Details

analyze101.0ms (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)

sample14.0ms (0.3%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify317.0ms (7.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (151.0ms)

Iter	Nodes	Cost
0	4932	10
1	4932	10

prune5.0ms (0.1%)

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 30 to 28 computations (6.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_15559`
3×	`add-log-exp_binary64_15598`
2×	`distribute-lft-out_binary64_15510` `times-frac_binary64_15565`
1×	`add-cbrt-cube_binary64_15595` `flip3-+_binary64_15562` `flip-+_binary64_15533` `pow1_binary64_15620` `frac-add_binary64_15567` `+-commutative_binary64_15489` `add-exp-log_binary64_15597` `add-sqr-sqrt_binary64_15581` `add-cube-cbrt_binary64_15594` `sum-log_binary64_15650`

Counts

1 → 14

Calls

1 calls:

15.0ms

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

series42.0ms (1%)

Counts

1 → 3

Calls

1 calls:

42.0ms

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

simplify83.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4850	239
1	4850	239

prune27.0ms (0.6%)

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 396 to 324 computations (18.2% saved)

localize9.0ms (0.2%)

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))))

rewrite93.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`*-un-lft-identity_binary64_15559`
43×	`cbrt-prod_binary64_15590`
33×	`cbrt-div_binary64_15591`
23×	`add-sqr-sqrt_binary64_15581`
16×	`distribute-lft-out_binary64_15510`
15×	`add-cube-cbrt_binary64_15594`
14×	`times-frac_binary64_15565`
11×	`flip3-+_binary64_15562` `flip-+_binary64_15533` `pow1_binary64_15620` `frac-add_binary64_15567`
10×	`swap-sqr_binary64_15526`
9×	`frac-times_binary64_15569` `pow1/3_binary64_15641`
8×	`associate-r_binary64_15499` `associate-l_binary64_15500`
6×	`add-exp-log_binary64_15597`
4×	`add-cbrt-cube_binary64_15595` `add-log-exp_binary64_15598` `unswap-sqr_binary64_15527`
3×	`associate-r/_binary64_15501` `associate-l/_binary64_15502`
2×	`pow-prod-down_binary64_15630` `pow-prod-up_binary64_15629` `pow-sqr_binary64_15532`
1×	`pow-plus_binary64_15622` `prod-exp_binary64_15608` `pow2_binary64_15640` `*-commutative_binary64_15490` `cbrt-unprod_binary64_15592`

Counts

4 → 111

Calls

4 calls:

37.0ms	(*.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)))
14.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
14.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

series751.0ms (17.5%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(*.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)))
184.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
170.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

simplify105.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4898	2939
1	4898	2939

prune258.0ms (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 4439 to 3503 computations (21.1% 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))

rewrite54.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64_15559`
16×	`cbrt-prod_binary64_15590`
10×	`distribute-lft-out_binary64_15510` `unpow-prod-down_binary64_15638` `times-frac_binary64_15565` `cube-prod_binary64_15587`
9×	`add-sqr-sqrt_binary64_15581` `add-cube-cbrt_binary64_15594`
6×	`cube-div_binary64_15588`
5×	`add-log-exp_binary64_15598`
4×	`add-cbrt-cube_binary64_15595` `pow1_binary64_15620` `add-exp-log_binary64_15597`
3×	`flip3-+_binary64_15562` `cbrt-div_binary64_15591` `flip-+_binary64_15533` `frac-add_binary64_15567` `pow-unpow_binary64_15636`
2×	`sqr-pow_binary64_15531` `unpow3_binary64_15625` `cube-mult_binary64_15589`
1×	`rem-cube-cbrt_binary64_15582` `pow-pow_binary64_15631` `pow-exp_binary64_15627` `pow1/3_binary64_15641` `+-commutative_binary64_15489` `pow-to-exp_binary64_15628` `sum-log_binary64_15650` `rem-cbrt-cube_binary64_15583`

Counts

3 → 72

Calls

3 calls:

