Details

analyze147.0ms

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%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

sample28.0ms

Algorithm

intervals

Results

20.0ms

256×

body

valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5055	46

prune3.0ms

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

localize16.0ms

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 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.6b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1_binary64` `add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
7×	`associate-r_binary64`
6×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`associate-*r/_binary64`
3×	`pow-unpow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unpow-prod-down_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 78

Calls

4 calls:

9.0ms	(+.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 1 (.f64 3 a))))))
8.0ms	(.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 1 (*.f64 3 a)))

series183.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+.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 1 (.f64 3 a))))))
33.0ms	(.f64 (.f64 a a) (+.f64 1 a))
32.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
36.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

simplify79.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5079	1820

prune108.0ms

Filtered

59 candidates to 90 candidates (-52.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	87	4	91

Merged error: 0.0b

Counts

91 → 4

localize21.0ms

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 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.6b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
2.0b	(.f64 (.f64 b b) (*.f64 a a))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

42×	`pow1_binary64`
32×	`associate-*r/_binary64`
26×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`pow-prod-down_binary64` `frac-add_binary64`
14×	`flip3-+_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `flip-+_binary64`
13×	`add-log-exp_binary64`
8×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64` `sum-log_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`pow-prod-up_binary64` `pow-plus_binary64`
3×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
2×	`sub-neg_binary64` `pow-sqr_binary64` `associate-+r+_binary64` `pow2_binary64`
1×	`distribute-lft-out_binary64` `associate-+l+_binary64` `+-commutative_binary64`

Counts

4 → 104

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 1 (.f64 3 a))))))
8.0ms	(.f64 (.f64 a a) (+.f64 1 a))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
9.0ms	(.f64 (.f64 b b) (*.f64 a a))

series183.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+.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 1 (.f64 3 a))))))
32.0ms	(.f64 (.f64 a a) (+.f64 1 a))
38.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
31.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify117.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5009	4860

prune214.0ms

Filtered

76 candidates to 116 candidates (-52.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	116	4	120

Merged error: 0.0b

Counts

120 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
20.9b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
20.9b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
20.9b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `unpow2_binary64` `pow1/3_binary64` `sqr-pow_binary64` `prod-exp_binary64`
2×	`sub-neg_binary64` `associate-*r/_binary64`
1×	`flip3--_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 71

Calls

4 calls:

8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
7.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
5.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
5.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))

series297.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
88.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
90.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
86.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))

simplify67.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5538	1568

prune138.0ms

Filtered

62 candidates to 83 candidates (-33.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	83	4	87

Merged error: 0.0b

Counts

87 → 4

localize54.0ms

Local error

Found 4 expressions with local error:

1.6b	(.f64 (.f64 b b) (-.f64 1 (pow.f64 (*.f64 a 3) 3)))
4.0b	(+.f64 (.f64 (+.f64 (pow.f64 (.f64 b b) 6) (.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (.f64 (.f64 b b) 2)) 3))) (.f64 (+.f64 1 (.f64 a (+.f64 3 (.f64 a 9)))) (-.f64 1 a))) (.f64 (+.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (pow.f64 b 4)))) (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a (+.f64 3 (.f64 a 9))))) (.f64 (.f64 (.f64 b b) (-.f64 1 (pow.f64 (.f64 a 3) 3))) (-.f64 1 a))))))
4.1b	(.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (.f64 (.f64 b b) 2)) 3))
48.0b	(/.f64 (+.f64 (.f64 (+.f64 (pow.f64 (.f64 b b) 6) (.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (.f64 (.f64 b b) 2)) 3))) (.f64 (+.f64 1 (.f64 a (+.f64 3 (.f64 a 9)))) (-.f64 1 a))) (.f64 (+.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (pow.f64 b 4)))) (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a (+.f64 3 (.f64 a 9))))) (.f64 (.f64 (.f64 b b) (-.f64 1 (pow.f64 (.f64 a 3) 3))) (-.f64 1 a)))))) (.f64 (+.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (pow.f64 b 4)))) (.f64 (+.f64 1 (.f64 a (+.f64 3 (*.f64 a 9)))) (-.f64 1 a))))

