Details

analyze65.0ms (2.2%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	37.5%	12.6%	7
56.2%	31.2%	12.6%	8
62.4%	18.7%	18.8%	9
65.6%	15.6%	18.8%	10
68.7%	9.4%	22%	11
70.2%	7.8%	22%	12
71.8%	4.7%	23.5%	13
72.6%	3.9%	23.5%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample13.0ms (0.5%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify112.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	268	10
1	268	10

prune2.0ms (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

0.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(.f64 (.f64 x y) (-.f64 1 y))
0.1b	(.f64 (.f64 x y) (-.f64 1 y))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441`
6×	`associate-r_binary64_359` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `cancel-sign-sub-inv_binary64_385` `pow1_binary64_480`
4×	`distribute-rgt-in_binary64_369` `add-cube-cbrt_binary64_454` `distribute-lft-in_binary64_368`
3×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
2×	`sub-neg_binary64_412` `difference-of-squares_binary64_388` `associate-*r/_binary64_361`
1×	`add-log-exp_binary64_458` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `-commutative_binary64_350` `associate-l*_binary64_360` `flip--_binary64_394`

Counts

1 → 31

Calls

2 calls:

9.0ms	(.f64 (.f64 x y) (-.f64 1 y))
0.0ms	(.f64 (.f64 x y) (-.f64 1 y))

series92.0ms (3.2%)

Counts

1 → 9

Calls

1 calls:

92.0ms

(*.f64 (*.f64 x y) (-.f64 1 y))

Compiler

Compiled 113 to 95 computations (15.9% saved)

simplify73.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4945	442
1	4945	442

prune40.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	5	41

Error

0.0b

Counts

41 → 5

Compiler

Compiled 436 to 205 computations (53% saved)

localize4.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.7b	(.f64 x (-.f64 y (.f64 y y)))
0.0b	(-.f64 y (*.f64 y y))
0.0b	(-.f64 y (*.f64 y y))
5.7b	(.f64 x (-.f64 y (.f64 y y)))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_441`
6×	`*-un-lft-identity_binary64_419`
5×	`associate-r_binary64_359`
4×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
3×	`sub-neg_binary64_412` `associate-l_binary64_360` `cancel-sign-sub-inv_binary64_385`
2×	`distribute-rgt-out--_binary64_373` `difference-of-squares_binary64_388` `distribute-rgt-in_binary64_369` `flip3--_binary64_423` `associate-*r/_binary64_361` `distribute-lft-in_binary64_368` `flip--_binary64_394`
1×	`pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `*-commutative_binary64_350` `diff-log_binary64_511`

Counts

2 → 40

Calls

4 calls:

8.0ms	(.f64 x (-.f64 y (.f64 y y)))
3.0ms	(-.f64 y (*.f64 y y))
0.0ms	(-.f64 y (*.f64 y y))
0.0ms	(.f64 x (-.f64 y (.f64 y y)))

series125.0ms (4.3%)

Counts

2 → 15

Calls

2 calls:

91.0ms	(.f64 x (-.f64 y (.f64 y y)))
34.0ms	(-.f64 y (*.f64 y y))

Compiler

Compiled 172 to 148 computations (14% saved)

simplify57.0ms (2%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5009	594

prune32.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	55	5	60

Error

0.0b

Counts

60 → 5

Compiler

Compiled 609 to 148 computations (75.7% saved)

localize8.0ms (0.3%)

Local error

Found 6 expressions with local error:

8.2b	(/.f64 (*.f64 x (-.f64 y (pow.f64 y 3))) (+.f64 1 y))
4.3b	(*.f64 x (-.f64 y (pow.f64 y 3)))
0.0b	(-.f64 y (pow.f64 y 3))
0.0b	(-.f64 y (pow.f64 y 3))
4.3b	(*.f64 x (-.f64 y (pow.f64 y 3)))
8.2b	(/.f64 (*.f64 x (-.f64 y (pow.f64 y 3))) (+.f64 1 y))

rewrite44.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cancel-sign-sub-inv_binary64_385`
32×	`add-sqr-sqrt_binary64_441`
26×	`*-un-lft-identity_binary64_419`
16×	`add-cube-cbrt_binary64_454`
13×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
11×	`unpow-prod-down_binary64_498` `cube-prod_binary64_447`
10×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
9×	`associate-r_binary64_359`
8×	`difference-of-squares_binary64_388`
5×	`add-log-exp_binary64_458` `unpow3_binary64_485` `sqr-pow_binary64_391` `pow1_binary64_480`
4×	`times-frac_binary64_425` `associate-r/_binary64_361` `associate-/r_binary64_363`
3×	`sub-neg_binary64_412` `cube-mult_binary64_449` `flip3--_binary64_423` `associate-l_binary64_360` `flip--_binary64_394`
2×	`distribute-rgt-out--_binary64_373` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `distribute-lft-out_binary64_370` `distribute-lft-out--_binary64_371` `associate-/r/_binary64_365` `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` `div-inv_binary64_416` `unswap-sqr_binary64_387` `-commutative_binary64_350` `frac-2neg_binary64_430` `flip-+_binary64_393` `diff-log_binary64_511` `associate-/l_binary64_364`

Counts

3 → 108

Calls

6 calls:

14.0ms	(*.f64 x (-.f64 y (pow.f64 y 3)))
14.0ms	(/.f64 (*.f64 x (-.f64 y (pow.f64 y 3))) (+.f64 1 y))
7.0ms	(-.f64 y (pow.f64 y 3))
0.0ms	(-.f64 y (pow.f64 y 3))
0.0ms	(/.f64 (*.f64 x (-.f64 y (pow.f64 y 3))) (+.f64 1 y))

series313.0ms (10.8%)

