Details

analyze130.0ms (2.8%)

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%	40.6%	34.4%	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 12 to 9 computations (25% saved)

sample31.0ms (0.7%)

Algorithm

1×

intervals

Results

20.0ms

256×

body

128

valid

Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify165.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	24	13
1	24	13

prune7.0ms (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

Merged error: 0.0b

Counts

2 → 2

Compiler

Compiled 29 to 22 computations (24.1% saved)

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_14422` `*-un-lft-identity_binary64_14400`
4×	`add-exp-log_binary64_14438` `add-cube-cbrt_binary64_14435` `add-log-exp_binary64_14439` `pow1_binary64_14461` `associate-r_binary64_14340` `add-cbrt-cube_binary64_14436`
3×	`associate-l_binary64_14341`
2×	`flip3-+_binary64_14403` `associate-+l+_binary64_14333` `associate-*r/_binary64_14342` `flip-+_binary64_14374` `distribute-rgt-in_binary64_14350` `distribute-lft-in_binary64_14349`
1×	`cbrt-unprod_binary64_14433` `+-commutative_binary64_14330` `pow-prod-down_binary64_14471` `prod-exp_binary64_14449` `distribute-lft-out_binary64_14351` `*-commutative_binary64_14331` `sum-log_binary64_14491` `unswap-sqr_binary64_14368`

Counts

2 → 36

Calls

2 calls:

13.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
12.0ms	(*.f64 x (+.f64 x 2))

series90.0ms (2%)

Counts

2 → 6

Calls

2 calls:

53.0ms	(*.f64 x (+.f64 x 2))
37.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))

simplify111.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5006	509

prune60.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Merged error: 0.0b

Counts

44 → 4

Compiler

Compiled 618 to 342 computations (44.7% saved)

localize14.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64_14439`
4×	`sum-log_binary64_14491`
2×	`+-commutative_binary64_14330` `flip3-+_binary64_14403` `add-exp-log_binary64_14438` `add-cube-cbrt_binary64_14435` `add-sqr-sqrt_binary64_14422` `*-un-lft-identity_binary64_14400` `pow1_binary64_14461` `flip-+_binary64_14374` `add-cbrt-cube_binary64_14436`
1×	`associate-+l+_binary64_14333` `distribute-lft-out_binary64_14351`

Counts

2 → 25

Calls

2 calls:

13.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
7.0ms	(+.f64 (.f64 x 2) (.f64 x x))

series107.0ms (2.3%)

Counts

2 → 6

Calls

2 calls:

65.0ms	(+.f64 (.f64 x 2) (.f64 x x))
38.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))

simplify139.0ms (3%)

Algorithm

1×	egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	4963	439
1	4963	439

prune46.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	31	4	35

Merged error: 0.0b

Counts

35 → 4

Compiler

Compiled 477 to 264 computations (44.7% saved)

localize33.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (-.f64 (.f64 2 2) (*.f64 x 2)))
0.0b	(+.f64 (/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2)))) (*.f64 y y))
0.0b	(*.f64 x (+.f64 (pow.f64 x 3) 8))
10.3b	(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2))))

rewrite112.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-exp-log_binary64_14438` `add-log-exp_binary64_14439` `add-cbrt-cube_binary64_14436`
10×	`add-sqr-sqrt_binary64_14422` `*-un-lft-identity_binary64_14400`
8×	`add-cube-cbrt_binary64_14435`
6×	`pow1_binary64_14461`
5×	`flip3-+_binary64_14403` `flip-+_binary64_14374`
4×	`associate-r/_binary64_14342` `associate-r*_binary64_14340`
3×	`associate-/r_binary64_14344` `associate-l*_binary64_14341` `sum-log_binary64_14491` `times-frac_binary64_14406`
2×	`associate-/l/_binary64_14347` `associate-+r+_binary64_14332` `cbrt-unprod_binary64_14433` `+-commutative_binary64_14330` `prod-exp_binary64_14449` `cbrt-undiv_binary64_14434` `div-exp_binary64_14451` `associate-/r/_binary64_14346`
1×	`sub-neg_binary64_14393` `cancel-sign-sub-inv_binary64_14366` `pow-prod-down_binary64_14471` `frac-2neg_binary64_14411` `clear-num_binary64_14399` `distribute-lft-out_binary64_14351` `associate-+r-_binary64_14334` `div-inv_binary64_14397` `distribute-rgt-in_binary64_14350` `diff-log_binary64_14492` `-commutative_binary64_14331` `distribute-lft-in_binary64_14349` `unswap-sqr_binary64_14368` `associate-/l_binary64_14345`

Counts

4 → 74

Calls

4 calls:

