Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 15 to 13 computations (13.3% saved)

sample16.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 29 to 26 computations (10.3% saved)

simplify376.0ms (12.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (281.0ms)

Iter	Nodes	Cost
0	5830	21

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 28 to 24 computations (14.3% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))
0.0b	(*.f64 6 (-.f64 x 1))
0.1b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))

rewrite37.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_22606`
12×	`*-un-lft-identity_binary64_22584`
10×	`add-cbrt-cube_binary64_22620` `add-exp-log_binary64_22622`
9×	`add-cube-cbrt_binary64_22619`
8×	`add-log-exp_binary64_22623`
7×	`associate-r_binary64_22524`
6×	`cancel-sign-sub-inv_binary64_22550`
5×	`pow1_binary64_22645`
4×	`associate-*r/_binary64_22526` `distribute-rgt-in_binary64_22534` `distribute-lft-in_binary64_22533`
3×	`associate-/r_binary64_22528` `associate-l*_binary64_22525` `sum-log_binary64_22675` `times-frac_binary64_22590`
2×	`flip3-+_binary64_22587` `associate-/l/_binary64_22531` `sub-neg_binary64_22577` `cbrt-undiv_binary64_22618` `difference-of-squares_binary64_22553` `div-exp_binary64_22635` `cbrt-unprod_binary64_22617` `prod-exp_binary64_22633` `flip--_binary64_22559` `associate-/r/_binary64_22530` `flip-+_binary64_22558` `flip3--_binary64_22588`
1×	`difference-of-sqr-1_binary64_22554` `distribute-lft-out--_binary64_22536` `associate-/l_binary64_22529` `div-inv_binary64_22581` `clear-num_binary64_22583` `+-commutative_binary64_22514` `associate-+l+_binary64_22517` `-commutative_binary64_22515` `frac-2neg_binary64_22595` `pow-prod-down_binary64_22655` `unswap-sqr_binary64_22552`

Counts

3 → 70

Calls

3 calls:

12.0ms	(*.f64 6 (-.f64 x 1))
12.0ms	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
7.0ms	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))

series71.0ms (2.3%)

Counts

3 → 9

Calls

3 calls:

35.0ms	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
22.0ms	(*.f64 6 (-.f64 x 1))
15.0ms	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))

simplify66.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5497	1395

prune89.0ms (2.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	5	80

Error

Counts

80 → 5

Compiler

Compiled 1686 to 1235 computations (26.7% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))
0.0b	(.f64 6 (/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))
0.0b	(/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))

rewrite48.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`add-sqr-sqrt_binary64_22606`
48×	`*-un-lft-identity_binary64_22584`
43×	`times-frac_binary64_22590`
27×	`associate-r_binary64_22524` `add-cube-cbrt_binary64_22619`
14×	`difference-of-squares_binary64_22553`
10×	`add-cbrt-cube_binary64_22620` `add-exp-log_binary64_22622`
8×	`add-log-exp_binary64_22623`
7×	`difference-of-sqr-1_binary64_22554` `distribute-lft-out--_binary64_22536` `associate-/l*_binary64_22529`
5×	`pow1_binary64_22645`
4×	`associate-/r/_binary64_22530`
3×	`flip3-+_binary64_22587` `associate-/r_binary64_22528` `associate-l*_binary64_22525` `sum-log_binary64_22675` `flip-+_binary64_22558`
2×	`associate-/l/_binary64_22531` `cbrt-undiv_binary64_22618` `div-exp_binary64_22635` `div-inv_binary64_22581` `cbrt-unprod_binary64_22617` `prod-exp_binary64_22633` `unswap-sqr_binary64_22552`
1×	`associate-r/_binary64_22526` `clear-num_binary64_22583` `+-commutative_binary64_22514` `associate-+l+_binary64_22517` `flip--_binary64_22559` `-commutative_binary64_22515` `div-sub_binary64_22589` `frac-2neg_binary64_22595` `pow-prod-down_binary64_22655` `flip3--_binary64_22588`

Counts

3 → 107

Calls

3 calls:

17.0ms	(.f64 6 (/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))
11.0ms	(/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))
10.0ms	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))

series80.0ms (2.6%)

Counts

3 → 9

Calls

3 calls:

34.0ms	(.f64 6 (/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))
32.0ms	(/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))
15.0ms	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))

simplify87.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4940	3245
1	4940	3245

prune155.0ms (5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	116	5	121

Error

Counts

121 → 5

Compiler

Compiled 3049 to 2192 computations (28.1% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))
0.0b	(/.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))) (-.f64 x 1))
0.0b	(/.f64 6 (/.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))) (-.f64 x 1)))

rewrite56.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

186×	`times-frac_binary64_22590`
151×	`add-sqr-sqrt_binary64_22606`
135×	`*-un-lft-identity_binary64_22584`
87×	`add-cube-cbrt_binary64_22619`
34×	`associate-/r*_binary64_22528`
32×	`difference-of-squares_binary64_22553`
16×	`difference-of-sqr-1_binary64_22554` `distribute-lft-out--_binary64_22536`
11×	`associate-/r/_binary64_22530`
10×	`add-cbrt-cube_binary64_22620` `add-exp-log_binary64_22622`
8×	`add-log-exp_binary64_22623`
6×	`associate-/l*_binary64_22529` `div-inv_binary64_22581`
5×	`flip--_binary64_22559` `flip3--_binary64_22588`
4×	`cbrt-undiv_binary64_22618` `div-exp_binary64_22635`
3×	`sum-log_binary64_22675` `pow1_binary64_22645`
2×	`flip3-+_binary64_22587` `associate-/l/_binary64_22531` `clear-num_binary64_22583` `frac-2neg_binary64_22595` `flip-+_binary64_22558`
1×	`+-commutative_binary64_22514` `associate-+l+_binary64_22517`