Counts

3 → 24

Calls

3 calls:

152.0ms	(/.f64 (*.f64 x (-.f64 y (pow.f64 y 3))) (+.f64 1 y))
115.0ms	(*.f64 x (-.f64 y (pow.f64 y 3)))
46.0ms	(-.f64 y (pow.f64 y 3))

Compiler

Compiled 405 to 333 computations (17.8% saved)

simplify74.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5138	1662

prune115.0ms (3.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	131	6	137

Error

0.0b

Counts

137 → 6

Compiler

Compiled 1956 to 1243 computations (36.5% saved)

localize9.0ms (0.3%)

Local error

Found 6 expressions with local error:

0.0b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
0.0b	(*.f64 x (+.f64 y (pow.f64 y 3/2)))
0.0b	(+.f64 y (pow.f64 y 3/2))
0.0b	(+.f64 y (pow.f64 y 3/2))
0.0b	(*.f64 x (+.f64 y (pow.f64 y 3/2)))
0.0b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))

rewrite36.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441`
13×	`associate-r_binary64_359`
12×	`cancel-sign-sub-inv_binary64_385`
10×	`add-cube-cbrt_binary64_454` `associate-*r/_binary64_361` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
9×	`sqrt-prod_binary64_435`
8×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
5×	`flip3-+_binary64_422` `add-log-exp_binary64_458` `flip-+_binary64_393`
4×	`pow-prod-down_binary64_490` `difference-of-squares_binary64_388` `frac-times_binary64_429` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360`
3×	`flip3--_binary64_423` `flip--_binary64_394`
2×	`associate-l/_binary64_362` `sub-neg_binary64_412` `distribute-lft-out_binary64_370` `distribute-lft-out--_binary64_371` `-commutative_binary64_350`
1×	`unswap-sqr_binary64_387` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

3 → 81

Calls

6 calls:

14.0ms	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
8.0ms	(*.f64 x (+.f64 y (pow.f64 y 3/2)))
7.0ms	(+.f64 y (pow.f64 y 3/2))
0.0ms	(+.f64 y (pow.f64 y 3/2))
0.0ms	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))

series372.0ms (12.8%)

Counts

3 → 19

Calls

3 calls:

158.0ms	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
150.0ms	(*.f64 x (+.f64 y (pow.f64 y 3/2)))
64.0ms	(+.f64 y (pow.f64 y 3/2))

Compiler

Compiled 455 to 378 computations (16.9% saved)

simplify94.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4949	1684
1	4949	1684

prune88.0ms (3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	1	2
Picked	0	1	1
Done	0	3	3
Total	100	6	106

Error

0.0b

Counts

106 → 6

Compiler

Compiled 1696 to 1015 computations (40.2% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	207	434
1	207	434

regimes115.0ms (3.9%)

Compiler: Compiled 864 to 680 computations (21.3% saved)

bsearch0.0ms (0%)

regimes61.0ms (2.1%)

Compiler: Compiled 40 to 52 computations (-30% saved)

bsearch22.0ms (0.8%)

Steps

Iters	Range		Point
9	0.023951678011460076	3575721.5253420603	1.0257109142889484
7	-17.981294520922052	-0.17450526090264706	-0.998902085042832

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes68.0ms (2.3%)

Compiler: Compiled 28 to 42 computations (-50% saved)

bsearch23.0ms (0.8%)

Steps

Iters	Range		Point
9	0.023951678011460076	3575721.5253420603	1.0257109142889484
7	-17.981294520922052	-0.17450526090264706	-0.998902085042832

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes17.0ms (0.6%)

Compiler: Compiled 16 to 32 computations (-100% saved)

bsearch0.0ms (0%)

regimes17.0ms (0.6%)

Accuracy

Total 0.1b remaining (82.6%)

Threshold costs 0.1b (82.6%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 58 to 38 computations (34.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	81	70
1	81	70

end0.0ms (0%)

sample774.0ms (26.6%)

Algorithm

1×

intervals

Results

191.0ms	8000×	body	128	valid
4.0ms	191×	body	128	invalid

Compiler

Compiled 338 to 269 computations (20.4% saved)

Pareto

0.5855355965391036

Details

analyze65.0ms (2.2%)

sample13.0ms (0.5%)

simplify112.0ms (3.8%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite11.0ms (0.4%)

series92.0ms (3.2%)

simplify73.0ms (2.5%)

prune40.0ms (1.4%)

localize4.0ms (0.2%)

rewrite14.0ms (0.5%)

series125.0ms (4.3%)

simplify57.0ms (2%)

prune32.0ms (1.1%)

localize8.0ms (0.3%)

rewrite44.0ms (1.5%)

series313.0ms (10.8%)

simplify74.0ms (2.6%)

prune115.0ms (3.9%)

localize9.0ms (0.3%)

rewrite36.0ms (1.2%)

series372.0ms (12.8%)

simplify94.0ms (3.2%)

prune88.0ms (3%)

simplify9.0ms (0.3%)

regimes115.0ms (3.9%)

bsearch0.0ms (0%)

regimes61.0ms (2.1%)

bsearch22.0ms (0.8%)

regimes68.0ms (2.3%)

bsearch23.0ms (0.8%)

regimes17.0ms (0.6%)

bsearch0.0ms (0%)

regimes17.0ms (0.6%)

bsearch4.0ms (0.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample774.0ms (26.6%)

Profiling