Details

analyze415.0ms (7.9%)

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
0%	99.9%	0.1%	5
15.6%	84.3%	0.1%	6
37.5%	62.4%	0.1%	7
46.8%	53.1%	0.1%	8
57.8%	39.8%	2.4%	9
64.6%	30.4%	5%	10
71.8%	20.3%	7.9%	11
74.1%	16.2%	9.7%	12
77.4%	10.7%	12%	13
78.6%	8.4%	13%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample31.0ms (0.6%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 49 to 37 computations (24.5% saved)

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

693×	`div-sub_binary64`
599×	`times-frac_binary64`
519×	`associate-/l*_binary64`
508×	`sub-neg_binary64`
357×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	36	29
2	93	29
3	336	29
4	1152	29
5	3231	29
6	4534	29
7	5241	29

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

15.0b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	15.0b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
	15.1b	(.f64 (.f64 (/.f64 PI.f64 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

Status

Error

Program

▶

15.0b

(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

15.1b

(*.f64 (*.f64 (/.f64 PI.f64 2) (/.f64 1 (-.f64 (*.f64 b b) (*.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

Compiler

Compiled 109 to 79 computations (27.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.6b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.9b	(-.f64 (.f64 b b) (.f64 a a))
9.0b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite535.0ms (10.1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

251×	`times-frac_binary64`
178×	`add-sqr-sqrt_binary64`
153×	`*-un-lft-identity_binary64`
121×	`add-cube-cbrt_binary64`
58×	`associate-l_binary64`

Counts

4 → 270

Calls

4 calls:

48.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
14.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
7.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
3.0ms	(-.f64 (.f64 b b) (.f64 a a))

Compiler

Compiled 8446 to 4094 computations (51.5% saved)

series93.0ms (1.8%)

Error

9.3b

Counts

4 → 42

Calls

4 calls:

25.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
21.0ms	(-.f64 (.f64 b b) (.f64 a a))
17.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
16.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))

Compiler

Compiled 1531 to 1170 computations (23.6% saved)

simplify330.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

286×	`associate-*l/_binary64`
225×	`*-commutative_binary64`
217×	`associate-*r/_binary64`
208×	`associate-/l/_binary64`
191×	`associate-/r*_binary64`

Counts

312 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	387	8945
1	1051	8423
2	3665	8406
3	4802	8406
4	4993	8406
5	4959	8406

prune179.0ms (3.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	234	8	242
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	236	8	244

Error

0.0b

Counts

244 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
	0.9b	(.f64 (/.f64 (sqrt.f64 (/.f64 PI.f64 2)) (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (sqrt.f64 (/.f64 PI.f64 2)) (-.f64 b a))))
	0.6b	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
▶	0.3b	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (.f64 a b))
	15.0b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 (-.f64 b a) (.f64 a b)))
	15.0b	(+.f64 (/.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a))) a) (/.f64 (/.f64 (neg.f64 (/.f64 PI.f64 2)) b) (-.f64 (.f64 b b) (.f64 a a))))
	20.8b	(/.f64 (.f64 (/.f64 PI.f64 2) (-.f64 b a)) (.f64 (-.f64 (.f64 b b) (.f64 a a)) (*.f64 a b)))
	15.0b	(.f64 (/.f64 PI.f64 2) (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 (.f64 b b) (*.f64 a a))))

Compiler

Compiled 5270 to 2591 computations (50.8% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (.f64 a b))
0.3b	(/.f64 (/.f64 PI.f64 2) (+.f64 a b))

rewrite144.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

98×	`times-frac_binary64`
79×	`*-un-lft-identity_binary64`
60×	`add-exp-log_binary64`
51×	`add-sqr-sqrt_binary64`
51×	`add-cube-cbrt_binary64`

Counts

2 → 122

Calls

2 calls:

13.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (.f64 a b))
10.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 a b))

Compiler

Compiled 2567 to 1250 computations (51.3% saved)

series59.0ms (1.1%)

