Details

analyze245.0ms (5.6%)

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 34 to 22 computations (35.3% saved)

sample31.0ms (0.7%)

Algorithm

1×

intervals

Results

22.0ms

256×

body

128

valid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify58.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
373×	`neg-sub0_binary64`
373×	`neg-mul-1_binary64`
340×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	46
1	61	46
2	152	46
3	438	46
4	1297	46
5	2510	46
6	4609	46
7	5033	46

prune3.0ms (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

Error

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (+.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)))))) 1)

Compiler

Compiled 99 to 63 computations (36.4% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite169.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

18×	`associate-*r/_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
16×	`add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`

Counts

4 → 93

Calls

4 calls:

11.0ms	(.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))
6.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 3675 to 2053 computations (44.1% saved)

series131.0ms (3%)

Error

0.0b

Counts

4 → 43

Calls

4 calls:

43.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
33.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))
21.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
10.0ms	(.f64 (.f64 a a) (+.f64 1 a))

Compiler

Compiled 2632 to 1870 computations (29% saved)

simplify141.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

588×	`associate-+r+_binary64`
385×	`associate-l_binary64`
318×	`associate-r_binary64`
273×	`exp-prod_binary64`
187×	`distribute-rgt-in_binary64`

Counts

136 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	262	3881
1	736	3708
2	2558	3615
3	4864	3612
4	5130	3612

prune88.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	3	119

Error

0.0b

Counts

119 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (+.f64 (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))) (pow.f64 b 4))) (+.f64 (pow.f64 a 4) -1))
	18.4b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (+.f64 (.f64 (.f64 a a) (+.f64 a 1)) (.f64 (.f64 b b) (-.f64 1 (.f64 a 3)))) (cbrt.f64 4)))) 1)

Compiler

Compiled 2753 to 1587 computations (42.4% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 4 (*.f64 a 12))
0.0b	(+.f64 (.f64 (.f64 b b) (-.f64 4 (*.f64 a 12))) (pow.f64 b 4))
0.2b	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))
1.3b	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1))))

rewrite134.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`

Counts

4 → 75

Calls

4 calls:

9.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))
8.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1))))
7.0ms	(+.f64 (.f64 (.f64 b b) (-.f64 4 (*.f64 a 12))) (pow.f64 b 4))
2.0ms	(-.f64 4 (*.f64 a 12))

Compiler

Compiled 3247 to 2092 computations (35.6% saved)

series135.0ms (3.1%)

Error

0.0b

Counts

4 → 36

Calls

4 calls:

38.0ms	(+.f64 (.f64 (.f64 b b) (-.f64 4 (*.f64 a 12))) (pow.f64 b 4))
37.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1))))
24.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))
11.0ms	(-.f64 4 (*.f64 a 12))

Compiler

Compiled 2665 to 1982 computations (25.6% saved)

simplify119.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

439×	`+-commutative_binary64`
433×	`sub-neg_binary64`
330×	`associate-l_binary64`
276×	`associate-r_binary64`
259×	`exp-prod_binary64`

Counts

111 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	3538
1	600	3187
2	2191	3145
3	4172	3145
4	5157	3145

prune68.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	83	3	86

Error

0.0b

Counts

86 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (+.f64 (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))) (pow.f64 b 4))) (+.f64 (pow.f64 a 4) -1))
	18.4b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (+.f64 (.f64 (.f64 a a) (+.f64 a 1)) (.f64 (.f64 b b) (-.f64 1 (.f64 a 3)))) (cbrt.f64 4)))) 1)

Compiler

Compiled 1864 to 1230 computations (34% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (+.f64 (.f64 (.f64 a a) (+.f64 a 1)) (.f64 (.f64 b b) (-.f64 1 (.f64 a 3)))) (cbrt.f64 4)))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.4b	(.f64 (+.f64 (.f64 (.f64 a a) (+.f64 a 1)) (.f64 (.f64 b b) (-.f64 1 (.f64 a 3)))) (cbrt.f64 4))
1.0b	(*.f64 (cbrt.f64 4) (cbrt.f64 4))

rewrite206.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

29×	`add-sqr-sqrt_binary64`
26×	`pow1_binary64`
22×	`associate-*r/_binary64`
21×	`add-exp-log_binary64`
20×	`cbrt-prod_binary64`

Counts

4 → 114

Calls

4 calls:

18.0ms	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (+.f64 (.f64 (.f64 a a) (+.f64 a 1)) (.f64 (.f64 b b) (-.f64 1 (.f64 a 3)))) (cbrt.f64 4)))
11.0ms	(.f64 (+.f64 (.f64 (.f64 a a) (+.f64 a 1)) (.f64 (.f64 b b) (-.f64 1 (.f64 a 3)))) (cbrt.f64 4))
5.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 5431 to 3467 computations (36.2% saved)

series167.0ms (3.8%)

