Details

analyze323.0ms (4.1%)

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
6.2%	93.6%	0.1%	6
15.6%	84.3%	0.1%	7
25%	74.9%	0.1%	8
37.4%	62.4%	0.1%	9
46.8%	53%	0.1%	10
55%	44.9%	0.1%	11
64.2%	35.7%	0.1%	12
70.3%	29.5%	0.1%	13
75.4%	24.4%	0.1%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample18.0ms (0.2%)

Algorithm

1×

intervals

Results

8.0ms	236×	body	128	valid
1.0ms	7×	body	1024	valid
0.0ms	6×	body	512	valid
0.0ms	5×	body	256	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify97.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	149	13
1	149	13

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
0.0b	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64_3868`
3×	`sum-log_binary64_3920` `*-un-lft-identity_binary64_3829`
1×	`flip3-+_binary64_3832` `add-exp-log_binary64_3867` `flip-+_binary64_3803` `add-cbrt-cube_binary64_3865` `add-cube-cbrt_binary64_3864` `associate-+r+_binary64_3761` `pow1_binary64_3890` `distribute-lft-out_binary64_3780` `+-commutative_binary64_3759` `add-sqr-sqrt_binary64_3851`

Counts

1 → 14

Calls

2 calls:

8.0ms	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
0.0ms	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))

series124.0ms (1.6%)

Counts

1 → 18

Calls

1 calls:

124.0ms

(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))

Compiler

Compiled 193 to 208 computations (-7.8% saved)

simplify61.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5241	419

prune28.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	3	33

Error

0.0b

Counts

33 → 3

Compiler

Compiled 385 to 201 computations (47.8% saved)

localize9.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
0.0b	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
0.0b	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
0.0b	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
0.0b	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
0.0b	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
0.0b	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
0.3b	(.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))) (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))

rewrite57.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`sqrt-prod_binary64_3845` `*-un-lft-identity_binary64_3829`
30×	`add-sqr-sqrt_binary64_3851`
21×	`pow1_binary64_3890`
16×	`sqrt-div_binary64_3846`
14×	`add-cube-cbrt_binary64_3864`
11×	`swap-sqr_binary64_3796`
10×	`pow1/2_binary64_3909` `sqrt-pow1_binary64_3847`
9×	`flip3-+_binary64_3832` `add-log-exp_binary64_3868` `flip-+_binary64_3803` `distribute-lft-out_binary64_3780`
7×	`associate-r_binary64_3769` `associate-l_binary64_3770`
6×	`add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865`
5×	`pow-prod-up_binary64_3899`
4×	`unswap-sqr_binary64_3797` `rem-sqrt-square_binary64_3842` `frac-times_binary64_3839`
3×	`pow-prod-down_binary64_3900` `sum-log_binary64_3920` `pow-sqr_binary64_3802`
2×	`associate-l/_binary64_3772` `associate-r/_binary64_3771`
1×	`sqr-abs_binary64_3844` `prod-exp_binary64_3878` `associate-+r+_binary64_3761` `rem-square-sqrt_binary64_3841` `+-commutative_binary64_3759` `*-commutative_binary64_3760` `pow-plus_binary64_3892` `cbrt-unprod_binary64_3862` `pow2_binary64_3910` `sqrt-unprod_binary64_3849`

Counts

4 → 109

Calls

8 calls:

21.0ms	(.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))) (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
10.0ms	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
8.0ms	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
7.0ms	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
0.0ms	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))

series439.0ms (5.6%)

Counts

4 → 60

Calls

4 calls:

134.0ms	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
133.0ms	(.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))) (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
87.0ms	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
84.0ms	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))

Compiler

Compiled 1826 to 1520 computations (16.8% saved)

simplify99.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5246	2810

prune172.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	167	5	172

Error

0.0b

Counts

172 → 5

Compiler

Compiled 3640 to 2015 computations (44.6% saved)

localize15.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
0.0b	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
0.0b	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
0.0b	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
0.2b	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
0.2b	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
0.2b	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
0.4b	(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))) 4)

rewrite47.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64_3860`
22×	`*-un-lft-identity_binary64_3829`
16×	`sqrt-prod_binary64_3845`
14×	`add-cube-cbrt_binary64_3864` `add-sqr-sqrt_binary64_3851`
10×	`unpow-prod-down_binary64_3908`
6×	`cbrt-div_binary64_3861` `sqrt-div_binary64_3846`
5×	`add-exp-log_binary64_3867` `pow1_binary64_3890`
4×	`add-log-exp_binary64_3868` `add-cbrt-cube_binary64_3865` `distribute-lft-out_binary64_3780` `pow1/3_binary64_3911`
3×	`flip3-+_binary64_3832` `flip-+_binary64_3803` `pow-unpow_binary64_3906`
2×	`pow-pow_binary64_3901`
1×	`pow-exp_binary64_3897` `sqr-pow_binary64_3801` `pow-to-exp_binary64_3898`

