Details

analyze100.0ms (2.4%)

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%	74.9%	0.1%	6
56.2%	43.7%	0.1%	7
56.2%	43.7%	0.1%	8
76.5%	23.4%	0.1%	9
76.5%	23.4%	0.1%	10
87.8%	12.1%	0.1%	11
87.8%	12.1%	0.1%	12
93.8%	6.1%	0.1%	13
93.8%	6.1%	0.1%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample13.0ms (0.3%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify306.0ms (7.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	5533	10

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 14 to 14 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_16253`
3×	`add-log-exp_binary64_16289`
2×	`distribute-lft-out_binary64_16206` `times-frac_binary64_16259`
1×	`+-commutative_binary64_16185` `add-sqr-sqrt_binary64_16274` `add-cube-cbrt_binary64_16285` `flip3-+_binary64_16256` `sum-log_binary64_16341` `frac-add_binary64_16261` `add-exp-log_binary64_16288` `add-cbrt-cube_binary64_16286` `flip-+_binary64_16227` `pow1_binary64_16311`

Counts

1 → 14

Calls

1 calls:

14.0ms

(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

series36.0ms (0.9%)

Counts

1 → 3

Calls

1 calls:

36.0ms

(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

simplify63.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4936	239
1	4936	239

prune18.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	14	3	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	4	18

Merged error: 0.0b

Counts

18 → 4

Compiler

Compiled 266 to 207 computations (22.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.6b	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.6b	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.6b	(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))

rewrite92.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`*-un-lft-identity_binary64_16253`
43×	`cbrt-prod_binary64_16281`
33×	`cbrt-div_binary64_16282`
23×	`add-sqr-sqrt_binary64_16274`
16×	`distribute-lft-out_binary64_16206`
15×	`add-cube-cbrt_binary64_16285`
14×	`times-frac_binary64_16259`
11×	`flip3-+_binary64_16256` `frac-add_binary64_16261` `flip-+_binary64_16227` `pow1_binary64_16311`
10×	`swap-sqr_binary64_16220`
9×	`frac-times_binary64_16263` `pow1/3_binary64_16332`
8×	`associate-l_binary64_16196` `associate-r_binary64_16195`
6×	`add-exp-log_binary64_16288`
4×	`add-log-exp_binary64_16289` `unswap-sqr_binary64_16221` `add-cbrt-cube_binary64_16286`
3×	`associate-r/_binary64_16197` `associate-l/_binary64_16198`
2×	`pow-prod-down_binary64_16321` `pow-prod-up_binary64_16320` `pow-sqr_binary64_16226`
1×	`cbrt-unprod_binary64_16283` `*-commutative_binary64_16186` `pow-plus_binary64_16313` `prod-exp_binary64_16299` `pow2_binary64_16331`

Counts

4 → 111

Calls

4 calls:

33.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
14.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
13.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
13.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

series726.0ms (17.5%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
186.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
170.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
168.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

simplify112.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4795	2939
1	4795	2939

prune247.0ms (6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	123	4	127

Merged error: 0.0b

Counts

127 → 4

Compiler

Compiled 4103 to 3215 computations (21.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
0.3b	(pow.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) 3)
39.5b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) 3))

rewrite49.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64_16253`
16×	`cbrt-prod_binary64_16281`
10×	`cube-prod_binary64_16278` `distribute-lft-out_binary64_16206` `times-frac_binary64_16259` `unpow-prod-down_binary64_16329`
9×	`add-sqr-sqrt_binary64_16274` `add-cube-cbrt_binary64_16285`
6×	`cube-div_binary64_16279`
5×	`add-log-exp_binary64_16289`
4×	`add-exp-log_binary64_16288` `add-cbrt-cube_binary64_16286` `pow1_binary64_16311`
3×	`pow-unpow_binary64_16327` `cbrt-div_binary64_16282` `flip3-+_binary64_16256` `frac-add_binary64_16261` `flip-+_binary64_16227`
2×	`cube-mult_binary64_16280` `unpow3_binary64_16316` `sqr-pow_binary64_16225`
1×	`rem-cbrt-cube_binary64_16276` `+-commutative_binary64_16185` `pow-pow_binary64_16322` `pow-exp_binary64_16318` `rem-cube-cbrt_binary64_16275` `sum-log_binary64_16341` `pow-to-exp_binary64_16319` `pow1/3_binary64_16332`

Counts

3 → 72

Calls

3 calls:

15.0ms	(pow.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) 3)
15.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) 3))
13.0ms	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

series137.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

59.0ms	(pow.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) 3)
43.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) 3))
34.0ms	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

simplify75.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4919	1354
1	4919	1354

prune77.0ms (1.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	81	4	85

Merged error: 0.0b

Counts

85 → 4

Compiler

Compiled 1264 to 979 computations (22.5% saved)

localize38.0ms (0.9%)

Local error

Found 4 expressions with local error:

