Details

analyze139.0ms (4.9%)

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)

sample24.0ms (0.8%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify79.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4966	46
1	4966	46

prune7.0ms (0.2%)

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 (0.6%)

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))
0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.6b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite35.0ms (1.2%)

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 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)

series56.0ms (2%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(+.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	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
6.0ms	(.f64 (.f64 a a) (+.f64 1 a))

simplify82.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5072	1820

prune101.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	87	4	91

Merged error: 0b

Counts

91 → 4

Compiler

Compiled 3426 to 1854 computations (45.9% saved)

localize25.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.0b	(+.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 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.6b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
2.9b	(.f64 (.f64 b b) (*.f64 a a))

rewrite49.0ms (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` `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:

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 1 (.f64 3 a))))))
9.0ms	(.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)))

series55.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(+.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 1 (.f64 3 a))))))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
8.0ms	(.f64 (.f64 b b) (*.f64 a a))
6.0ms	(.f64 (.f64 a a) (+.f64 1 a))

simplify122.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5056	4824

prune207.0ms (7.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	116	4	120

Merged error: 0b

Counts

120 → 4

Compiler

Compiled 6469 to 3829 computations (40.8% saved)

localize21.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
15.8b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
15.8b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
15.8b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))

rewrite29.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `unpow2_binary64` `pow1/3_binary64` `sqr-pow_binary64` `prod-exp_binary64`
2×	`sub-neg_binary64` `associate-*r/_binary64`
1×	`flip3--_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 71

Calls

4 calls:

8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
7.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
5.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
5.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))

series80.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
23.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
23.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

simplify117.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4870	1568
1	4870	1568

prune115.0ms (4.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	83	4	87

Merged error: 0b

Counts

87 → 4

Compiler

Compiled 4986 to 2333 computations (53.2% saved)

localize20.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.6b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
4.0b	(exp.f64 (.f64 (log.f64 (+.f64 (.f64 b b) (*.f64 a a))) 2))
8.8b	(log.f64 (+.f64 (.f64 b b) (.f64 a a)))

rewrite29.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`pow1_binary64` `add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`associate-r_binary64` `add-cube-cbrt_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
5×	`add-log-exp_binary64`
4×	`associate-*r/_binary64`
3×	`log-prod_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `log-div_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `exp-lft-sqr_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `log-pow_binary64` `rem-exp-log_binary64` `flip--_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

4 → 72

Calls

4 calls:

9.0ms	(.f64 (.f64 a a) (+.f64 1 a))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
5.0ms	(exp.f64 (.f64 (log.f64 (+.f64 (.f64 b b) (*.f64 a a))) 2))
5.0ms	(log.f64 (+.f64 (.f64 b b) (.f64 a a)))

series33.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(exp.f64 (.f64 (log.f64 (+.f64 (.f64 b b) (*.f64 a a))) 2))
9.0ms	(log.f64 (+.f64 (.f64 b b) (.f64 a a)))
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
6.0ms	(.f64 (.f64 a a) (+.f64 1 a))

simplify118.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5017	1186

prune81.0ms (2.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	84	4	88

Merged error: 0b

Counts

88 → 4

Compiler

Compiled 3122 to 1692 computations (45.8% saved)

regimes173.0ms (6.1%)

Compiler: Compiled 1039 to 679 computations (34.6% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	80	58
1	80	58

end0.0ms (0%)

sample1.0s (35.8%)

Algorithm

1×

intervals

Results

529.0ms	8000×	body	80	valid
0.0ms	6×	body	80	invalid

Compiler

Compiled 228 to 152 computations (33.3% saved)

Details

analyze139.0ms (4.9%)

sample24.0ms (0.8%)

simplify79.0ms (2.8%)

prune7.0ms (0.2%)

localize17.0ms (0.6%)

rewrite35.0ms (1.2%)

series56.0ms (2%)

simplify82.0ms (2.9%)

prune101.0ms (3.6%)

localize25.0ms (0.9%)

rewrite49.0ms (1.7%)

series55.0ms (1.9%)

simplify122.0ms (4.3%)

prune207.0ms (7.3%)

localize21.0ms (0.7%)

rewrite29.0ms (1%)

series80.0ms (2.8%)

simplify117.0ms (4.1%)

prune115.0ms (4.1%)

localize20.0ms (0.7%)

rewrite29.0ms (1%)

series33.0ms (1.2%)

simplify118.0ms (4.2%)

prune81.0ms (2.9%)

regimes173.0ms (6.1%)

bsearch0.0ms (0%)

simplify5.0ms (0.2%)

end0.0ms (0%)

sample1.0s (35.8%)

Profiling