Details

analyze139.0ms

Algorithm

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%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

sample32.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5101	43

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.2b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.7b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1_binary64_520` `add-exp-log_binary64_538`
14×	`add-cbrt-cube_binary64_546`
13×	`*-un-lft-identity_binary64_574` `add-sqr-sqrt_binary64_559`
10×	`associate-r_binary64_633`
8×	`add-cube-cbrt_binary64_545`
6×	`cbrt-unprod_binary64_543` `add-log-exp_binary64_539` `pow-prod-down_binary64_501` `prod-exp_binary64_525`
4×	`associate-*r/_binary64_635`
3×	`unpow-prod-down_binary64_509` `distribute-lft-in_binary64_616` `pow-unpow_binary64_507` `distribute-rgt-in_binary64_617`
2×	`associate-+r+_binary64_625` `associate-l_binary64_634` `unswap-sqr_binary64_602` `flip3-+_binary64_572` `flip-+_binary64_599` `sub-neg_binary64_578` `difference-of-squares_binary64_603` `*-commutative_binary64_642`
1×	`flip3--_binary64_573` `pow-to-exp_binary64_499` `sqr-pow_binary64_606` `+-commutative_binary64_641` `unpow2_binary64_517` `pow-exp_binary64_498` `distribute-lft-out--_binary64_619` `pow-pow_binary64_502` `distribute-lft-out_binary64_618` `flip--_binary64_600` `sum-log_binary64_489`

Counts

4 → 81

Calls

4 calls:

12.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
9.0ms	(.f64 (.f64 a a) (-.f64 1 a))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))

series170.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
33.0ms	(.f64 (.f64 a a) (-.f64 1 a))
29.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
25.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify77.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5551	1735

prune314.0ms

Filtered

64 candidates to 93 candidates (-45.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	3	94

Merged error: 0.0b

Counts

94 → 3

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.7b	(.f64 (.f64 b b) (+.f64 3 a))
2.9b	(.f64 (.f64 b b) (*.f64 a a))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

42×	`pow1_binary64_520`
32×	`associate-*r/_binary64_635`
26×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
20×	`frac-add_binary64_564` `pow-prod-down_binary64_501`
14×	`flip3-+_binary64_572` `flip-+_binary64_599` `cbrt-unprod_binary64_543` `prod-exp_binary64_525`
13×	`add-log-exp_binary64_539`
11×	`-un-lft-identity_binary64_574` `add-sqr-sqrt_binary64_559` `associate-r*_binary64_633`
6×	`add-cube-cbrt_binary64_545` `sum-log_binary64_489`
5×	`flip3--_binary64_573` `flip--_binary64_600`
4×	`pow-plus_binary64_515` `pow-prod-up_binary64_500`
3×	`associate-l_binary64_634` `unswap-sqr_binary64_602` `distribute-lft-in_binary64_616` `distribute-rgt-in_binary64_617` `*-commutative_binary64_642`
2×	`associate-+r+_binary64_625` `pow2_binary64_511` `sub-neg_binary64_578` `difference-of-squares_binary64_603` `pow-sqr_binary64_607`
1×	`associate-+l+_binary64_626` `+-commutative_binary64_641` `distribute-lft-out--_binary64_619` `distribute-lft-out_binary64_618`

Counts

4 → 107

Calls

4 calls:

17.0ms	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
9.0ms	(.f64 (.f64 a a) (-.f64 1 a))
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
9.0ms	(.f64 (.f64 b b) (*.f64 a a))

series171.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
33.0ms	(.f64 (.f64 a a) (-.f64 1 a))
27.0ms	(.f64 (.f64 b b) (+.f64 3 a))
32.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify111.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4976	4648
1	4976	4648

prune424.0ms

Filtered

76 candidates to 119 candidates (-56.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Merged error: 0b

