Details

analyze347.0ms (6.1%)

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
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
40.6%	56.9%	2.5%	9
46%	49.5%	4.4%	10
50.3%	44.9%	4.8%	11
60.3%	30.5%	9.2%	12
62.9%	25.7%	11.4%	13
65.2%	23.2%	11.7%	14

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample20.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	32×	body	128	invalid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify153.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4743	13
1	4743	13

prune4.0ms (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

0.0b

Counts

2 → 2

Compiler

Compiled 31 to 30 computations (3.2% saved)

localize10.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_5875` `add-log-exp_binary64_5914`
8×	`add-exp-log_binary64_5913` `add-sqr-sqrt_binary64_5897` `add-cbrt-cube_binary64_5911`
6×	`add-cube-cbrt_binary64_5910`
3×	`associate-/r*_binary64_5819` `times-frac_binary64_5881` `cancel-sign-sub-inv_binary64_5841` `pow1_binary64_5936`
2×	`cbrt-undiv_binary64_5909` `diff-log_binary64_5967` `associate-/l/_binary64_5822` `div-exp_binary64_5926` `associate-*r/_binary64_5817` `sum-log_binary64_5966` `flip3--_binary64_5879` `flip--_binary64_5850`
1×	`distribute-lft-out--_binary64_5827` `flip-+_binary64_5849` `distribute-lft-out_binary64_5826` `flip3-+_binary64_5878` `div-inv_binary64_5872` `cbrt-unprod_binary64_5908` `sub-neg_binary64_5868` `associate-/l*_binary64_5820` `difference-of-squares_binary64_5844` `frac-2neg_binary64_5886` `+-commutative_binary64_5805` `prod-exp_binary64_5924` `clear-num_binary64_5874` `associate--l+_binary64_5812`

Counts

3 → 53

Calls

6 calls:

12.0ms	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y)
8.0ms	(-.f64 (+.f64 x (*.f64 y 1/4)) z)
7.0ms	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
0.0ms	(-.f64 (+.f64 x (*.f64 y 1/4)) z)
0.0ms	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))

series537.0ms (9.5%)

Counts

3 → 54

Calls

3 calls:

222.0ms	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y)
212.0ms	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
103.0ms	(-.f64 (+.f64 x (*.f64 y 1/4)) z)

Compiler

Compiled 929 to 903 computations (2.8% saved)

simplify62.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5164	1389

prune102.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	106	3	109

Error

Counts

109 → 3

Compiler

Compiled 1475 to 938 computations (36.4% saved)

localize7.0ms (0.1%)

Local error

Found 6 expressions with local error:

0.0b	(/.f64 (-.f64 x z) y)
0.0b	(*.f64 4 (/.f64 (-.f64 x z) y))
0.0b	(+.f64 (*.f64 4 (/.f64 (-.f64 x z) y)) 2)
0.0b	(+.f64 (*.f64 4 (/.f64 (-.f64 x z) y)) 2)
0.0b	(*.f64 4 (/.f64 (-.f64 x z) y))
0.0b	(/.f64 (-.f64 x z) y)

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64_5897`
37×	`*-un-lft-identity_binary64_5875`
31×	`times-frac_binary64_5881`
23×	`add-cube-cbrt_binary64_5910`
19×	`associate-r_binary64_5815`
10×	`add-exp-log_binary64_5913` `add-cbrt-cube_binary64_5911`
7×	`distribute-lft-out--_binary64_5827` `difference-of-squares_binary64_5844`
5×	`associate-/l*_binary64_5820` `pow1_binary64_5936` `add-log-exp_binary64_5914`
3×	`associate-/r_binary64_5819` `associate-l*_binary64_5816`
2×	`cbrt-undiv_binary64_5909` `div-inv_binary64_5872` `cbrt-unprod_binary64_5908` `associate-/l/_binary64_5822` `div-exp_binary64_5926` `unswap-sqr_binary64_5843` `prod-exp_binary64_5924`
1×	`flip-+_binary64_5849` `flip3-+_binary64_5878` `div-sub_binary64_5880` `pow-prod-down_binary64_5946` `frac-2neg_binary64_5886` `associate-r/_binary64_5817` `sum-log_binary64_5966` `+-commutative_binary64_5805` `flip3--_binary64_5879` `-commutative_binary64_5806` `clear-num_binary64_5874` `flip--_binary64_5850`

Counts

3 → 87

Calls

6 calls:

