Details

analyze98.0ms (4.7%)

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
25%	62.4%	12.6%	6
25%	46.8%	28.2%	7
31.2%	35.9%	32.9%	8
39%	25%	36%	9
42.9%	18.7%	38.3%	10
47.2%	12.9%	39.9%	11
49.4%	9.6%	41.1%	12
51.6%	6.5%	41.9%	13
52.7%	4.8%	42.4%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample15.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	80	valid
0.0ms	7×	body	80	invalid

Compiler

Compiled 27 to 21 computations (22.2% saved)

simplify13.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	38	16
1	38	16

prune4.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 24 to 17 computations (29.2% saved)

localize15.0ms (0.7%)

Local error

Found 2 expressions with local error:

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

rewrite17.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
4×	`sum-log_binary64`
2×	`flip3-+_binary64` `*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64`
1×	`associate-+l+_binary64`

Counts

2 → 24

Calls

2 calls:

9.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 x 2) y))
8.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))

series15.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

7.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 x 2) y))
7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))

simplify156.0ms (7.4%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	4945	549
1	4945	549

prune43.0ms (2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	28	2	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	2	31

Merged error: 0.0b

Counts

31 → 2

Compiler

Compiled 547 to 298 computations (45.5% saved)

localize10.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

rewrite13.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip-+_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 35

Calls

2 calls:

8.0ms	(.f64 y (+.f64 (.f64 x 2) y))
5.0ms	(+.f64 (.f64 x x) (.f64 y (+.f64 (*.f64 x 2) y)))

series14.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

7.0ms	(+.f64 (.f64 x x) (.f64 y (+.f64 (*.f64 x 2) y)))
7.0ms	(.f64 y (+.f64 (.f64 x 2) y))

simplify96.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4953	646
1	4953	646

prune29.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	40	3	43

Merged error: 0b

Counts

43 → 3

Compiler

Compiled 721 to 393 computations (45.5% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 y (+.f64 y (.f64 x 2)))
0.0b	(.f64 (sqrt.f64 (+.f64 (.f64 y (+.f64 y (.f64 x 2))) (.f64 x x))) (sqrt.f64 (+.f64 (.f64 y (+.f64 y (.f64 x 2))) (*.f64 x x))))
6.4b	(sqrt.f64 (+.f64 (.f64 y (+.f64 y (.f64 x 2))) (*.f64 x x)))
6.4b	(sqrt.f64 (+.f64 (.f64 y (+.f64 y (.f64 x 2))) (*.f64 x x)))

rewrite43.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
23×	`pow1_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
9×	`flip3-+_binary64` `associate-r_binary64` `associate-l_binary64` `flip-+_binary64`
8×	`swap-sqr_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-up_binary64` `unswap-sqr_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-*r/_binary64` `frac-times_binary64`
3×	`pow-sqr_binary64`
2×	`cbrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`rem-square-sqrt_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `pow2_binary64`

Counts

4 → 109

Calls

4 calls:

17.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y (+.f64 y (.f64 x 2))) (.f64 x x))) (sqrt.f64 (+.f64 (.f64 y (+.f64 y (.f64 x 2))) (*.f64 x x))))
9.0ms	(sqrt.f64 (+.f64 (.f64 y (+.f64 y (.f64 x 2))) (*.f64 x x)))
7.0ms	(sqrt.f64 (+.f64 (.f64 y (+.f64 y (.f64 x 2))) (*.f64 x x)))
6.0ms	(.f64 y (+.f64 y (.f64 x 2)))

series43.0ms (2%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt.f64 (+.f64 (.f64 y (+.f64 y (.f64 x 2))) (*.f64 x x)))
11.0ms	(sqrt.f64 (+.f64 (.f64 y (+.f64 y (.f64 x 2))) (*.f64 x x)))
9.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y (+.f64 y (.f64 x 2))) (.f64 x x))) (sqrt.f64 (+.f64 (.f64 y (+.f64 y (.f64 x 2))) (*.f64 x x))))
7.0ms	(.f64 y (+.f64 y (.f64 x 2)))

simplify192.0ms (9.2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	4939	2539
1	4939	2539

prune104.0ms (5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	121	3	124

Merged error: 0b

Counts

124 → 3

Compiler

Compiled 3386 to 1892 computations (44.1% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
0.0b	(.f64 x (+.f64 x (.f64 2 y)))
0.2b	(pow.f64 (+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y)) 3)
36.2b	(cbrt.f64 (pow.f64 (+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y)) 3))

rewrite47.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `cbrt-prod_binary64`
7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
4×	`flip3-+_binary64` `cube-div_binary64` `flip-+_binary64`
3×	`pow-unpow_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`cbrt-div_binary64` `associate-*r/_binary64` `associate-+l+_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `pow-pow_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

14.0ms	(pow.f64 (+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y)) 3)
12.0ms	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
10.0ms	(.f64 x (+.f64 x (.f64 2 y)))
8.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y)) 3))

series68.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow.f64 (+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y)) 3)
12.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y)) 3))
10.0ms	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
6.0ms	(.f64 x (+.f64 x (.f64 2 y)))

simplify86.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5207	2021

prune110.0ms (5.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	95	3	98

Merged error: 0b

Counts

98 → 3

Compiler

Compiled 1964 to 1164 computations (40.7% saved)

regimes82.0ms (3.9%)

Compiler: Compiled 104 to 78 computations (25% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	13	16

end0.0ms (0%)

sample766.0ms (36.4%)

Algorithm

1×

intervals

Results

323.0ms	8000×	body	80	valid
7.0ms	191×	body	80	invalid

Compiler

Compiled 88 to 64 computations (27.3% saved)

Details

analyze98.0ms (4.7%)

sample15.0ms (0.7%)

simplify13.0ms (0.6%)

prune4.0ms (0.2%)

localize15.0ms (0.7%)

rewrite17.0ms (0.8%)

series15.0ms (0.7%)

simplify156.0ms (7.4%)

prune43.0ms (2%)

localize10.0ms (0.5%)

rewrite13.0ms (0.6%)

series14.0ms (0.6%)

simplify96.0ms (4.6%)

prune29.0ms (1.4%)

localize9.0ms (0.4%)

rewrite43.0ms (2.1%)

series43.0ms (2%)

simplify192.0ms (9.2%)

prune104.0ms (5%)

localize9.0ms (0.4%)

rewrite47.0ms (2.2%)

series68.0ms (3.2%)

simplify86.0ms (4.1%)

prune110.0ms (5.2%)

regimes82.0ms (3.9%)

bsearch0.0ms (0%)

simplify6.0ms (0.3%)

end0.0ms (0%)

sample766.0ms (36.4%)

Profiling