Counts

122 → 4

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 b (.f64 b (+.f64 3 a)))
0.3b	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 b (.f64 b (+.f64 3 a))) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3)
0.4b	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2)
31.6b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 b (.f64 b (+.f64 3 a))) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_574` `add-cube-cbrt_binary64_545` `add-sqr-sqrt_binary64_559`
12×	`cbrt-prod_binary64_541`
11×	`pow1_binary64_520` `add-exp-log_binary64_538`
10×	`add-cbrt-cube_binary64_546`
9×	`unpow-prod-down_binary64_509`
6×	`pow-unpow_binary64_507` `cube-prod_binary64_547`
4×	`cube-div_binary64_548` `distribute-lft-in_binary64_616` `distribute-rgt-in_binary64_617` `add-log-exp_binary64_539` `associate-*r/_binary64_635`
3×	`associate-l_binary64_634` `sqr-pow_binary64_606` `flip3-+_binary64_572` `flip-+_binary64_599` `cbrt-unprod_binary64_543` `pow-prod-down_binary64_501` `prod-exp_binary64_525`
2×	`pow-to-exp_binary64_499` `cbrt-div_binary64_542` `pow-exp_binary64_498` `pow-pow_binary64_502` `unpow3_binary64_518` `cube-mult_binary64_549`
1×	`pow1/3_binary64_512` `unpow2_binary64_517` `rem-cube-cbrt_binary64_550` `rem-cbrt-cube_binary64_551` `associate-r_binary64_633` `*-commutative_binary64_642`

Counts

4 → 90

Calls

4 calls:

11.0ms	(.f64 b (.f64 b (+.f64 3 a)))
9.0ms	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 b (.f64 b (+.f64 3 a))) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3)
5.0ms	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2)
8.0ms	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 b (.f64 b (+.f64 3 a))) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3))

series769.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(.f64 b (.f64 b (+.f64 3 a)))
628.0ms	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 b (.f64 b (+.f64 3 a))) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3)
32.0ms	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2)
82.0ms	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 b (.f64 b (+.f64 3 a))) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3))

simplify79.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5052	3620

prune267.0ms

Filtered

62 candidates to 102 candidates (-64.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	102	4	106

Merged error: 0b

Counts

106 → 4

localize76.0ms

Local error

Found 4 expressions with local error:

1.3b	(.f64 (.f64 b b) (-.f64 9 (*.f64 a a)))
1.4b	(-.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (*.f64 a a))) 2))))
3.6b	(+.f64 (.f64 (-.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)))) (.f64 (+.f64 a 1) (-.f64 3 a))) (.f64 (-.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2))) (.f64 4 (+.f64 (.f64 a (.f64 (+.f64 a (neg.f64 (pow.f64 a 3))) (-.f64 3 a))) (.f64 (.f64 (.f64 b b) (-.f64 9 (*.f64 a a))) (+.f64 a 1))))))
37.1b	(/.f64 (+.f64 (.f64 (-.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)))) (.f64 (+.f64 a 1) (-.f64 3 a))) (.f64 (-.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2))) (.f64 4 (+.f64 (.f64 a (.f64 (+.f64 a (neg.f64 (pow.f64 a 3))) (-.f64 3 a))) (.f64 (.f64 (.f64 b b) (-.f64 9 (.f64 a a))) (+.f64 a 1)))))) (.f64 (-.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2))) (*.f64 (+.f64 a 1) (-.f64 3 a))))

rewrite4.6s

Algorithm

rewrite-expression-head

Rules

41808×	`associate-*r/_binary64_635`
28076×	`frac-times_binary64_566`
20384×	`frac-add_binary64_564`
18192×	`flip3--_binary64_573` `flip--_binary64_600`
11255×	`flip3-+_binary64_572` `flip-+_binary64_599`
8304×	`associate-*l/_binary64_636`
5202×	`associate-/l/_binary64_640`
26×	`associate-/r/_binary64_639`
18×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
11×	`add-sqr-sqrt_binary64_559`
10×	`distribute-lft-in_binary64_616` `distribute-rgt-in_binary64_617`
9×	`pow1_binary64_520`
8×	`add-log-exp_binary64_539`
7×	`*-un-lft-identity_binary64_574` `add-cube-cbrt_binary64_545` `sub-neg_binary64_578`
6×	`cbrt-unprod_binary64_543` `prod-exp_binary64_525`
4×	`associate-+r+_binary64_625` `associate-+l+_binary64_626` `associate-r_binary64_633` `difference-of-squares_binary64_603`
3×	`associate-/l*_binary64_638` `div-exp_binary64_527` `cbrt-undiv_binary64_544` `pow-prod-down_binary64_501` `times-frac_binary64_569`
2×	`associate--r+_binary64_629`
1×	`associate-l_binary64_634` `sqr-pow_binary64_606` `+-commutative_binary64_641` `div-inv_binary64_575` `unpow-prod-down_binary64_509` `unswap-sqr_binary64_602` `frac-2neg_binary64_567` `diff-log_binary64_490` `clear-num_binary64_577` `associate-/r_binary64_637` `-commutative_binary64_642` `sum-log_binary64_489`

