Details

analyze135.0ms (1.9%)

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%	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

Compiler

Compiled 32 to 22 computations (31.3% saved)

sample26.0ms (0.4%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4974	46
1	4974	46

prune3.0ms (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

Compiler

Compiled 62 to 42 computations (32.3% saved)

localize17.0ms (0.2%)

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))))))
0.0b	(.f64 (.f64 a a) (+.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.5b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite41.0ms (0.6%)

Algorithm

1×	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:

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

series332.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

148.0ms	(+.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))))))
68.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
66.0ms	(.f64 (.f64 a a) (+.f64 1 a))
50.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify40.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4970	1820
1	4970	1820

prune145.0ms (2.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	2	91

Merged error: 0b

Counts

91 → 2

Compiler

Compiled 3432 to 1855 computations (45.9% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.0b	(.f64 (.f64 a a) (+.f64 1 a))
0.5b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
2.8b	(.f64 (.f64 b b) (*.f64 a a))

rewrite78.0ms (1.1%)

Algorithm

1×	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:

33.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
10.0ms	(.f64 (.f64 b b) (*.f64 a a))
9.0ms	(.f64 (.f64 a a) (+.f64 1 a))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series328.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

142.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
74.0ms	(.f64 (.f64 a a) (+.f64 1 a))
63.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
48.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify258.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4941	4749
1	4941	4749

prune306.0ms (4.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	116	2	118

Merged error: 0b

Counts

118 → 2

Compiler

Compiled 6431 to 3902 computations (39.3% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
2.8b	(+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a)))) 3))
5.8b	(+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a)))) (pow.f64 (+.f64 (.f64 b b) (*.f64 a a)) 2)))))
44.7b	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a)))) 3)) (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a)))) (pow.f64 (+.f64 (.f64 b b) (*.f64 a a)) 2))))))

rewrite84.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
17×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64` `associate-+r+_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64`
8×	`add-log-exp_binary64` `associate--l+_binary64`
6×	`sub-neg_binary64`
5×	`distribute-lft-out_binary64`
4×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `associate-r*_binary64` `prod-exp_binary64`
2×	`associate-/l/_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `+-commutative_binary64` `sum-log_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

25.0ms	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a)))) 3)) (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a)))) (pow.f64 (+.f64 (.f64 b b) (*.f64 a a)) 2))))))
12.0ms	(+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a)))) 3))
11.0ms	(+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a)))) (pow.f64 (+.f64 (.f64 b b) (*.f64 a a)) 2)))))
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series3.7s (52.2%)

Counts

4 → 12

Calls

4 calls:

1.7s	(+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a)))) 3))
1.1s	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a)))) 3)) (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a)))) (pow.f64 (+.f64 (.f64 b b) (*.f64 a a)) 2))))))
866.0ms	(+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a)))) (pow.f64 (+.f64 (.f64 b b) (*.f64 a a)) 2)))))
69.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

simplify109.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5109	10001

prune525.0ms (7.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	105	2	107

Merged error: 0b

Counts

107 → 2

Compiler

Compiled 12454 to 6562 computations (47.3% saved)

regimes37.0ms (0.5%)

Compiler: Compiled 406 to 254 computations (37.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	77	58
1	77	58

end0.0ms (0%)

sample803.0ms (11.4%)

Algorithm

1×

intervals

Results

519.0ms	8000×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 203 to 131 computations (35.5% saved)

Details

analyze135.0ms (1.9%)

sample26.0ms (0.4%)

simplify39.0ms (0.6%)

prune3.0ms (0%)

localize17.0ms (0.2%)

rewrite41.0ms (0.6%)

series332.0ms (4.7%)

simplify40.0ms (0.6%)

prune145.0ms (2.1%)

localize22.0ms (0.3%)

rewrite78.0ms (1.1%)

series328.0ms (4.7%)

simplify258.0ms (3.7%)

prune306.0ms (4.4%)

localize30.0ms (0.4%)

rewrite84.0ms (1.2%)

series3.7s (52.2%)

simplify109.0ms (1.5%)

prune525.0ms (7.5%)

regimes37.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample803.0ms (11.4%)

Profiling