Error

0.0b

Counts

2 → 27

Calls

2 calls:

27.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 a b))
22.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (.f64 a b))

Compiler

Compiled 1072 to 795 computations (25.8% saved)

simplify130.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

464×	`associate-/r/_binary64`
439×	`associate-r_binary64`
341×	`*-commutative_binary64`
316×	`unswap-sqr_binary64`
229×	`cancel-sign-sub-inv_binary64`

Counts

149 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	248	3516
1	609	3123
2	1901	3086
3	3778	3086
4	4963	3086

prune106.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	137	9	146

Error

0.0b

Counts

146 → 9

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (.f64 b a))) (cbrt.f64 (/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (.f64 b a)))) (cbrt.f64 (/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (*.f64 b a))))
	0.6b	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
	0.9b	(.f64 (/.f64 (sqrt.f64 (/.f64 PI.f64 2)) (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (sqrt.f64 (/.f64 PI.f64 2)) (-.f64 b a))))
✓	0.3b	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (.f64 a b))
	15.0b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 (-.f64 b a) (.f64 a b)))
	15.0b	(+.f64 (/.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a))) a) (/.f64 (/.f64 (neg.f64 (/.f64 PI.f64 2)) b) (-.f64 (.f64 b b) (.f64 a a))))
▶	0.3b	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
	0.9b	(/.f64 (.f64 (/.f64 PI.f64 2) 1) (.f64 (+.f64 b a) (*.f64 b a)))
	15.0b	(.f64 (/.f64 PI.f64 2) (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 (.f64 b b) (*.f64 a a))))

Compiler

Compiled 2131 to 1087 computations (49% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1/2 (+.f64 b a))
0.2b	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
0.4b	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))

rewrite120.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

63×	`add-exp-log_binary64`
42×	`add-cbrt-cube_binary64`
35×	`*-un-lft-identity_binary64`
29×	`prod-exp_binary64`
26×	`times-frac_binary64`

Counts

3 → 106

Calls

3 calls:

10.0ms	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
9.0ms	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))
4.0ms	(/.f64 1/2 (+.f64 b a))

Compiler

Compiled 2134 to 1047 computations (50.9% saved)

series85.0ms (1.6%)

Error

0.0b

Counts

3 → 42

Calls

3 calls:

28.0ms	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))
23.0ms	(/.f64 1/2 (+.f64 b a))
22.0ms	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))

Compiler

Compiled 1710 to 1283 computations (25% saved)

simplify159.0ms (3%)

Algorithm

1×	egg-herbie

Rules

564×	`associate-/r/_binary64`
447×	`times-frac_binary64`
227×	`cancel-sign-sub-inv_binary64`
218×	`unswap-sqr_binary64`
202×	`associate-/l*_binary64`

Counts

148 → 124

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	203	2757
1	518	2325
2	2153	2287
3	3437	2257
4	4772	2256
5	4978	2256
6	4959	2256

prune78.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	126	7	133

Error

Counts

133 → 7

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (.f64 b a))) (cbrt.f64 (/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (.f64 b a)))) (cbrt.f64 (/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (*.f64 b a))))
	0.6b	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
▶	0.3b	(/.f64 (.f64 (.f64 (.f64 PI.f64 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (+.f64 b a))) 1) (.f64 a b))
	15.0b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 (-.f64 b a) (.f64 a b)))
	15.0b	(+.f64 (/.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a))) a) (/.f64 (/.f64 (neg.f64 (/.f64 PI.f64 2)) b) (-.f64 (.f64 b b) (.f64 a a))))
✓	0.3b	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
	0.9b	(/.f64 (.f64 (/.f64 PI.f64 2) 1) (.f64 (+.f64 b a) (*.f64 b a)))

Compiler

Compiled 1577 to 826 computations (47.6% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b

(/.f64 (*.f64 (*.f64 (*.f64 PI.f64 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (+.f64 b a))) 1) (*.f64 a b))