rewrite4.5s

Algorithm

rewrite-expression-head

Rules

39314×	`associate-*r/_binary64`
28076×	`frac-times_binary64`
20384×	`frac-add_binary64`
14842×	`flip3--_binary64` `flip--_binary64`
14605×	`flip3-+_binary64` `flip-+_binary64`
8304×	`associate-*l/_binary64`
5202×	`associate-/l/_binary64`
34×	`add-sqr-sqrt_binary64`
30×	`add-exp-log_binary64`
26×	`associate-/r/_binary64`
20×	`associate-r_binary64` `add-cbrt-cube_binary64`
16×	`*-un-lft-identity_binary64`
15×	`prod-exp_binary64`
13×	`unswap-sqr_binary64` `unpow-prod-down_binary64`
12×	`add-cube-cbrt_binary64`
11×	`sqr-pow_binary64`
9×	`pow1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
8×	`associate-l_binary64`
7×	`cbrt-unprod_binary64`
6×	`pow-to-exp_binary64` `add-log-exp_binary64` `sub-neg_binary64` `cube-prod_binary64` `pow-exp_binary64`
4×	`associate-+l+_binary64` `difference-of-squares_binary64` `associate-+r+_binary64`
3×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`cube-div_binary64` `*-commutative_binary64`
1×	`associate-/r*_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `+-commutative_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 10549

Calls

4 calls:

11.0ms	(.f64 (.f64 b b) (-.f64 1 (pow.f64 (*.f64 a 3) 3)))
167.0ms	(+.f64 (.f64 (+.f64 (pow.f64 (.f64 b b) 6) (.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (.f64 (.f64 b b) 2)) 3))) (.f64 (+.f64 1 (.f64 a (+.f64 3 (.f64 a 9)))) (-.f64 1 a))) (.f64 (+.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (pow.f64 b 4)))) (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a (+.f64 3 (.f64 a 9))))) (.f64 (.f64 (.f64 b b) (-.f64 1 (pow.f64 (.f64 a 3) 3))) (-.f64 1 a))))))
13.0ms	(.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (.f64 (.f64 b b) 2)) 3))
494.0ms	(/.f64 (+.f64 (.f64 (+.f64 (pow.f64 (.f64 b b) 6) (.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (.f64 (.f64 b b) 2)) 3))) (.f64 (+.f64 1 (.f64 a (+.f64 3 (.f64 a 9)))) (-.f64 1 a))) (.f64 (+.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (pow.f64 b 4)))) (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a (+.f64 3 (.f64 a 9))))) (.f64 (.f64 (.f64 b b) (-.f64 1 (pow.f64 (.f64 a 3) 3))) (-.f64 1 a)))))) (.f64 (+.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (pow.f64 b 4)))) (.f64 (+.f64 1 (.f64 a (+.f64 3 (*.f64 a 9)))) (-.f64 1 a))))

series3.9s

Counts

4 → 12

Calls

4 calls:

78.0ms	(.f64 (.f64 b b) (-.f64 1 (pow.f64 (*.f64 a 3) 3)))
2.5s	(+.f64 (.f64 (+.f64 (pow.f64 (.f64 b b) 6) (.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (.f64 (.f64 b b) 2)) 3))) (.f64 (+.f64 1 (.f64 a (+.f64 3 (.f64 a 9)))) (-.f64 1 a))) (.f64 (+.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (pow.f64 b 4)))) (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a (+.f64 3 (.f64 a 9))))) (.f64 (.f64 (.f64 b b) (-.f64 1 (pow.f64 (.f64 a 3) 3))) (-.f64 1 a))))))
98.0ms	(.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (.f64 (.f64 b b) 2)) 3))
1.3s	(/.f64 (+.f64 (.f64 (+.f64 (pow.f64 (.f64 b b) 6) (.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (.f64 (.f64 b b) 2)) 3))) (.f64 (+.f64 1 (.f64 a (+.f64 3 (.f64 a 9)))) (-.f64 1 a))) (.f64 (+.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (pow.f64 b 4)))) (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a (+.f64 3 (.f64 a 9))))) (.f64 (.f64 (.f64 b b) (-.f64 1 (pow.f64 (.f64 a 3) 3))) (-.f64 1 a)))))) (.f64 (+.f64 (pow.f64 b 8) (.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (pow.f64 b 4)))) (.f64 (+.f64 1 (.f64 a (+.f64 3 (*.f64 a 9)))) (-.f64 1 a))))

simplify28.9s

Algorithm

egg-herbie

Counts

10561 → 10561

Iterations

Useful iterations: 0 (648.0ms)

Iter	Nodes	Cost
0	27129	5016568

prune1.8min

Filtered: 10540 candidates to 10561 candidates (-0.2%)

Details

analyze147.0ms

sample28.0ms

simplify51.0ms

prune3.0ms

localize16.0ms

rewrite32.0ms

series183.0ms

simplify79.0ms

prune108.0ms

localize21.0ms

rewrite46.0ms

series183.0ms

simplify117.0ms

prune214.0ms

localize20.0ms

rewrite26.0ms

series297.0ms

simplify67.0ms

prune138.0ms

localize54.0ms

rewrite4.5s

series3.9s

simplify28.9s

prune1.8min

Profiling