11.0ms	(*.f64 4 (/.f64 (-.f64 x z) y))
11.0ms	(+.f64 (*.f64 4 (/.f64 (-.f64 x z) y)) 2)
7.0ms	(/.f64 (-.f64 x z) y)
0.0ms	(+.f64 (*.f64 4 (/.f64 (-.f64 x z) y)) 2)
0.0ms	(*.f64 4 (/.f64 (-.f64 x z) y))

series472.0ms (8.3%)

Counts

3 → 48

Calls

3 calls:

208.0ms	(+.f64 (*.f64 4 (/.f64 (-.f64 x z) y)) 2)
149.0ms	(*.f64 4 (/.f64 (-.f64 x z) y))
114.0ms	(/.f64 (-.f64 x z) y)

Compiler

Compiled 781 to 763 computations (2.3% saved)

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4925	1628
1	4925	1628

prune87.0ms (1.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	135	3	138

Error

Counts

138 → 3

Compiler

Compiled 1744 to 774 computations (55.6% saved)

localize9.0ms (0.2%)

Local error

Found 6 expressions with local error:

0.1b	(/.f64 (/.f64 (-.f64 x z) (sqrt.f64 y)) (sqrt.f64 y))
0.1b	(/.f64 (-.f64 x z) (sqrt.f64 y))
0.0b	(*.f64 4 (/.f64 (/.f64 (-.f64 x z) (sqrt.f64 y)) (sqrt.f64 y)))
0.0b	(*.f64 4 (/.f64 (/.f64 (-.f64 x z) (sqrt.f64 y)) (sqrt.f64 y)))
0.1b	(/.f64 (-.f64 x z) (sqrt.f64 y))
0.1b	(/.f64 (/.f64 (-.f64 x z) (sqrt.f64 y)) (sqrt.f64 y))

rewrite179.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

838×	`times-frac_binary64_5881`
577×	`add-sqr-sqrt_binary64_5897`
553×	`*-un-lft-identity_binary64_5875`
425×	`sqrt-prod_binary64_5891`
383×	`add-cube-cbrt_binary64_5910`
208×	`associate-r_binary64_5815`
85×	`distribute-lft-out--_binary64_5827` `difference-of-squares_binary64_5844`
39×	`associate-/l*_binary64_5820`
19×	`add-exp-log_binary64_5913` `add-cbrt-cube_binary64_5911`
16×	`div-inv_binary64_5872`
12×	`associate-/r*_binary64_5819`
7×	`cbrt-undiv_binary64_5909` `div-exp_binary64_5926` `unswap-sqr_binary64_5843`
5×	`pow1_binary64_5936`
3×	`div-sub_binary64_5880` `cbrt-unprod_binary64_5908` `associate-/l/_binary64_5822` `associate-l_binary64_5816` `prod-exp_binary64_5924` `add-log-exp_binary64_5914`
2×	`frac-2neg_binary64_5886` `clear-num_binary64_5874`
1×	`pow-prod-down_binary64_5946` `associate-r/_binary64_5817` `flip3--_binary64_5879` `-commutative_binary64_5806` `flip--_binary64_5850`

Counts

3 → 550

Calls

6 calls:

64.0ms	(*.f64 4 (/.f64 (/.f64 (-.f64 x z) (sqrt.f64 y)) (sqrt.f64 y)))
17.0ms	(/.f64 (/.f64 (-.f64 x z) (sqrt.f64 y)) (sqrt.f64 y))
8.0ms	(/.f64 (-.f64 x z) (sqrt.f64 y))
0.0ms	(*.f64 4 (/.f64 (/.f64 (-.f64 x z) (sqrt.f64 y)) (sqrt.f64 y)))
0.0ms	(/.f64 (-.f64 x z) (sqrt.f64 y))

series421.0ms (7.4%)

Counts

3 → 45

Calls

3 calls:

157.0ms	(/.f64 (-.f64 x z) (sqrt.f64 y))
146.0ms	(*.f64 4 (/.f64 (/.f64 (-.f64 x z) (sqrt.f64 y)) (sqrt.f64 y)))
118.0ms	(/.f64 (/.f64 (-.f64 x z) (sqrt.f64 y)) (sqrt.f64 y))

Compiler

Compiled 992 to 924 computations (6.9% saved)

simplify179.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

595 → 595

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5209	12629

prune547.0ms (9.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	595	0	595
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	595	3	598

Error

Counts

598 → 3

Compiler

Compiled 13217 to 3785 computations (71.4% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	323
1	102	323

regimes198.0ms (3.5%)