Counts

3 → 186

Calls

3 calls:

14.0ms	(/.f64 6 (/.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))) (-.f64 x 1)))
11.0ms	(/.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))) (-.f64 x 1))
6.0ms	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))

series78.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

35.0ms	(/.f64 6 (/.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))) (-.f64 x 1)))
26.0ms	(/.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))) (-.f64 x 1))
16.0ms	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))

simplify117.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5001	7080

prune315.0ms (10.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	195	5	200

Error

Counts

200 → 5

Compiler

Compiled 5519 to 4023 computations (27.1% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 x 1) (*.f64 x x))
0.0b	(.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))) (+.f64 (+.f64 x 1) (*.f64 x x)))
0.0b	(*.f64 6 (-.f64 (pow.f64 x 3) (pow.f64 1 3)))
20.5b	(/.f64 (.f64 6 (-.f64 (pow.f64 x 3) (pow.f64 1 3))) (.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))) (+.f64 (+.f64 x 1) (.f64 x x))))

rewrite95.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64_22606`
37×	`associate-r_binary64_22524`
33×	`*-un-lft-identity_binary64_22584`
24×	`difference-of-squares_binary64_22553` `unpow-prod-down_binary64_22663` `cancel-sign-sub-inv_binary64_22550` `cube-prod_binary64_22612`
20×	`add-cbrt-cube_binary64_22620` `add-exp-log_binary64_22622`
14×	`distribute-rgt-in_binary64_22534` `distribute-lft-in_binary64_22533` `add-cube-cbrt_binary64_22619`
13×	`flip3-+_binary64_22587` `flip-+_binary64_22558`
12×	`sqr-pow_binary64_22556`
9×	`add-log-exp_binary64_22623`
8×	`associate-*r/_binary64_22526` `pow1_binary64_22645` `frac-times_binary64_22594` `associate-/r/_binary64_22530`
6×	`distribute-lft-out--_binary64_22536` `associate-l_binary64_22525` `cbrt-unprod_binary64_22617` `prod-exp_binary64_22633`
4×	`cbrt-undiv_binary64_22618` `div-exp_binary64_22635` `associate-*l/_binary64_22527`
3×	`cube-mult_binary64_22614` `sum-log_binary64_22675`
2×	`associate-/l/_binary64_22531` `sub-neg_binary64_22577` `flip--_binary64_22559` `*-commutative_binary64_22515` `pow-prod-down_binary64_22655` `unswap-sqr_binary64_22552` `unpow3_binary64_22650` `flip3--_binary64_22588`
1×	`difference-cubes_binary64_22586` `associate-/l_binary64_22529` `div-inv_binary64_22581` `associate-/r_binary64_22528` `clear-num_binary64_22583` `+-commutative_binary64_22514` `times-frac_binary64_22590` `associate-+l+_binary64_22517` `frac-2neg_binary64_22595`

Counts

4 → 149

Calls

4 calls:

30.0ms	(/.f64 (.f64 6 (-.f64 (pow.f64 x 3) (pow.f64 1 3))) (.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))) (+.f64 (+.f64 x 1) (.f64 x x))))
23.0ms	(*.f64 6 (-.f64 (pow.f64 x 3) (pow.f64 1 3)))
18.0ms	(.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))) (+.f64 (+.f64 x 1) (*.f64 x x)))
6.0ms	(+.f64 (+.f64 x 1) (*.f64 x x))

series142.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(*.f64 6 (-.f64 (pow.f64 x 3) (pow.f64 1 3)))
49.0ms	(/.f64 (.f64 6 (-.f64 (pow.f64 x 3) (pow.f64 1 3))) (.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))) (+.f64 (+.f64 x 1) (.f64 x x))))
33.0ms	(.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))) (+.f64 (+.f64 x 1) (*.f64 x x)))
8.0ms	(+.f64 (+.f64 x 1) (*.f64 x x))

simplify103.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4920	3543
1	4920	3543

prune289.0ms (9.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	161	5	166

Error

Counts

166 → 5

Compiler

Compiled 5338 to 3715 computations (30.4% saved)

regimes66.0ms (2.1%)

Accuracy

Total 0.0b remaining (92.6%)

Threshold costs 0.0b (92.6%)

Compiler

Compiled 653 to 549 computations (15.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	21
1	26	21

end0.0ms (0%)

sample740.0ms (24%)

Algorithm

1×

intervals

Results

335.0ms	8000×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 302 to 256 computations (15.2% saved)

Details

analyze3.0ms (0.1%)

sample16.0ms (0.5%)

simplify376.0ms (12.2%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

rewrite37.0ms (1.2%)

series71.0ms (2.3%)

simplify66.0ms (2.1%)

prune89.0ms (2.9%)

localize8.0ms (0.3%)

rewrite48.0ms (1.6%)

series80.0ms (2.6%)

simplify87.0ms (2.8%)

prune155.0ms (5%)

localize10.0ms (0.3%)

rewrite56.0ms (1.8%)

series78.0ms (2.5%)

simplify117.0ms (3.8%)

prune315.0ms (10.2%)

localize15.0ms (0.5%)

rewrite95.0ms (3.1%)

series142.0ms (4.6%)

simplify103.0ms (3.4%)

prune289.0ms (9.4%)

regimes66.0ms (2.1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample740.0ms (24%)

Profiling