Details

analyze138.0ms (3%)

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)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify78.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4912	46
1	4912	46

prune6.0ms (0.1%)

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 (0.4%)

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)
1.0b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite42.0ms (0.9%)

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` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `associate-l_binary64` `cancel-sign-sub-inv_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 → 80

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

series318.0ms (7%)

Counts

4 → 12

Calls

4 calls:

140.0ms	(+.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))))))
65.0ms	(.f64 (.f64 a a) (+.f64 1 a))
60.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
52.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify44.0ms (1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5112	1848

prune331.0ms (7.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 0.0b

Counts

93 → 5

Compiler

Compiled 7922 to 4634 computations (41.5% saved)

localize21.0ms (0.5%)

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))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
1.0b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
3.2b	(.f64 (.f64 b b) (*.f64 a a))

rewrite77.0ms (1.7%)

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` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
2×	`sub-neg_binary64` `cancel-sign-sub-inv_binary64` `pow-sqr_binary64` `associate-+r+_binary64` `pow2_binary64`
1×	`distribute-lft-out_binary64` `associate-+l+_binary64` `+-commutative_binary64`

Counts

4 → 106

Calls

4 calls:

31.0ms	(+.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))
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series322.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

148.0ms	(+.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))))))
70.0ms	(.f64 (.f64 a a) (+.f64 1 a))
59.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
44.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify98.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4935	4777
1	4935	4777

prune329.0ms (7.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	118	5	123

Merged error: 0.0b

Counts

123 → 5

Compiler

Compiled 7091 to 4302 computations (39.3% saved)

localize25.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (pow.f64 (.f64 b a) 2)) (+.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))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.2b	(pow.f64 (*.f64 b a) 2)
1.0b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite60.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`associate-*r/_binary64`
20×	`frac-add_binary64`
17×	`pow1_binary64` `add-exp-log_binary64`
14×	`flip3-+_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
13×	`add-log-exp_binary64`
9×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`pow-prod-down_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
6×	`cbrt-unprod_binary64` `sum-log_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
3×	`pow-unpow_binary64`
2×	`sub-neg_binary64` `pow-pow_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `unswap-sqr_binary64` `associate-+r+_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `associate-+l+_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `+-commutative_binary64`

Counts

4 → 95

Calls

4 calls:

21.0ms	(+.f64 (+.f64 (.f64 2 (pow.f64 (.f64 b a) 2)) (+.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))))))
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
9.0ms	(.f64 (.f64 a a) (+.f64 1 a))
4.0ms	(pow.f64 (*.f64 b a) 2)

series317.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(+.f64 (+.f64 (.f64 2 (pow.f64 (.f64 b a) 2)) (+.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))))))
66.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
65.0ms	(.f64 (.f64 a a) (+.f64 1 a))
41.0ms	(pow.f64 (*.f64 b a) 2)

simplify74.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5183	4474

prune286.0ms (6.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	107	5	112

Merged error: 0.0b

Counts

112 → 5

Compiler

Compiled 6330 to 4175 computations (34% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
1.0b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
11.7b	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))
11.7b	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))

rewrite48.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow1_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `cancel-sign-sub-inv_binary64` `sqrt-div_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

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

series410.0ms (9%)

Counts

4 → 12

Calls

4 calls:

148.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))
136.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))
64.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
63.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

simplify74.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5054	2656

prune305.0ms (6.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	91	6	97

Merged error: 0.0b

Counts

97 → 6

Compiler

Compiled 7444 to 4060 computations (45.5% saved)

regimes104.0ms (2.3%)

Compiler: Compiled 1755 to 1051 computations (40.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	55
1	78	55

end0.0ms (0%)

sample992.0ms (21.7%)

Algorithm

1×

intervals

Results

537.0ms	8000×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 513 to 318 computations (38% saved)

Details

analyze138.0ms (3%)

sample25.0ms (0.5%)

simplify78.0ms (1.7%)

prune6.0ms (0.1%)

localize17.0ms (0.4%)

rewrite42.0ms (0.9%)

series318.0ms (7%)

simplify44.0ms (1%)

prune331.0ms (7.2%)

localize21.0ms (0.5%)

rewrite77.0ms (1.7%)

series322.0ms (7.1%)

simplify98.0ms (2.2%)

prune329.0ms (7.2%)

localize25.0ms (0.5%)

rewrite60.0ms (1.3%)

series317.0ms (6.9%)

simplify74.0ms (1.6%)

prune286.0ms (6.3%)

localize21.0ms (0.5%)

rewrite48.0ms (1.1%)

series410.0ms (9%)

simplify74.0ms (1.6%)

prune305.0ms (6.7%)

regimes104.0ms (2.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample992.0ms (21.7%)

Profiling