Compiler: Compiled 1241 to 1257 computations (-1.3% saved)

bsearch0.0ms (0%)

regimes54.0ms (1%)

Compiler: Compiled 180 to 246 computations (-36.7% saved)

bsearch0.0ms (0%)

regimes143.0ms (2.5%)

Compiler: Compiled 153 to 219 computations (-43.1% saved)

bsearch76.0ms (1.3%)

Steps

Iters	Range		Point
9	5.172757940027439e+101	3.721457279265766e+106	1.4475075010385267e+104
6	4.2752277346347696e+55	2.052579210411766e+56	1.3189226260259516e+56
9	9.978864797351856e+19	1.8996878515088723e+26	5.874341237735803e+21
9	-1.1289324044013317e+18	-2958566582.3121223	-1.0589087533869587e+17

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes100.0ms (1.8%)

Compiler: Compiled 90 to 147 computations (-63.3% saved)

bsearch30.0ms (0.5%)

Steps

Iters	Range		Point
8	1.4311209921530756e+90	2.3787445977051323e+93	2.409903717142705e+92
7	-3.4582152245416053e+40	-2.5339967081610928e+38	-5.0165204552405096e+39

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes81.0ms (1.4%)

Compiler: Compiled 69 to 126 computations (-82.6% saved)

bsearch49.0ms (0.9%)

Steps

Iters	Range		Point
10	1.1102052046813721e+82	9.639452968534987e+95	9.10570446057653e+88
10	-2.231068753325641e+171	-5.885949678034317e+156	-1.1277552894287812e+164

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes144.0ms (2.5%)

Compiler: Compiled 48 to 102 computations (-112.5% saved)

bsearch86.0ms (1.5%)

Steps

Iters	Range		Point
7	2.472572216886423e+88	1.4311209921530756e+90	1.2681581838857139e+90
8	7.936855791329761e-23	2.2544256231384656e-18	3.253206934821027e-20
11	-8.151738850844899e-207	-7.714713583451253e-239	-9.265674590328694e-238
7	-3.4582152245416053e+40	-2.5339967081610928e+38	-2.8642440419412266e+38

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes81.0ms (1.4%)

Compiler: Compiled 33 to 84 computations (-154.5% saved)

bsearch33.0ms (0.6%)

Steps

Iters	Range		Point
8	1.4311209921530756e+90	2.3787445977051323e+93	1.4524766039954287e+90
10	-3.4466106640752266e+36	-2.7243413876519367e+20	-1.279966576344936e+28

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes29.0ms (0.5%)

Compiler: Compiled 18 to 66 computations (-266.7% saved)

bsearch0.0ms (0%)

regimes27.0ms (0.5%)

Accuracy

Total 0.0b remaining (73.5%)

Threshold costs 0.0b (73.5%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch9.0ms (0.2%)

Compiler: Compiled 173 to 143 computations (17.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	110	209
1	110	209

end0.0ms (0%)

sample1.2s (22%)

Algorithm

1×

intervals

Results

297.0ms	8000×	body	128	valid
41.0ms	1000×	body	128	invalid

Compiler

Compiled 379 to 364 computations (4% saved)

Pareto

0.26665955911742617

Details

analyze347.0ms (6.1%)

sample20.0ms (0.4%)

simplify153.0ms (2.7%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite31.0ms (0.6%)

series537.0ms (9.5%)

simplify62.0ms (1.1%)

prune102.0ms (1.8%)

localize7.0ms (0.1%)

rewrite36.0ms (0.6%)

series472.0ms (8.3%)

simplify73.0ms (1.3%)

prune87.0ms (1.5%)

localize9.0ms (0.2%)

rewrite179.0ms (3.1%)

series421.0ms (7.4%)

simplify179.0ms (3.2%)

prune547.0ms (9.6%)

simplify6.0ms (0.1%)

regimes198.0ms (3.5%)

bsearch0.0ms (0%)

regimes54.0ms (1%)

bsearch0.0ms (0%)

regimes143.0ms (2.5%)

bsearch76.0ms (1.3%)

regimes100.0ms (1.8%)

bsearch30.0ms (0.5%)

regimes81.0ms (1.4%)

bsearch49.0ms (0.9%)

regimes144.0ms (2.5%)

bsearch86.0ms (1.5%)

regimes81.0ms (1.4%)

bsearch33.0ms (0.6%)

regimes29.0ms (0.5%)

bsearch0.0ms (0%)

regimes27.0ms (0.5%)

bsearch9.0ms (0.2%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.2s (22%)

Profiling