4.6b	(/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 1/2 x) (.f64 y -1/2))) (cbrt.f64 (+.f64 (pow.f64 (/.f64 1/2 y) 3) (pow.f64 (/.f64 -1/2 x) 3)))) (.f64 (cbrt.f64 (.f64 y x)) (cbrt.f64 (+.f64 (.f64 1/4 (pow.f64 y -2)) (/.f64 (+.f64 (/.f64 1/4 y) (/.f64 1/4 x)) x)))))
13.0b	(cbrt.f64 (*.f64 y x))
27.8b	(cbrt.f64 (+.f64 (*.f64 1/4 (pow.f64 y -2)) (/.f64 (+.f64 (/.f64 1/4 y) (/.f64 1/4 x)) x)))
39.5b	(cbrt.f64 (+.f64 (pow.f64 (/.f64 1/2 y) 3) (pow.f64 (/.f64 -1/2 x) 3)))

rewrite188.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64_16253`
24×	`cbrt-div_binary64_16282`
17×	`cbrt-prod_binary64_16281`
16×	`add-exp-log_binary64_16288`
11×	`associate-/l/_binary64_16202`
10×	`flip3-+_binary64_16256` `flip-+_binary64_16227`
9×	`distribute-lft-out_binary64_16206` `times-frac_binary64_16259`
8×	`cube-prod_binary64_16278` `unpow-prod-down_binary64_16329` `cube-div_binary64_16279` `add-cbrt-cube_binary64_16286`
6×	`add-sqr-sqrt_binary64_16274` `add-cube-cbrt_binary64_16285` `frac-times_binary64_16263`
5×	`associate-*r/_binary64_16197`
4×	`cbrt-unprod_binary64_16283` `add-log-exp_binary64_16289` `div-exp_binary64_16301` `frac-add_binary64_16261` `prod-exp_binary64_16299` `pow1_binary64_16311` `cbrt-undiv_binary64_16284`
3×	`pow1/3_binary64_16332`
2×	`associate-*l/_binary64_16198` `associate-/r/_binary64_16201`
1×	`clear-num_binary64_16252` `sum-cubes_binary64_16254` `div-inv_binary64_16250` `associate-/l_binary64_16200` `frac-2neg_binary64_16264` `associate-/r_binary64_16199`

Counts

4 → 80

Calls

4 calls:

91.0ms	(/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 1/2 x) (.f64 y -1/2))) (cbrt.f64 (+.f64 (pow.f64 (/.f64 1/2 y) 3) (pow.f64 (/.f64 -1/2 x) 3)))) (.f64 (cbrt.f64 (.f64 y x)) (cbrt.f64 (+.f64 (.f64 1/4 (pow.f64 y -2)) (/.f64 (+.f64 (/.f64 1/4 y) (/.f64 1/4 x)) x)))))
56.0ms	(cbrt.f64 (+.f64 (pow.f64 (/.f64 1/2 y) 3) (pow.f64 (/.f64 -1/2 x) 3)))
23.0ms	(cbrt.f64 (+.f64 (*.f64 1/4 (pow.f64 y -2)) (/.f64 (+.f64 (/.f64 1/4 y) (/.f64 1/4 x)) x)))
2.0ms	(cbrt.f64 (*.f64 y x))

series871.0ms (21%)

Counts

4 → 12

Calls

4 calls:

399.0ms	(/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 1/2 x) (.f64 y -1/2))) (cbrt.f64 (+.f64 (pow.f64 (/.f64 1/2 y) 3) (pow.f64 (/.f64 -1/2 x) 3)))) (.f64 (cbrt.f64 (.f64 y x)) (cbrt.f64 (+.f64 (.f64 1/4 (pow.f64 y -2)) (/.f64 (+.f64 (/.f64 1/4 y) (/.f64 1/4 x)) x)))))
190.0ms	(cbrt.f64 (+.f64 (*.f64 1/4 (pow.f64 y -2)) (/.f64 (+.f64 (/.f64 1/4 y) (/.f64 1/4 x)) x)))
177.0ms	(cbrt.f64 (+.f64 (pow.f64 (/.f64 1/2 y) 3) (pow.f64 (/.f64 -1/2 x) 3)))
105.0ms	(cbrt.f64 (*.f64 y x))

simplify66.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5116	3798

prune343.0ms (8.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	92	4	96

Merged error: 0.0b

Counts

96 → 4

Compiler

Compiled 5770 to 4314 computations (25.2% saved)

regimes30.0ms (0.7%)

Compiler: Compiled 194 to 170 computations (12.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	9	10

end0.0ms (0%)

sample514.0ms (12.4%)

Algorithm

1×

intervals

Results

227.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 119 to 105 computations (11.8% saved)

Details

analyze100.0ms (2.4%)

sample13.0ms (0.3%)

simplify306.0ms (7.4%)

prune7.0ms (0.2%)

localize5.0ms (0.1%)

rewrite15.0ms (0.4%)

series36.0ms (0.9%)

simplify63.0ms (1.5%)

prune18.0ms (0.4%)

localize12.0ms (0.3%)

rewrite92.0ms (2.2%)

series726.0ms (17.5%)

simplify112.0ms (2.7%)

prune247.0ms (6%)

localize8.0ms (0.2%)

rewrite49.0ms (1.2%)

series137.0ms (3.3%)

simplify75.0ms (1.8%)

prune77.0ms (1.9%)

localize38.0ms (0.9%)

rewrite188.0ms (4.5%)

series871.0ms (21%)

simplify66.0ms (1.6%)

prune343.0ms (8.3%)

regimes30.0ms (0.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample514.0ms (12.4%)

Profiling