Counts

4 → 76

Calls

8 calls:

11.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))) 4)
10.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
8.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
8.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
0.0ms	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))

series1.2s (15.7%)

Counts

4 → 48

Calls

4 calls:

720.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))) 4)
170.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
167.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
166.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))

Compiler

Compiled 4832 to 3888 computations (19.5% saved)

simplify103.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4894	2795
1	4894	2795

prune252.0ms (3.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	123	6	129

Error

0.0b

Counts

129 → 6

Compiler

Compiled 5320 to 3325 computations (37.5% saved)

localize21.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
0.0b	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
0.0b	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
0.0b	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
0.3b	(cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))
0.3b	(cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))
0.4b	(pow.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))) 4)
0.4b	(pow.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))) 4)

rewrite61.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`sqrt-prod_binary64_3845`
40×	`cbrt-prod_binary64_3860`
28×	`*-un-lft-identity_binary64_3829`
26×	`unpow-prod-down_binary64_3908`
20×	`add-cube-cbrt_binary64_3864` `add-sqr-sqrt_binary64_3851`
8×	`sqrt-div_binary64_3846`
6×	`add-exp-log_binary64_3867` `pow1_binary64_3890` `pow-unpow_binary64_3906`
4×	`add-log-exp_binary64_3868` `add-cbrt-cube_binary64_3865` `pow-pow_binary64_3901` `distribute-lft-out_binary64_3780` `pow1/3_binary64_3911` `cbrt-div_binary64_3861`
2×	`flip3-+_binary64_3832` `flip-+_binary64_3803` `pow-exp_binary64_3897` `sqr-pow_binary64_3801` `pow-to-exp_binary64_3898`

Counts

4 → 96

Calls

8 calls:

14.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))) 4)
12.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))) 4)
9.0ms	(cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))
9.0ms	(cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))
0.0ms	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))

series1.8s (22.8%)

Counts

4 → 50

Calls

4 calls:

681.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))) 4)
670.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))) 4)
214.0ms	(cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))
211.0ms	(cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))

Compiler

Compiled 6540 to 5096 computations (22.1% saved)

simplify81.0ms (1%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4907	3994
1	4907	3994

prune459.0ms (5.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	146	6	152

Error

0.0b

Counts

152 → 6

Compiler

Compiled 8674 to 5583 computations (35.6% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	161	748
1	161	748

regimes141.0ms (1.8%)

Compiler: Compiled 1479 to 1128 computations (23.7% saved)

bsearch0.0ms (0%)

regimes102.0ms (1.3%)

Compiler: Compiled 87 to 144 computations (-65.5% saved)

bsearch31.0ms (0.4%)

Steps

Iters	Range		Point
9	122249519.29068768	386186386728203.6	32332440428.776733
9	-14353921522567776.0	-1909013704.1252432	-4429505744626565.5

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes130.0ms (1.7%)

Compiler: Compiled 66 to 123 computations (-86.4% saved)

bsearch78.0ms (1%)

Steps

Iters	Range		Point
4	5.3551259046388595e+175	1.0318434393472616e+176	5.447935918106146e+175
8	1.5545830097785987e+142	3.3497547023307558e+146	9.231738273350996e+145
10	40.24951949853529	144708799448604.4	1815967673.5985475
8	-2.172158571748429e-50	-5.216222961197243e-54	-2.1300916330879537e-50
8	-5.1738840681863654e+42	-4.257065944874858e+39	-7.556894985165785e+39
9	-1.8034523122519494e+85	-5.062311207152137e+77	-1.5746241265694534e+79

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes134.0ms (1.7%)

Compiler: Compiled 51 to 108 computations (-111.8% saved)

bsearch47.0ms (0.6%)

Steps

Iters	Range		Point
6	4.41699078116414e+232	2.2797192969123643e+233	4.462965352906481e+232
8	3.1053485276793388e+178	1.2127100983774818e+183	2.3009499683882742e+182
8	2.260746488984492e+88	2.2307521774780793e+91	7.003794247188141e+89
8	-2.432923344120338e+123	-3.6086955590216116e+120	-1.873162488547066e+121

