Details

analyze136.0ms (1.4%)

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 (0.3%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5055	46

prune4.0ms (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: 0.1b

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))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.4b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite42.0ms (0.4%)

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:

12.0ms	(+.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))))))
11.0ms	(.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)

series365.0ms (3.7%)

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))))))
93.0ms	(.f64 (.f64 a a) (+.f64 1 a))
69.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
54.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5091	1907

prune158.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	4	95

Merged error: 0b

Counts

95 → 4

Compiler

Compiled 3658 to 1981 computations (45.8% saved)

localize21.0ms (0.2%)

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))
0.4b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
1.4b	(.f64 (.f64 b b) (*.f64 a a))

rewrite75.0ms (0.8%)

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:

37.0ms	(+.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))))))
11.0ms	(.f64 (.f64 b b) (*.f64 a a))
10.0ms	(.f64 (.f64 a a) (+.f64 1 a))
10.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series341.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(+.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))
65.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
57.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify118.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4955	4845
1	4955	4845

prune321.0ms (3.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	120	4	124

Merged error: 0b

Counts

124 → 4

Compiler

Compiled 6689 to 4052 computations (39.4% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.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)))))) (cbrt.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)))))))
9.3b	(cbrt.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))))))
9.3b	(cbrt.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))))))
9.3b	(cbrt.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))))))

rewrite56.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `insert-posit16` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 91

Calls

4 calls:

25.0ms	(.f64 (cbrt.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)))))) (cbrt.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)))))))
9.0ms	(cbrt.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))))))
9.0ms	(cbrt.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))))))
9.0ms	(cbrt.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))))))

series1.3s (13.6%)

Counts

4 → 12

Calls

4 calls:

434.0ms	(.f64 (cbrt.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)))))) (cbrt.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)))))))
311.0ms	(cbrt.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))))))
305.0ms	(cbrt.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))))))
298.0ms	(cbrt.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))))))

simplify206.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	4888	7039
1	4888	7039

prune529.0ms (5.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	103	4	107

Merged error: 0b

Counts

107 → 4

Compiler

Compiled 11081 to 5938 computations (46.4% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
1.8b	(+.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))
5.6b	(+.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)))))
40.8b	(/.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))))))

rewrite72.0ms (0.7%)

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` `insert-posit16` `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 → 97

Calls

4 calls:

29.0ms	(/.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))))))
14.0ms	(+.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))
14.0ms	(+.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)))))
11.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series4.0s (40.3%)

Counts

4 → 12

Calls

4 calls:

1.8s	(+.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))
1.2s	(/.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))))))
977.0ms	(+.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)))))
66.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

simplify201.0ms (2%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	4943	10292
1	4943	10292

prune625.0ms (6.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	109	4	113

Merged error: 0b

Counts

113 → 4

Compiler

Compiled 12834 to 6762 computations (47.3% saved)

regimes119.0ms (1.2%)

Compiler: Compiled 1639 to 1003 computations (38.8% saved)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	80	58
1	80	58

end0.0ms (0%)

sample918.0ms (9.3%)

Algorithm

1×

intervals

Results

555.0ms	8000×	body	80	valid
0.0ms	5×	body	80	invalid

Compiler

Compiled 328 to 206 computations (37.2% saved)

Details

analyze136.0ms (1.4%)

sample25.0ms (0.3%)

simplify72.0ms (0.7%)

prune4.0ms (0%)

localize17.0ms (0.2%)

rewrite42.0ms (0.4%)

series365.0ms (3.7%)

simplify63.0ms (0.6%)

prune158.0ms (1.6%)

localize21.0ms (0.2%)

rewrite75.0ms (0.8%)

series341.0ms (3.4%)

simplify118.0ms (1.2%)

prune321.0ms (3.2%)

localize27.0ms (0.3%)

rewrite56.0ms (0.6%)

series1.3s (13.6%)

simplify206.0ms (2.1%)

prune529.0ms (5.4%)

localize32.0ms (0.3%)

rewrite72.0ms (0.7%)

series4.0s (40.3%)

simplify201.0ms (2%)

prune625.0ms (6.3%)

regimes119.0ms (1.2%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample918.0ms (9.3%)

Profiling