Details

analyze483.0ms (5.6%)

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
21.8%	78%	0.1%	6
26.5%	73.3%	0.1%	7
32%	67.9%	0.1%	8
46.4%	52.7%	0.9%	9
50.9%	47.2%	1.9%	10
54.3%	43.3%	2.4%	11
62.1%	32.5%	5.4%	12
64.3%	28.1%	7.6%	13
66.3%	24.6%	9.2%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample22.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
2.0ms	45×	body	128	invalid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify214.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	738	15
1	738	15

prune5.0ms (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 32 to 28 computations (12.5% saved)

localize9.0ms (0.1%)

Local error

Found 6 expressions with local error:

4.1b	(*.f64 (/.f64 x y) z)
0.0b	(/.f64 (+.f64 x 4) y)
0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
0.0b	(/.f64 (+.f64 x 4) y)
4.1b	(*.f64 (/.f64 x y) z)

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_419`
25×	`add-sqr-sqrt_binary64_441`
22×	`times-frac_binary64_425`
20×	`add-cube-cbrt_binary64_454`
13×	`associate-l_binary64_360`
10×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
5×	`add-log-exp_binary64_458` `pow1_binary64_480`
4×	`distribute-lft-out_binary64_370` `associate-/l*_binary64_364`
3×	`associate-l/_binary64_362` `associate-r_binary64_359` `associate-/r_binary64_363`
2×	`div-inv_binary64_416` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `clear-num_binary64_418` `sub-neg_binary64_412` `flip3--_binary64_423` `*-commutative_binary64_350` `frac-2neg_binary64_430` `flip-+_binary64_393` `diff-log_binary64_511` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385` `sub-div_binary64_426` `frac-sub_binary64_428`

Counts

3 → 79

Calls

6 calls:

15.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
7.0ms	(*.f64 (/.f64 x y) z)
6.0ms	(/.f64 (+.f64 x 4) y)
0.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
0.0ms	(/.f64 (+.f64 x 4) y)

series601.0ms (6.9%)

Counts

3 → 33

Calls

3 calls:

343.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
167.0ms	(*.f64 (/.f64 x y) z)
91.0ms	(/.f64 (+.f64 x 4) y)

Compiler

Compiled 722 to 601 computations (16.8% saved)

simplify105.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5171	1334

prune235.0ms (2.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	107	5	112
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	108	6	114

Error

0.0b

Counts

114 → 6

Compiler

Compiled 1878 to 909 computations (51.6% saved)

localize18.0ms (0.2%)

Local error

Found 6 expressions with local error:

4.1b	(*.f64 (/.f64 x y) z)
0.0b	(+.f64 (/.f64 x y) (/.f64 4 y))
0.0b	(-.f64 (+.f64 (/.f64 x y) (/.f64 4 y)) (*.f64 (/.f64 x y) z))
0.0b	(-.f64 (+.f64 (/.f64 x y) (/.f64 4 y)) (*.f64 (/.f64 x y) z))
0.0b	(+.f64 (/.f64 x y) (/.f64 4 y))
4.1b	(*.f64 (/.f64 x y) z)

rewrite79.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_419`
18×	`add-sqr-sqrt_binary64_441`
16×	`times-frac_binary64_425`
13×	`add-cube-cbrt_binary64_454` `associate-l_binary64_360`
10×	`add-log-exp_binary64_458`
8×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
5×	`pow1_binary64_480`
4×	`associate-*l/_binary64_362` `distribute-lft-out_binary64_370`
3×	`div-inv_binary64_416` `associate-r_binary64_359` `frac-sub_binary64_428`
2×	`flip3-+_binary64_422` `frac-add_binary64_427` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `sum-log_binary64_510` `flip-+_binary64_393` `diff-log_binary64_511`
1×	`pow-prod-down_binary64_490` `associate--l+_binary64_356` `sub-neg_binary64_412` `flip3--_binary64_423` `*-commutative_binary64_350` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385` `distribute-rgt-out_binary64_372` `+-commutative_binary64_349` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

3 → 66

Calls

6 calls:

32.0ms	(-.f64 (+.f64 (/.f64 x y) (/.f64 4 y)) (*.f64 (/.f64 x y) z))
23.0ms	(+.f64 (/.f64 x y) (/.f64 4 y))
13.0ms	(*.f64 (/.f64 x y) z)
0.0ms	(-.f64 (+.f64 (/.f64 x y) (/.f64 4 y)) (*.f64 (/.f64 x y) z))
0.0ms	(+.f64 (/.f64 x y) (/.f64 4 y))

series668.0ms (7.7%)

Counts

3 → 33

Calls

3 calls:

381.0ms	(-.f64 (+.f64 (/.f64 x y) (/.f64 4 y)) (*.f64 (/.f64 x y) z))
173.0ms	(*.f64 (/.f64 x y) z)
113.0ms	(+.f64 (/.f64 x y) (/.f64 4 y))