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes162.0ms (2.1%)

Compiler: Compiled 36 to 90 computations (-150% saved)

bsearch150.0ms (1.9%)

Steps

Iters	Range		Point
4	5.3551259046388595e+175	1.0318434393472616e+176	6.190416025844443e+175
8	1.5545830097785987e+142	3.3497547023307558e+146	3.2935562786785273e+146
8	1.4978985995502138e+88	1.9850683848393153e+92	2.7248247480791156e+91
7	1.416577397025157e+30	6.0075133485330095e+31	1.8149576817243297e+30
10	40.24951949853529	144708799448604.4	15344855150607.389
6	5.407165790022725e-45	4.814345385042591e-44	7.825255972969949e-45
9	7.721677075432995e-174	1.9620315449333778e-168	7.220278433245301e-173
9	6.772901666763102e-288	2.3401240358259833e-281	9.718539567503092e-284
9	-3.7359247727352837e-256	-2.5577223801631075e-262	-6.2243467008708644e-260
8	-8.959300600723279e-146	-8.276611906231829e-150	-2.1814180357360506e-147
8	-5.1738840681863654e+42	-4.257065944874858e+39	-2.1595592120073467e+42
9	-1.8034523122519494e+85	-5.062311207152137e+77	-3.2253954486367324e+81

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes94.0ms (1.2%)

Compiler: Compiled 27 to 75 computations (-177.8% saved)

bsearch30.0ms (0.4%)

Steps

Iters	Range		Point
11	31793386114800564.0	2.4327253727475667e+40	5.701171549051062e+26
9	-14353921522567776.0	-1909013704.1252432	-3091657514221.233

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes30.0ms (0.4%)

Compiler: Compiled 18 to 63 computations (-250% saved)

bsearch0.0ms (0%)

regimes26.0ms (0.3%)

Compiler: Compiled 15 to 54 computations (-260% saved)

bsearch0.0ms (0%)

regimes22.0ms (0.3%)

Accuracy

Total 0.0b remaining (52.6%)

Threshold costs 0.0b (52.6%)

Compiler

Compiled 12 to 42 computations (-250% saved)

bsearch11.0ms (0.1%)

Compiler: Compiled 227 to 152 computations (33% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	192	269
1	192	269

end0.0ms (0%)

sample1.1s (14%)

Algorithm

1×

intervals

Results

196.0ms	7414×	body	128	valid
20.0ms	220×	body	1024	valid
15.0ms	175×	body	512	valid
10.0ms	90×	body	2048	valid
8.0ms	101×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 687 to 526 computations (23.4% saved)

Pareto

0.29868883778537103

Details

analyze323.0ms (4.1%)

sample18.0ms (0.2%)

simplify97.0ms (1.2%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

rewrite10.0ms (0.1%)

series124.0ms (1.6%)

simplify61.0ms (0.8%)

prune28.0ms (0.4%)

localize9.0ms (0.1%)

rewrite57.0ms (0.7%)

series439.0ms (5.6%)

simplify99.0ms (1.3%)

prune172.0ms (2.2%)

localize15.0ms (0.2%)

rewrite47.0ms (0.6%)

series1.2s (15.7%)

simplify103.0ms (1.3%)

prune252.0ms (3.2%)

localize21.0ms (0.3%)

rewrite61.0ms (0.8%)

series1.8s (22.8%)

simplify81.0ms (1%)

prune459.0ms (5.9%)

simplify11.0ms (0.1%)

regimes141.0ms (1.8%)

bsearch0.0ms (0%)

regimes102.0ms (1.3%)

bsearch31.0ms (0.4%)

regimes130.0ms (1.7%)

bsearch78.0ms (1%)

regimes134.0ms (1.7%)

bsearch47.0ms (0.6%)

regimes162.0ms (2.1%)

bsearch150.0ms (1.9%)

regimes94.0ms (1.2%)

bsearch30.0ms (0.4%)

regimes30.0ms (0.4%)

bsearch0.0ms (0%)

regimes26.0ms (0.3%)

bsearch0.0ms (0%)

regimes22.0ms (0.3%)

bsearch11.0ms (0.1%)

simplify9.0ms (0.1%)

end0.0ms (0%)

sample1.1s (14%)

Profiling