_binary64_18097`
8×	`div-exp_binary64_18202` `add-log-exp_binary64_18190`
6×	`div-inv_binary64_18148` `flip3--_binary64_18155` `associate-/l*_binary64_18096` `flip--_binary64_18126`
5×	`pow1_binary64_18212`
4×	`cbrt-undiv_binary64_18185`
2×	`1-exp_binary64_18195` `rec-exp_binary64_18201` `associate-/l/_binary64_18098` `flip-+_binary64_18125` `clear-num_binary64_18150` `frac-2neg_binary64_18162` `flip3-+_binary64_18154`
1×	`inv-pow_binary64_18236` `diff-log_binary64_18243` `pow-flip_binary64_18225` `cancel-sign-sub-inv_binary64_18117` `+-commutative_binary64_18081` `sub-neg_binary64_18144` `sum-log_binary64_18242`

Counts

4 → 138

Calls

4 calls:

62.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (-.f64 (.f64 x x) (.f64 y (.f64 y 4)))))
61.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (-.f64 (.f64 x x) (.f64 y (.f64 y 4))))
23.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
16.0ms	(-.f64 (.f64 x x) (.f64 y (*.f64 y 4)))

series640.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (-.f64 (.f64 x x) (.f64 y (.f64 y 4)))))
220.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (-.f64 (.f64 x x) (.f64 y (.f64 y 4))))
136.0ms	(-.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
60.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))

simplify435.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (194.0ms)

Iter	Nodes	Cost
0	5798	5718

prune5.5s (2.7%)

Pruning

67 alts after pruning (65 fresh and 2 done)

	Pruned	Kept	Total
New	108	42	150
Fresh	3	23	26
Picked	0	1	1
Done	0	1	1
Total	111	67	178

Merged error: 0.9b

Counts

178 → 67

Compiler

Compiled 7812 to 4562 computations (41.6% saved)

localize53.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
0.0b	(/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y 4))) (cbrt.f64 1))))
4.4b	(-.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
30.3b	(/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (.f64 (-.f64 (.f64 x x) (.f64 y (*.f64 y 4))) (cbrt.f64 1)))

rewrite272.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-exp-log_binary64_18189`
21×	`add-cbrt-cube_binary64_18187`
18×	`times-frac_binary64_18157`
12×	`div-exp_binary64_18202` `cbrt-undiv_binary64_18185`
10×	`-un-lft-identity_binary64_18151` `add-sqr-sqrt_binary64_18173` `add-cube-cbrt_binary64_18186` `associate-/r_binary64_18095`
8×	`add-log-exp_binary64_18190`
7×	`associate-/r/_binary64_18097`
6×	`associate-*l/_binary64_18094` `prod-exp_binary64_18200` `cbrt-unprod_binary64_18184`
4×	`div-inv_binary64_18148` `flip3--_binary64_18155` `pow1_binary64_18212` `associate-/l*_binary64_18096` `flip--_binary64_18126`
2×	`associate-/l/_binary64_18098` `flip-+_binary64_18125` `clear-num_binary64_18150` `frac-2neg_binary64_18162` `flip3-+_binary64_18154`
1×	`diff-log_binary64_18243` `cancel-sign-sub-inv_binary64_18117` `+-commutative_binary64_18081` `sub-neg_binary64_18144` `sum-log_binary64_18242`

Counts

4 → 90

Calls

4 calls:

131.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (.f64 (-.f64 (.f64 x x) (.f64 y (*.f64 y 4))) (cbrt.f64 1)))
69.0ms	(/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y 4))) (cbrt.f64 1))))
20.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
15.0ms	(-.f64 (.f64 x x) (.f64 y (*.f64 y 4)))

series631.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

214.0ms	(/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y 4))) (cbrt.f64 1))))
166.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
149.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (.f64 (-.f64 (.f64 x x) (.f64 y (*.f64 y 4))) (cbrt.f64 1)))
101.0ms	(-.f64 (.f64 x x) (.f64 y (*.f64 y 4)))

simplify251.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	4994	3121
1	4994	3121

prune7.2s (3.5%)

Pruning

86 alts after pruning (83 fresh and 3 done)

	Pruned	Kept	Total
New	79	23	102
Fresh	4	60	64
Picked	0	1	1
Done	0	2	2
Total	83	86	169