Compiler

Compiled 758 to 619 computations (18.3% saved)

simplify93.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4971	1351
1	4971	1351

prune121.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	98	7	105

Error

Counts

105 → 7

Compiler

Compiled 1872 to 808 computations (56.8% saved)

localize23.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y)))
0.3b	(*.f64 z (cbrt.f64 (/.f64 x y)))
0.0b	(/.f64 (+.f64 x 4) y)
0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y)))))
1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))
10.7b	(cbrt.f64 (/.f64 x y))
10.7b	(cbrt.f64 (/.f64 x y))
10.7b	(cbrt.f64 (/.f64 x y))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`cbrt-prod_binary64_450`
27×	`times-frac_binary64_425`
25×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
16×	`add-exp-log_binary64_457` `pow1_binary64_480`
15×	`cbrt-div_binary64_451`
10×	`add-cbrt-cube_binary64_455`
8×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
7×	`associate-*r/_binary64_361`
5×	`associate-*l/_binary64_362` `frac-times_binary64_429`
4×	`add-log-exp_binary64_458`
3×	`pow1/3_binary64_501` `div-inv_binary64_416`
1×	`associate-r_binary64_359` `-commutative_binary64_350` `associate-l*_binary64_360`

Counts

4 → 95

Calls

8 calls:

16.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))
3.0ms	(cbrt.f64 (/.f64 x y))
2.0ms	(cbrt.f64 (/.f64 x y))
2.0ms	(cbrt.f64 (/.f64 x y))
0.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y)))))

series1.1s (12.7%)

Counts

4 → 27

Calls

4 calls:

344.0ms	(cbrt.f64 (/.f64 x y))
271.0ms	(cbrt.f64 (/.f64 x y))
270.0ms	(cbrt.f64 (/.f64 x y))
213.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))

Compiler

Compiled 1336 to 1012 computations (24.3% saved)

simplify106.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5044	1461

prune174.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	122	7	129

Error

Counts

129 → 7

Compiler

Compiled 3110 to 1028 computations (66.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.6b	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)
0.0b	(-.f64 (+.f64 x 4) (*.f64 x z))
0.0b	(-.f64 (+.f64 x 4) (*.f64 x z))
2.6b	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
9×	`times-frac_binary64_425`
7×	`add-log-exp_binary64_458`
4×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`associate-/r_binary64_363` `associate-/l_binary64_364`
2×	`flip3--_binary64_423` `diff-log_binary64_511` `flip--_binary64_394` `pow1_binary64_480` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `associate--l+_binary64_356` `sub-neg_binary64_412` `div-inv_binary64_416` `sum-log_binary64_510` `frac-2neg_binary64_430` `cancel-sign-sub-inv_binary64_385` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `div-sub_binary64_424`

Counts

2 → 44

Calls

4 calls:

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

series328.0ms (3.8%)

Counts

2 → 27

Calls

2 calls:

233.0ms	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)
94.0ms	(-.f64 (+.f64 x 4) (*.f64 x z))

Compiler

Compiled 464 to 416 computations (10.3% saved)

simplify93.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4960	1108
1	4960	1108

prune93.0ms (1.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	71	7	78

Error

Counts

78 → 7

Compiler

Compiled 1022 to 536 computations (47.6% saved)

simplify25.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	630	777
1	630	777

regimes294.0ms (3.4%)

Accuracy

Total 0.2b remaining (97.2%)

Threshold costs 0.2b (97.2%)

Compiler

Compiled 1527 to 1185 computations (22.4% saved)

bsearch59.0ms (0.7%)

Steps

Iters	Range		Point
5	4.694686199164076e+24	1.5642149181224514e+25	4.7579917362672096e+24
7	-1.888312890188662e-13	-2.6617015160681638e-15	-2.8755087116004516e-15

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	119	99
1	119	99

end0.0ms (0%)

sample3.6s (41.5%)

Algorithm

1×

intervals

Results

438.0ms	8000×	body	128	valid
66.0ms	1247×	body	128	invalid

Compiler

Compiled 1666 to 1259 computations (24.4% saved)

Pareto

0.3414282225432822

Details

analyze483.0ms (5.6%)

sample22.0ms (0.3%)

simplify214.0ms (2.5%)

prune5.0ms (0.1%)

localize9.0ms (0.1%)

rewrite41.0ms (0.5%)

series601.0ms (6.9%)

simplify105.0ms (1.2%)

prune235.0ms (2.7%)

localize18.0ms (0.2%)

rewrite79.0ms (0.9%)

series668.0ms (7.7%)

simplify93.0ms (1.1%)

prune121.0ms (1.4%)

localize23.0ms (0.3%)

rewrite38.0ms (0.4%)

series1.1s (12.7%)

simplify106.0ms (1.2%)

prune174.0ms (2%)

localize13.0ms (0.1%)

rewrite19.0ms (0.2%)

series328.0ms (3.8%)

simplify93.0ms (1.1%)

prune93.0ms (1.1%)

simplify25.0ms (0.3%)

regimes294.0ms (3.4%)

bsearch59.0ms (0.7%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample3.6s (41.5%)

Profiling