35.0ms	(+.f64 (/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2)))) (*.f64 y y))
31.0ms	(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2))))
18.0ms	(*.f64 x (+.f64 (pow.f64 x 3) 8))
13.0ms	(+.f64 (.f64 x x) (-.f64 (.f64 2 2) (*.f64 x 2)))

series418.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

196.0ms	(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2))))
112.0ms	(*.f64 x (+.f64 (pow.f64 x 3) 8))
91.0ms	(+.f64 (/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2)))) (*.f64 y y))
19.0ms	(+.f64 (.f64 x x) (-.f64 (.f64 2 2) (*.f64 x 2)))

simplify85.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4985	1710
1	4985	1710

prune213.0ms (4.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	86	4	90

Merged error: 0.0b

Counts

90 → 4

Compiler

Compiled 2356 to 1544 computations (34.5% saved)

localize30.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (/.f64 x (sqrt.f64 (+.f64 4 (.f64 x (-.f64 x 2))))) (/.f64 (+.f64 (pow.f64 x 3) 8) (sqrt.f64 (+.f64 4 (.f64 x (-.f64 x 2)))))) (.f64 y y))
0.0b	(/.f64 x (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))
0.0b	(.f64 (/.f64 x (sqrt.f64 (+.f64 4 (.f64 x (-.f64 x 2))))) (/.f64 (+.f64 (pow.f64 x 3) 8) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2))))))
7.0b	(/.f64 (+.f64 (pow.f64 x 3) 8) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))

rewrite177.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64_14406`
94×	`add-sqr-sqrt_binary64_14422`
90×	`*-un-lft-identity_binary64_14400`
64×	`add-cube-cbrt_binary64_14435`
54×	`sqrt-prod_binary64_14416`
30×	`associate-r_binary64_14340`
24×	`associate-l_binary64_14341`
20×	`add-exp-log_binary64_14438` `add-cbrt-cube_binary64_14436`
13×	`distribute-lft-out_binary64_14351`
12×	`associate-/r*_binary64_14344`
9×	`unswap-sqr_binary64_14368`
8×	`sqrt-div_binary64_14417` `associate-/r/_binary64_14346`
7×	`associate-/l*_binary64_14345`
6×	`flip3-+_binary64_14403` `cbrt-undiv_binary64_14434` `div-exp_binary64_14451` `add-log-exp_binary64_14439` `pow1_binary64_14461` `flip-+_binary64_14374`
4×	`cbrt-unprod_binary64_14433` `prod-exp_binary64_14449` `div-inv_binary64_14397`
2×	`associate-/l/_binary64_14347` `frac-2neg_binary64_14411` `clear-num_binary64_14399`
1×	`associate-l/_binary64_14343` `+-commutative_binary64_14330` `pow-prod-down_binary64_14471` `frac-times_binary64_14410` `associate-r/_binary64_14342` `*-commutative_binary64_14331` `sum-log_binary64_14491`

Counts

4 → 185

Calls

4 calls:

53.0ms	(.f64 (/.f64 x (sqrt.f64 (+.f64 4 (.f64 x (-.f64 x 2))))) (/.f64 (+.f64 (pow.f64 x 3) 8) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2))))))
41.0ms	(+.f64 (.f64 (/.f64 x (sqrt.f64 (+.f64 4 (.f64 x (-.f64 x 2))))) (/.f64 (+.f64 (pow.f64 x 3) 8) (sqrt.f64 (+.f64 4 (.f64 x (-.f64 x 2)))))) (.f64 y y))
21.0ms	(/.f64 (+.f64 (pow.f64 x 3) 8) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))
10.0ms	(/.f64 x (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))

series370.0ms (8%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(.f64 (/.f64 x (sqrt.f64 (+.f64 4 (.f64 x (-.f64 x 2))))) (/.f64 (+.f64 (pow.f64 x 3) 8) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2))))))
98.0ms	(+.f64 (.f64 (/.f64 x (sqrt.f64 (+.f64 4 (.f64 x (-.f64 x 2))))) (/.f64 (+.f64 (pow.f64 x 3) 8) (sqrt.f64 (+.f64 4 (.f64 x (-.f64 x 2)))))) (.f64 y y))
46.0ms	(/.f64 x (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))
41.0ms	(/.f64 (+.f64 (pow.f64 x 3) 8) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))

simplify214.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4940	6600
1	4940	6600

prune754.0ms (16.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	197	4	201

Merged error: 0.0b

Counts

201 → 4

Compiler

Compiled 7672 to 5461 computations (28.8% saved)

regimes194.0ms (4.2%)

Compiler: Compiled 711 to 562 computations (21% 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 (22.4%)

Algorithm

1×

intervals

Results

428.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 165 to 130 computations (21.2% saved)

Details

analyze130.0ms (2.8%)

sample31.0ms (0.7%)

simplify165.0ms (3.6%)

prune7.0ms (0.1%)

localize12.0ms (0.3%)

rewrite31.0ms (0.7%)

series90.0ms (2%)

simplify111.0ms (2.4%)

prune60.0ms (1.3%)

localize14.0ms (0.3%)

rewrite24.0ms (0.5%)

series107.0ms (2.3%)

simplify139.0ms (3%)

prune46.0ms (1%)

localize33.0ms (0.7%)

rewrite112.0ms (2.4%)

series418.0ms (9.1%)

simplify85.0ms (1.9%)

prune213.0ms (4.6%)

localize30.0ms (0.7%)

rewrite177.0ms (3.9%)

series370.0ms (8%)

simplify214.0ms (4.6%)

prune754.0ms (16.4%)

regimes194.0ms (4.2%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.0s (22.4%)

Profiling