17.0ms	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
16.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) 3))
16.0ms	(pow.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) 3)

series137.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

61.0ms	(pow.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) 3)
40.0ms	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
36.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) 3))

simplify81.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5146	1351

prune85.0ms (2%)

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 1379 to 1075 computations (22% saved)

localize34.0ms (0.8%)

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

rewrite195.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64_15559`
24×	`cbrt-div_binary64_15591`
17×	`cbrt-prod_binary64_15590`
16×	`add-exp-log_binary64_15597`
11×	`associate-/l/_binary64_15506`
10×	`flip3-+_binary64_15562` `flip-+_binary64_15533`
9×	`distribute-lft-out_binary64_15510` `times-frac_binary64_15565`
8×	`add-cbrt-cube_binary64_15595` `unpow-prod-down_binary64_15638` `cube-prod_binary64_15587` `cube-div_binary64_15588`
6×	`frac-times_binary64_15569` `add-sqr-sqrt_binary64_15581` `add-cube-cbrt_binary64_15594`
5×	`associate-*r/_binary64_15501`
4×	`prod-exp_binary64_15608` `pow1_binary64_15620` `frac-add_binary64_15567` `cbrt-undiv_binary64_15593` `add-log-exp_binary64_15598` `div-exp_binary64_15610` `cbrt-unprod_binary64_15592`
3×	`pow1/3_binary64_15641`
2×	`associate-/r/_binary64_15505` `associate-*l/_binary64_15502`
1×	`associate-/r_binary64_15503` `frac-2neg_binary64_15570` `associate-/l_binary64_15504` `div-inv_binary64_15556` `clear-num_binary64_15558` `sum-cubes_binary64_15560`

Counts

4 → 80

Calls

4 calls:

92.0ms	(/.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 x) (/.f64 1/4 y)) x)))))
56.0ms	(cbrt.f64 (+.f64 (pow.f64 (/.f64 1/2 y) 3) (pow.f64 (/.f64 -1/2 x) 3)))
29.0ms	(cbrt.f64 (+.f64 (*.f64 1/4 (pow.f64 y -2)) (/.f64 (+.f64 (/.f64 1/4 x) (/.f64 1/4 y)) x)))
2.0ms	(cbrt.f64 (*.f64 y x))

series865.0ms (20.2%)

Counts

4 → 12

Calls

4 calls:

383.0ms	(/.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 x) (/.f64 1/4 y)) x)))))
201.0ms	(cbrt.f64 (+.f64 (*.f64 1/4 (pow.f64 y -2)) (/.f64 (+.f64 (/.f64 1/4 x) (/.f64 1/4 y)) x)))
175.0ms	(cbrt.f64 (+.f64 (pow.f64 (/.f64 1/2 y) 3) (pow.f64 (/.f64 -1/2 x) 3)))
106.0ms	(cbrt.f64 (*.f64 y x))

simplify100.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4948	3755
1	4948	3755

prune330.0ms (7.7%)

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 5740 to 4278 computations (25.5% saved)

regimes30.0ms (0.7%)

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

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	10
1	9	10

end0.0ms (0%)

sample538.0ms (12.6%)

Algorithm

1×

intervals

Results

241.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 119 to 105 computations (11.8% saved)

Details

analyze101.0ms (2.4%)

sample14.0ms (0.3%)

simplify317.0ms (7.4%)

prune5.0ms (0.1%)

localize5.0ms (0.1%)

rewrite16.0ms (0.4%)

series42.0ms (1%)

simplify83.0ms (1.9%)

prune27.0ms (0.6%)

localize9.0ms (0.2%)

rewrite93.0ms (2.2%)

series751.0ms (17.5%)

simplify105.0ms (2.4%)

prune258.0ms (6%)

localize8.0ms (0.2%)

rewrite54.0ms (1.3%)

series137.0ms (3.2%)

simplify81.0ms (1.9%)

prune85.0ms (2%)

localize34.0ms (0.8%)

rewrite195.0ms (4.6%)

series865.0ms (20.2%)

simplify100.0ms (2.3%)

prune330.0ms (7.7%)

regimes30.0ms (0.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample538.0ms (12.6%)

Profiling