Merged error: 0.9b

Counts

169 → 86

Compiler

Compiled 7028 to 4484 computations (36.2% saved)

localize32.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
0.0b	(/.f64 (neg.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (.f64 (cbrt.f64 1) (-.f64 (.f64 y (.f64 y 4)) (.f64 x x)))))
4.2b	(-.f64 (.f64 y (.f64 y 4)) (*.f64 x x))
30.3b	(/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (.f64 (cbrt.f64 1) (-.f64 (.f64 y (.f64 y 4)) (*.f64 x x))))

rewrite185.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64_18157`
30×	`*-un-lft-identity_binary64_18151` `add-sqr-sqrt_binary64_18173` `add-cube-cbrt_binary64_18186`
18×	`add-exp-log_binary64_18189`
17×	`associate-/r/_binary64_18097`
16×	`associate-*r/_binary64_18093` `add-cbrt-cube_binary64_18187`
10×	`distribute-rgt-neg-in_binary64_18109` `distribute-lft-neg-in_binary64_18108` `neg-mul-1_binary64_18147` `associate-/r*_binary64_18095`
9×	`div-inv_binary64_18148` `flip3--_binary64_18155` `associate-/l*_binary64_18096` `flip--_binary64_18126`
8×	`add-log-exp_binary64_18190`
7×	`div-exp_binary64_18202` `cbrt-undiv_binary64_18185`
4×	`pow1_binary64_18212`
2×	`associate-/l/_binary64_18098` `flip-+_binary64_18125` `clear-num_binary64_18150` `frac-2neg_binary64_18162` `prod-exp_binary64_18200` `cbrt-unprod_binary64_18184` `flip3-+_binary64_18154`
1×	`diff-log_binary64_18243` `distribute-frac-neg_binary64_18114` `cancel-sign-sub-inv_binary64_18117` `+-commutative_binary64_18081` `sub-neg_binary64_18144` `neg-sub0_binary64_18146` `sum-log_binary64_18242` `div-sub_binary64_18156`

Counts

4 → 136

Calls

4 calls:

65.0ms	(/.f64 (neg.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (.f64 (cbrt.f64 1) (-.f64 (.f64 y (.f64 y 4)) (.f64 x x)))))
48.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (.f64 (cbrt.f64 1) (-.f64 (.f64 y (.f64 y 4)) (*.f64 x x))))
26.0ms	(-.f64 (.f64 y (.f64 y 4)) (*.f64 x x))
9.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))

series633.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

253.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (.f64 (cbrt.f64 1) (-.f64 (.f64 y (.f64 y 4)) (*.f64 x x))))
210.0ms	(/.f64 (neg.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))) (.f64 (cbrt.f64 1) (-.f64 (.f64 y (.f64 y 4)) (.f64 x x)))))
100.0ms	(-.f64 (.f64 y (.f64 y 4)) (*.f64 x x))
69.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))

simplify434.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	5024	6558

prune11.8s (5.7%)

Pruning

112 alts after pruning (108 fresh and 4 done)

	Pruned	Kept	Total
New	112	36	148
Fresh	10	72	82
Picked	0	1	1
Done	0	3	3
Total	122	112	234

Merged error: 0.9b

Counts

234 → 112

Compiler

Compiled 5696 to 3729 computations (34.5% saved)

regimes35.0s (17.1%)

Compiler: Compiled 59497 to 41398 computations (30.4% saved)

bsearch1.4min (40.6%)

Compiler: Compiled 3 to 3 computations (0% saved)

simplify79.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	70	135
1	70	135

end0.0ms (0%)

sample54.9s (26.8%)

Algorithm

1×

intervals

Results

1.6s

8000×

body

128

valid

Compiler

Compiled 12541 to 8670 computations (30.9% saved)

Pareto

0.3007068413389576

Details

analyze24.0ms (0%)

sample62.0ms (0%)

simplify801.0ms (0.4%)

prune22.0ms (0%)

localize42.0ms (0%)

rewrite115.0ms (0.1%)

series357.0ms (0.2%)

simplify315.0ms (0.2%)

prune1.6s (0.8%)

localize50.0ms (0%)

rewrite252.0ms (0.1%)

series640.0ms (0.3%)

simplify435.0ms (0.2%)

prune5.5s (2.7%)

localize53.0ms (0%)

rewrite272.0ms (0.1%)

series631.0ms (0.3%)

simplify251.0ms (0.1%)

prune7.2s (3.5%)

localize32.0ms (0%)

rewrite185.0ms (0.1%)

series633.0ms (0.3%)

simplify434.0ms (0.2%)

prune11.8s (5.7%)

regimes35.0s (17.1%)

bsearch1.4min (40.6%)

simplify79.0ms (0%)

end0.0ms (0%)

sample54.9s (26.8%)

Profiling