Details

analyze132.0ms (4.1%)

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
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 16 to 8 computations (50% saved)

sample23.0ms (0.7%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 31 to 17 computations (45.2% saved)

simplify160.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	39	13
1	39	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

0.1b

Counts

2 → 2

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y (*.f64 y 3)))
0.2b	(.f64 y (.f64 y 3))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64_8323` `add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298`
4×	`add-log-exp_binary64_8301`
3×	`prod-exp_binary64_8311` `add-sqr-sqrt_binary64_8284` `cbrt-unprod_binary64_8295` `associate-l_binary64_8203` `pow-prod-down_binary64_8333` `add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
1×	`flip-+_binary64_8236` `flip3-+_binary64_8265` `+-commutative_binary64_8192` `sum-log_binary64_8353` `associate-r_binary64_8202` `*-commutative_binary64_8193`

Counts

2 → 29

Calls

2 calls:

5.0ms	(.f64 y (.f64 y 3))
4.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 3)))

series49.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

26.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 3)))
23.0ms	(.f64 y (.f64 y 3))

simplify112.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4949	410
1	4949	410

prune50.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	32	3	35
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	32	5	37

Error

0.0b

Counts

37 → 5

Compiler

Compiled 514 to 291 computations (43.4% saved)

localize13.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

rewrite28.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-log-exp_binary64_8301`
10×	`sum-log_binary64_8353`
3×	`flip-+_binary64_8236` `flip3-+_binary64_8265` `pow1_binary64_8323` `+-commutative_binary64_8192` `add-sqr-sqrt_binary64_8284` `add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298` `add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
2×	`associate-+l+_binary64_8195`

Counts

3 → 38

Calls

3 calls:

14.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series121.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

47.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
41.0ms	(+.f64 (.f64 x x) (.f64 y y))
32.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

simplify126.0ms (4%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	5013	758

prune48.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	46	6	52

Error

0.0b

Counts

52 → 6

Compiler

Compiled 916 to 242 computations (73.6% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 y (.f64 y 3))
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 y (.f64 y 3)) (.f64 x x))) (sqrt.f64 (+.f64 (.f64 y (.f64 y 3)) (*.f64 x x))))
6.1b	(sqrt.f64 (+.f64 (.f64 y (.f64 y 3)) (*.f64 x x)))
6.1b	(sqrt.f64 (+.f64 (.f64 y (.f64 y 3)) (*.f64 x x)))

rewrite84.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_8284`
26×	`pow1_binary64_8323`
24×	`sqrt-prod_binary64_8278`
16×	`sqrt-div_binary64_8279`
15×	`add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
11×	`add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298`
10×	`sqrt-pow1_binary64_8280` `pow1/2_binary64_8342`
9×	`associate-l_binary64_8203`
8×	`flip-+_binary64_8236` `flip3-+_binary64_8265` `swap-sqr_binary64_8229`
7×	`associate-r_binary64_8202`
6×	`pow-prod-down_binary64_8333`
5×	`pow-prod-up_binary64_8332`
4×	`prod-exp_binary64_8311` `unswap-sqr_binary64_8230` `frac-times_binary64_8272` `cbrt-unprod_binary64_8295` `rem-sqrt-square_binary64_8275` `add-log-exp_binary64_8301`
3×	`pow-sqr_binary64_8235`
2×	`associate-r/_binary64_8204` `associate-l/_binary64_8205` `*-commutative_binary64_8193`
1×	`pow2_binary64_8343` `sqr-abs_binary64_8277` `sqrt-unprod_binary64_8282` `pow-plus_binary64_8325` `rem-square-sqrt_binary64_8274`

Counts

4 → 106

Calls

4 calls:

31.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y (.f64 y 3)) (.f64 x x))) (sqrt.f64 (+.f64 (.f64 y (.f64 y 3)) (*.f64 x x))))
13.0ms	(.f64 y (.f64 y 3))
10.0ms	(sqrt.f64 (+.f64 (.f64 y (.f64 y 3)) (*.f64 x x)))
7.0ms	(sqrt.f64 (+.f64 (.f64 y (.f64 y 3)) (*.f64 x x)))

series149.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt.f64 (+.f64 (.f64 y (.f64 y 3)) (*.f64 x x)))
43.0ms	(sqrt.f64 (+.f64 (.f64 y (.f64 y 3)) (*.f64 x x)))
33.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y (.f64 y 3)) (.f64 x x))) (sqrt.f64 (+.f64 (.f64 y (.f64 y 3)) (*.f64 x x))))
21.0ms	(.f64 y (.f64 y 3))

simplify144.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4901	1944
1	4901	1944

prune205.0ms (6.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	117	7	124

Error

0.0b

Counts

124 → 7

Compiler

Compiled 2753 to 1587 computations (42.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) (.f64 y y))
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 y y)))))
6.1b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
6.1b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))

rewrite52.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_8284`
24×	`sqrt-prod_binary64_8278`
21×	`pow1_binary64_8323`
16×	`sqrt-div_binary64_8279`
14×	`add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
10×	`sqrt-pow1_binary64_8280` `pow1/2_binary64_8342`
9×	`flip-+_binary64_8236` `flip3-+_binary64_8265`
8×	`swap-sqr_binary64_8229`
6×	`add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298` `associate-l_binary64_8203` `associate-r_binary64_8202` `add-log-exp_binary64_8301`
5×	`pow-prod-up_binary64_8332`
4×	`unswap-sqr_binary64_8230` `frac-times_binary64_8272` `rem-sqrt-square_binary64_8275`
3×	`pow-sqr_binary64_8235` `pow-prod-down_binary64_8333`
2×	`associate-r/_binary64_8204` `associate-l/_binary64_8205`
1×	`prod-exp_binary64_8311` `+-commutative_binary64_8192` `pow2_binary64_8343` `cbrt-unprod_binary64_8295` `sqr-abs_binary64_8277` `sum-log_binary64_8353` `*-commutative_binary64_8193` `sqrt-unprod_binary64_8282` `pow-plus_binary64_8325` `rem-square-sqrt_binary64_8274`

Counts

4 → 99

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 y y)))))
12.0ms	(+.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) (.f64 y y))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))

series169.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
48.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
42.0ms	(+.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) (.f64 y y))
30.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 y y)))))

simplify130.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4942	2032
1	4942	2032

prune102.0ms (3.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	111	7	118

Error

0.0b

Counts

118 → 7

Compiler

Compiled 2821 to 495 computations (82.5% saved)

regimes207.0ms (6.5%)

Accuracy

Total 0.1b remaining (94%)

Threshold costs 0.1b (94%)

Compiler

Compiled 1723 to 1103 computations (36% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms (0%)

sample1.0s (32.3%)

Algorithm

1×

intervals

Results

361.0ms	8000×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 362 to 232 computations (35.9% saved)

Details

analyze132.0ms (4.1%)

sample23.0ms (0.7%)

simplify160.0ms (5%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

rewrite11.0ms (0.4%)

series49.0ms (1.6%)

simplify112.0ms (3.5%)

prune50.0ms (1.6%)

localize13.0ms (0.4%)

rewrite28.0ms (0.9%)

series121.0ms (3.8%)

simplify126.0ms (4%)

prune48.0ms (1.5%)

localize8.0ms (0.3%)

rewrite84.0ms (2.7%)

series149.0ms (4.7%)

simplify144.0ms (4.5%)

prune205.0ms (6.5%)

localize10.0ms (0.3%)

rewrite52.0ms (1.6%)

series169.0ms (5.3%)

simplify130.0ms (4.1%)

prune102.0ms (3.2%)

regimes207.0ms (6.5%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.0s (32.3%)

Profiling