Error

0.0b

Counts

4 → 40

Calls

4 calls:

53.0ms	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (+.f64 (.f64 (.f64 a a) (+.f64 a 1)) (.f64 (.f64 b b) (-.f64 1 (.f64 a 3)))) (cbrt.f64 4)))
44.0ms	(.f64 (+.f64 (.f64 (.f64 a a) (+.f64 a 1)) (.f64 (.f64 b b) (-.f64 1 (.f64 a 3)))) (cbrt.f64 4))
44.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))

Compiler

Compiled 2916 to 2297 computations (21.2% saved)

simplify186.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

445×	`associate-l_binary64`
422×	`associate-+l+_binary64`
408×	`associate-r_binary64`
222×	`exp-prod_binary64`
186×	`cancel-sign-sub-inv_binary64`

Counts

154 → 130

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	246	5508
1	683	4333
2	2668	4299
3	4727	4289
4	4956	4289

prune150.0ms (3.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	130	3	133

Error

0.0b

Counts

133 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (+.f64 (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))) (pow.f64 b 4))) (+.f64 (pow.f64 a 4) -1))
▶	18.4b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (+.f64 (.f64 (.f64 a a) (+.f64 a 1)) (.f64 (.f64 b b) (-.f64 1 (.f64 a 3)))) (cbrt.f64 4)))) 1)

Compiler

Compiled 3395 to 2115 computations (37.7% saved)

localize24.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.2b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
0.2b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)
28.0b	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6))

rewrite117.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

15×	`add-exp-log_binary64`
15×	`pow1_binary64`
14×	`add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

4 → 81

Calls

4 calls:

7.0ms	(.f64 (.f64 a a) (+.f64 1 a))
7.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)
4.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6))

Compiler

Compiled 2996 to 1640 computations (45.3% saved)

series105.0ms (2.4%)

Error

0.0b

Counts

4 → 38

Calls

4 calls:

44.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6))
20.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
15.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)
12.0ms	(.f64 (.f64 a a) (+.f64 1 a))

Compiler

Compiled 2465 to 1766 computations (28.4% saved)

simplify152.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

471×	`distribute-rgt-in_binary64`
417×	`distribute-lft-in_binary64`
389×	`*-commutative_binary64`
382×	`exp-prod_binary64`
284×	`associate-+l+_binary64`

Counts

119 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	3214
1	500	3026
2	1538	2923
3	3856	2867
4	4782	2867
5	5048	2867

prune64.0ms (1.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	105	3	108

Error

0.0b

Counts

108 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (+.f64 (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))) (pow.f64 b 4))) (+.f64 (pow.f64 a 4) -1))
✓	18.4b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (+.f64 (.f64 (.f64 a a) (+.f64 a 1)) (.f64 (.f64 b b) (-.f64 1 (.f64 a 3)))) (cbrt.f64 4)))) 1)

Compiler

Compiled 1964 to 1110 computations (43.5% saved)

regimes805.0ms (18.5%)

Accuracy

Total 0.0b remaining (75.5%)

Threshold costs 0.0b (75.5%)

Compiler

Compiled 21258 to 14621 computations (31.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	46
1	31	46
2	31	46

end1.0ms (0%)

Compiler: Compiled 33 to 23 computations (30.3% saved)

sample993.0ms (22.8%)

Algorithm

1×

intervals

Results

662.0ms	8000×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 180 to 123 computations (31.7% saved)

Details

analyze245.0ms (5.6%)

sample31.0ms (0.7%)

simplify58.0ms (1.3%)

prune3.0ms (0.1%)

localize18.0ms (0.4%)

rewrite169.0ms (3.9%)

series131.0ms (3%)

simplify141.0ms (3.2%)

prune88.0ms (2%)

localize20.0ms (0.5%)

rewrite134.0ms (3.1%)

series135.0ms (3.1%)

simplify119.0ms (2.7%)

prune68.0ms (1.6%)

localize20.0ms (0.5%)

rewrite206.0ms (4.7%)

series167.0ms (3.8%)

simplify186.0ms (4.3%)

prune150.0ms (3.4%)

localize24.0ms (0.6%)

rewrite117.0ms (2.7%)

series105.0ms (2.4%)

simplify152.0ms (3.5%)

prune64.0ms (1.5%)

regimes805.0ms (18.5%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample993.0ms (22.8%)

Profiling