Details

analyze134.0ms

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

sample23.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5159	29

prune6.0ms

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:

0.1b	(+.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))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.0b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1_binary64` `add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
13×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
10×	`associate-r_binary64`
8×	`add-cube-cbrt_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` `difference-of-squares_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` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 81

Calls

4 calls:

10.0ms	(+.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)))))
12.0ms	(.f64 (.f64 a a) (-.f64 1 a))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
9.0ms	(.f64 (.f64 b b) (+.f64 3 a))

series56.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+.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)))))
8.0ms	(.f64 (.f64 a a) (-.f64 1 a))
10.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
7.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify30.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5156	1172

prune110.0ms

Filtered

63 candidates to 93 candidates (-47.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	2	94

Merged error: 0.0b

Counts

94 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.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))
1.0b	(.f64 (.f64 b b) (+.f64 3 a))
2.6b	(.f64 (.f64 b b) (*.f64 a a))

rewrite52.0ms

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`
11×	`-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` `difference-of-squares_binary64` `pow-sqr_binary64` `associate-+r+_binary64` `pow2_binary64`
1×	`distribute-lft-out_binary64` `associate-+l+_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64`

Counts

4 → 107

Calls

4 calls:

18.0ms	(+.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)))))
10.0ms	(.f64 (.f64 a a) (-.f64 1 a))
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
10.0ms	(.f64 (.f64 b b) (*.f64 a a))

series58.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+.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)))))
8.0ms	(.f64 (.f64 a a) (-.f64 1 a))
7.0ms	(.f64 (.f64 b b) (+.f64 3 a))
12.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify68.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4988	3077
1	4988	3077

prune172.0ms

Filtered

76 candidates to 119 candidates (-56.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	118	3	121

Merged error: 0.0b

Counts

121 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 a (-.f64 a (.f64 a a))) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.1b	(.f64 a (-.f64 a (.f64 a a)))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.0b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `pow1_binary64` `add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
9×	`associate-r_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `associate-l*_binary64` `prod-exp_binary64`
3×	`pow-unpow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unpow-prod-down_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `unswap-sqr_binary64` `flip-+_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `distribute-rgt-out--_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 79

Calls

4 calls:

9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 a (-.f64 a (.f64 a a))) (.f64 (*.f64 b b) (+.f64 3 a)))))
6.0ms	(.f64 a (-.f64 a (.f64 a a)))
6.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
9.0ms	(.f64 (.f64 b b) (+.f64 3 a))

series59.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 a (-.f64 a (.f64 a a))) (.f64 (*.f64 b b) (+.f64 3 a)))))
9.0ms	(.f64 a (-.f64 a (.f64 a a)))
10.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
7.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify28.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5198	1164

prune91.0ms

Filtered

65 candidates to 91 candidates (-40.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Merged error: 0.0b

Counts

94 → 3

localize54.0ms

Local error

Found 4 expressions with local error:

2.0b	(.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)))
3.7b	(.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (.f64 (.f64 b b) 2)) 3))
3.8b	(+.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 (pow.f64 a 4) (.f64 (-.f64 1 a) (-.f64 1 a))) (.f64 b (.f64 (.f64 b (+.f64 a 3)) (-.f64 (.f64 (.f64 b b) (+.f64 a 3)) (.f64 (.f64 a a) (-.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 (pow.f64 (.f64 (.f64 b b) (+.f64 a 3)) 3) (pow.f64 (.f64 (.f64 a a) (-.f64 1 a)) 3)))))
50.9b	(/.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 (pow.f64 a 4) (.f64 (-.f64 1 a) (-.f64 1 a))) (.f64 b (.f64 (.f64 b (+.f64 a 3)) (-.f64 (.f64 (.f64 b b) (+.f64 a 3)) (.f64 (.f64 a a) (-.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 (pow.f64 (.f64 (.f64 b b) (+.f64 a 3)) 3) (pow.f64 (.f64 (.f64 a a) (-.f64 1 a)) 3))))) (.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 (pow.f64 a 4) (.f64 (-.f64 1 a) (-.f64 1 a))) (.f64 b (.f64 (.f64 b (+.f64 a 3)) (-.f64 (.f64 (.f64 b b) (+.f64 a 3)) (.f64 (*.f64 a a) (-.f64 1 a))))))))