Counts

4 → 10510

Calls

4 calls:

17.0ms	(.f64 (.f64 b b) (-.f64 9 (*.f64 a a)))
5.0ms	(-.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (*.f64 a a))) 2))))
154.0ms	(+.f64 (.f64 (-.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)))) (.f64 (+.f64 a 1) (-.f64 3 a))) (.f64 (-.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2))) (.f64 4 (+.f64 (.f64 a (.f64 (+.f64 a (neg.f64 (pow.f64 a 3))) (-.f64 3 a))) (.f64 (.f64 (.f64 b b) (-.f64 9 (*.f64 a a))) (+.f64 a 1))))))
521.0ms	(/.f64 (+.f64 (.f64 (-.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)))) (.f64 (+.f64 a 1) (-.f64 3 a))) (.f64 (-.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2))) (.f64 4 (+.f64 (.f64 a (.f64 (+.f64 a (neg.f64 (pow.f64 a 3))) (-.f64 3 a))) (.f64 (.f64 (.f64 b b) (-.f64 9 (.f64 a a))) (+.f64 a 1)))))) (.f64 (-.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2))) (*.f64 (+.f64 a 1) (-.f64 3 a))))

series1.6s

Counts

4 → 12

Calls

4 calls:

49.0ms	(.f64 (.f64 b b) (-.f64 9 (*.f64 a a)))
116.0ms	(-.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (*.f64 a a))) 2))))
742.0ms	(+.f64 (.f64 (-.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)))) (.f64 (+.f64 a 1) (-.f64 3 a))) (.f64 (-.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2))) (.f64 4 (+.f64 (.f64 a (.f64 (+.f64 a (neg.f64 (pow.f64 a 3))) (-.f64 3 a))) (.f64 (.f64 (.f64 b b) (-.f64 9 (*.f64 a a))) (+.f64 a 1))))))
652.0ms	(/.f64 (+.f64 (.f64 (-.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2)))) (.f64 (+.f64 a 1) (-.f64 3 a))) (.f64 (-.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2))) (.f64 4 (+.f64 (.f64 a (.f64 (+.f64 a (neg.f64 (pow.f64 a 3))) (-.f64 3 a))) (.f64 (.f64 (.f64 b b) (-.f64 9 (.f64 a a))) (+.f64 a 1)))))) (.f64 (-.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 b (.f64 b (.f64 a a))) 2))) (*.f64 (+.f64 a 1) (-.f64 3 a))))

simplify23.4s

Algorithm

egg-herbie

Counts

10522 → 10522

Iterations

Useful iterations: 0 (575.0ms)

Iter	Nodes	Cost
0	27073	3877575

prune2.0min

Filtered: 10514 candidates to 10522 candidates (-0.1%)

Details

analyze139.0ms

sample32.0ms

simplify66.0ms

prune12.0ms

localize26.0ms

rewrite36.0ms

series170.0ms

simplify77.0ms

prune314.0ms

localize42.0ms

rewrite47.0ms

series171.0ms

simplify111.0ms

prune424.0ms

localize33.0ms

rewrite36.0ms

series769.0ms

simplify79.0ms

prune267.0ms

localize76.0ms

rewrite4.6s

series1.6s

simplify23.4s

prune2.0min

Profiling