Details

analyze137.0ms (0.1%)

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%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify75.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4975	46
1	4975	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%)

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)
0.8b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite41.0ms (0%)

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` `insert-posit16`
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 → 82

Calls

4 calls:

13.0ms	(+.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))
10.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
6.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series352.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

153.0ms	(+.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))))))
73.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
69.0ms	(.f64 (.f64 a a) (+.f64 1 a))
57.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify64.0ms (0%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4977	1907
1	4977	1907

prune156.0ms (0.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	4	95

Merged error: 0.0b

Counts

95 → 4

Compiler

Compiled 3659 to 1987 computations (45.7% saved)

localize22.0ms (0%)

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))
0.8b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
2.2b	(.f64 (.f64 b b) (*.f64 a a))

rewrite74.0ms (0%)

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` `insert-posit16`
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 → 108

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))))))
13.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
11.0ms	(.f64 (.f64 b b) (*.f64 a a))
11.0ms	(.f64 (.f64 a a) (+.f64 1 a))

series356.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

147.0ms	(+.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))))))
73.0ms	(.f64 (.f64 a a) (+.f64 1 a))
69.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
67.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify116.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4948	4845
1	4948	4845

prune305.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	121	3	124

Merged error: 0.0b

Counts

124 → 3

Compiler

Compiled 6698 to 4078 computations (39.1% saved)

localize27.0ms (0%)

Local error

Found 4 expressions with local error:

0.8b	(.f64 (.f64 b b) (-.f64 1 (*.f64 a 3)))
0.8b	(.f64 (.f64 b b) (-.f64 1 (*.f64 a 3)))
8.3b	(sqrt.f64 (+.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (+.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
8.3b	(sqrt.f64 (+.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (+.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))

rewrite104.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`associate-*r/_binary64`
40×	`frac-add_binary64`
28×	`sqrt-div_binary64`
26×	`flip3-+_binary64` `flip-+_binary64`
16×	`pow1_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`flip3--_binary64` `flip--_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` `insert-posit16`
2×	`pow1/2_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`

Counts

4 → 104

Calls

4 calls:

40.0ms	(sqrt.f64 (+.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (+.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
37.0ms	(sqrt.f64 (+.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (+.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
10.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 a 3)))
10.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 a 3)))

series452.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

160.0ms	(sqrt.f64 (+.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (+.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
152.0ms	(sqrt.f64 (+.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (+.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
72.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 a 3)))
68.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 a 3)))

simplify181.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4907	8610
1	4907	8610

prune650.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	116	3	119

Merged error: 0.0b

Counts

119 → 3

Compiler

Compiled 12809 to 7720 computations (39.7% saved)

localize44.0ms (0%)

Local error

Found 4 expressions with local error:

2.2b	(*.f64 (pow.f64 b 4) (pow.f64 a 4))
2.3b	(-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (*.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))
3.6b	(+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
40.0b	(/.f64 (+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))

rewrite5.5s (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

33576×	`associate-*r/_binary64`
28076×	`frac-times_binary64`
21935×	`flip3--_binary64` `flip--_binary64`
20384×	`frac-add_binary64`
14038×	`associate-*l/_binary64`
7511×	`flip3-+_binary64` `flip-+_binary64`
5202×	`associate-/l/_binary64`
26×	`associate-/r/_binary64`
25×	`add-exp-log_binary64`
22×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
12×	`unpow-prod-down_binary64` `prod-exp_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`unswap-sqr_binary64`
8×	`add-log-exp_binary64` `sqr-pow_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`pow-to-exp_binary64` `pow-exp_binary64`
5×	`sub-neg_binary64`
4×	`pow1_binary64` `cbrt-unprod_binary64` `insert-posit16`
3×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-/l*_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`associate--r+_binary64` `associate-+l+_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 10525

Calls

4 calls:

650.0ms	(/.f64 (+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
202.0ms	(+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
10.0ms	(-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (*.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))
9.0ms	(*.f64 (pow.f64 b 4) (pow.f64 a 4))

series2.0s (1.3%)

Counts

4 → 12

Calls

4 calls:

1.1s	(+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
608.0ms	(/.f64 (+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
168.0ms	(-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (*.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))
103.0ms	(*.f64 (pow.f64 b 4) (pow.f64 a 4))

simplify23.1s (15.4%)

Algorithm

1×	egg-herbie

Counts

10537 → 10537

Iterations

Useful iterations: 0 (547.0ms)

Iter	Nodes	Cost
0	27065	3858694

Details

analyze137.0ms (0.1%)

sample25.0ms (0%)

simplify75.0ms (0.1%)

prune3.0ms (0%)

localize17.0ms (0%)

rewrite41.0ms (0%)

series352.0ms (0.2%)

simplify64.0ms (0%)

prune156.0ms (0.1%)

localize22.0ms (0%)

rewrite74.0ms (0%)

series356.0ms (0.2%)

simplify116.0ms (0.1%)

prune305.0ms (0.2%)

localize27.0ms (0%)

rewrite104.0ms (0.1%)

series452.0ms (0.3%)

simplify181.0ms (0.1%)

prune650.0ms (0.4%)

localize44.0ms (0%)

rewrite5.5s (3.7%)

series2.0s (1.3%)

simplify23.1s (15.4%)

prune1.9min (77.5%)

Profiling