rewrite10.6s

Algorithm

rewrite-expression-head

Rules

141070×	`associate-*r/_binary64`
50912×	`frac-add_binary64`
46648×	`frac-times_binary64`
35220×	`flip3-+_binary64` `flip-+_binary64`
29475×	`flip3--_binary64` `flip--_binary64`
23426×	`cube-div_binary64`
11808×	`frac-sub_binary64`
9762×	`associate-/l/_binary64`
8924×	`associate-*l/_binary64`
488×	`associate-/r/_binary64`
37×	`add-sqr-sqrt_binary64`
23×	`add-exp-log_binary64`
19×	`associate-r_binary64`
15×	`*-un-lft-identity_binary64`
14×	`unpow-prod-down_binary64`
13×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
11×	`prod-exp_binary64`
10×	`sqr-pow_binary64` `associate-l_binary64`
7×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
6×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow1_binary64` `cube-prod_binary64` `pow-exp_binary64`
4×	`associate-+r+_binary64`
3×	`cbrt-unprod_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64`
2×	`sub-neg_binary64` `cbrt-undiv_binary64` `associate-+l+_binary64` `div-exp_binary64` `associate--l+_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `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 → 20133

Calls

4 calls:

17.0ms	(.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)))
31.0ms	(.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (.f64 (.f64 b b) 2)) 3))
298.0ms	(+.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 (pow.f64 a 4) (.f64 (-.f64 1 a) (-.f64 1 a))) (.f64 b (.f64 (.f64 b (+.f64 a 3)) (-.f64 (.f64 (.f64 b b) (+.f64 a 3)) (.f64 (.f64 a a) (-.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 (pow.f64 (.f64 (.f64 b b) (+.f64 a 3)) 3) (pow.f64 (.f64 (.f64 a a) (-.f64 1 a)) 3)))))
1.0s	(/.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 (pow.f64 a 4) (.f64 (-.f64 1 a) (-.f64 1 a))) (.f64 b (.f64 (.f64 b (+.f64 a 3)) (-.f64 (.f64 (.f64 b b) (+.f64 a 3)) (.f64 (.f64 a a) (-.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 (pow.f64 (.f64 (.f64 b b) (+.f64 a 3)) 3) (pow.f64 (.f64 (.f64 a a) (-.f64 1 a)) 3))))) (.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 (pow.f64 a 4) (.f64 (-.f64 1 a) (-.f64 1 a))) (.f64 b (.f64 (.f64 b (+.f64 a 3)) (-.f64 (.f64 (.f64 b b) (+.f64 a 3)) (.f64 (*.f64 a a) (-.f64 1 a))))))))

series1.9s

Counts

4 → 12

Calls

4 calls:

39.0ms	(.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)))
29.0ms	(.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (.f64 (.f64 b b) 2)) 3))
1.4s	(+.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 (pow.f64 a 4) (.f64 (-.f64 1 a) (-.f64 1 a))) (.f64 b (.f64 (.f64 b (+.f64 a 3)) (-.f64 (.f64 (.f64 b b) (+.f64 a 3)) (.f64 (.f64 a a) (-.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 (pow.f64 (.f64 (.f64 b b) (+.f64 a 3)) 3) (pow.f64 (.f64 (.f64 a a) (-.f64 1 a)) 3)))))
434.0ms	(/.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 (pow.f64 a 4) (.f64 (-.f64 1 a) (-.f64 1 a))) (.f64 b (.f64 (.f64 b (+.f64 a 3)) (-.f64 (.f64 (.f64 b b) (+.f64 a 3)) (.f64 (.f64 a a) (-.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 (pow.f64 (.f64 (.f64 b b) (+.f64 a 3)) 3) (pow.f64 (.f64 (.f64 a a) (-.f64 1 a)) 3))))) (.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 (pow.f64 a 4) (.f64 (-.f64 1 a) (-.f64 1 a))) (.f64 b (.f64 (.f64 b (+.f64 a 3)) (-.f64 (.f64 (.f64 b b) (+.f64 a 3)) (.f64 (*.f64 a a) (-.f64 1 a))))))))

simplify28.1s

Algorithm

egg-herbie

Counts

20145 → 20145

Iterations

Useful iterations: 0 (1.4s)

Iter	Nodes	Cost
0	44395	6814920

prune1.8min

Filtered: 20124 candidates to 20145 candidates (-0.1%)

Details

analyze134.0ms

sample23.0ms

simplify49.0ms

prune6.0ms

localize16.0ms

rewrite38.0ms

series56.0ms

simplify30.0ms

prune110.0ms

localize19.0ms

rewrite52.0ms

series58.0ms

simplify68.0ms

prune172.0ms

localize16.0ms

rewrite33.0ms

series59.0ms

simplify28.0ms

prune91.0ms

localize54.0ms

rewrite10.6s

series1.9s

simplify28.1s

prune1.8min

Profiling