0.3b

(*.f64 (*.f64 PI.f64 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (+.f64 b a)))

0.5b

(/.f64 (sqrt.f64 1/2) (+.f64 b a))

rewrite172.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

114×	`add-exp-log_binary64`
73×	`add-cbrt-cube_binary64`
61×	`prod-exp_binary64`
61×	`*-un-lft-identity_binary64`
49×	`times-frac_binary64`

Counts

3 → 146

Calls

3 calls:

15.0ms

(/.f64 (*.f64 (*.f64 (*.f64 PI.f64 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (+.f64 b a))) 1) (*.f64 a b))

12.0ms

(*.f64 (*.f64 PI.f64 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (+.f64 b a)))

5.0ms

(/.f64 (sqrt.f64 1/2) (+.f64 b a))

Compiler

Compiled 3503 to 2084 computations (40.5% saved)

series109.0ms (2.1%)

Error

Counts

3 → 42

Calls

3 calls:

38.0ms

(*.f64 (*.f64 PI.f64 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (+.f64 b a)))

30.0ms

(/.f64 (*.f64 (*.f64 (*.f64 PI.f64 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (+.f64 b a))) 1) (*.f64 a b))

26.0ms

(/.f64 (sqrt.f64 1/2) (+.f64 b a))

Compiler

Compiled 2106 to 1682 computations (20.1% saved)

simplify220.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

759×	`associate-/r/_binary64`
670×	`times-frac_binary64`
299×	`associate-/l*_binary64`
250×	`associate-l_binary64`
185×	`associate-/r*_binary64`

Counts

188 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	3931
1	593	3337
2	2514	3215
3	4535	3183
4	4937	3183
5	5029	3183

prune90.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	173	6	179

Error

Counts

179 → 6

Alt Table

Status	Error	Program
	0.3b	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
	1.1b	(/.f64 (.f64 (.f64 (.f64 PI.f64 (sqrt.f64 1/2)) (sqrt.f64 1/2)) 1) (.f64 (+.f64 a b) (*.f64 a b)))
	0.6b	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
	0.3b	(/.f64 (.f64 (.f64 (.f64 PI.f64 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (+.f64 b a))) 1) (.f64 a b))
	15.0b	(+.f64 (/.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a))) a) (/.f64 (/.f64 (neg.f64 (/.f64 PI.f64 2)) b) (-.f64 (.f64 b b) (.f64 a a))))
	0.9b	(/.f64 (.f64 (/.f64 PI.f64 2) 1) (.f64 (+.f64 b a) (*.f64 b a)))

Compiler

Compiled 1773 to 1018 computations (42.6% saved)

regimes1.1s (20.8%)

Accuracy

Total 0.3b remaining (97.2%)

Threshold costs 0.3b (97.2%)

Compiler

Compiled 20641 to 14625 computations (29.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	20
1	19	20
2	17	20

end0.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

sample1.0s (19.4%)

Algorithm

1×

intervals

Results

680.0ms	8000×	body	128	valid
27.0ms	382×	body	128	invalid

Compiler

Compiled 160 to 114 computations (28.8% saved)

Details

analyze415.0ms (7.9%)

sample31.0ms (0.6%)

simplify58.0ms (1.1%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite535.0ms (10.1%)

series93.0ms (1.8%)

simplify330.0ms (6.2%)

prune179.0ms (3.4%)

localize8.0ms (0.2%)

rewrite144.0ms (2.7%)

series59.0ms (1.1%)

simplify130.0ms (2.5%)

prune106.0ms (2%)

localize8.0ms (0.2%)

rewrite120.0ms (2.3%)

series85.0ms (1.6%)

simplify159.0ms (3%)

prune78.0ms (1.5%)

localize10.0ms (0.2%)

rewrite172.0ms (3.3%)

series109.0ms (2.1%)

simplify220.0ms (4.2%)

prune90.0ms (1.7%)

regimes1.1s (20.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.0s (19.4%)

Profiling