Details

analyze337.0ms (8.8%)

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)

sample1.2s (32.8%)

Results

1.1s	8256×	body	128	valid
53.0ms	359×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify19.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

597×	`times-frac_binary64`
509×	`associate-/l*_binary64`
356×	`associate-/l/_binary64`
274×	`distribute-rgt-in_binary64`
238×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	37	29
2	100	29
3	400	29
4	1790	28

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

13.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.2b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
▶	13.2b	(/.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 2) (-.f64 (.f64 b b) (.f64 a a)))

Status

Error

Program

13.2b

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

▶

13.2b

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

Compiler

Compiled 127 to 84 computations (33.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
✓	0.3b	(/.f64 (PI.f64) a)
✓	4.7b	(-.f64 (.f64 b b) (.f64 a a))
✓	7.6b	(/.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 2) (-.f64 (.f64 b b) (.f64 a a)))

series39.0ms (1%)

Counts

4 → 72

Calls

4 calls:

22.0ms	(/.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 2) (-.f64 (.f64 b b) (.f64 a a)))
8.0ms	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
6.0ms	(-.f64 (.f64 b b) (.f64 a a))
2.0ms	(/.f64 (PI.f64) a)

rewrite94.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

891×	`prod-diff_binary64`
219×	`egg-rr`
160×	`add-sqr-sqrt_binary64`
152×	`add-cbrt-cube_binary64`
152×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	321	56
2	4548	56

Stop Event

1×	node limit

Counts

4 → 219

Calls

4 calls:

89.0ms	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
89.0ms	(/.f64 (PI.f64) a)
89.0ms	(-.f64 (.f64 b b) (.f64 a a))
89.0ms	(/.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 2) (-.f64 (.f64 b b) (.f64 a a)))

simplify46.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

644×	`cancel-sign-sub-inv_binary64`
573×	`fma-neg_binary64`
298×	`associate-/l/_binary64`
182×	`distribute-neg-frac_binary64`
172×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	1266
1	196	1230
2	597	1164
3	2308	1146

Stop Event

1×	node limit

Counts

291 → 245

prune262.0ms (6.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	236	9	245
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	237	10	247

Error

0.0b

Counts

247 → 10

Alt Table

Status	Error	Program
	31.2b	(-.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a (pow.f64 b 2)))) (*.f64 1/2 (/.f64 (PI.f64) (pow.f64 b 3))))
	19.7b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a)) (/.f64 1/2 (-.f64 b a)))) 2)
	13.2b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
	0.7b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 1/2)) 2) (+.f64 b a)) (/.f64 (cbrt.f64 (*.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 1/2)) (-.f64 b a)))
	23.2b	(*.f64 1/2 (/.f64 (/.f64 (/.f64 (PI.f64) b) a) a))
▶	0.3b	(*.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a)) (/.f64 1/2 (-.f64 b a)))
	0.8b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a)) (/.f64 1/2 (-.f64 b a)))) 3)
	7.7b	(/.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 2) (*.f64 (+.f64 b a) (-.f64 b a)))
	13.2b	(.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (/.f64 1 (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))))
	13.6b	(.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 1/2)) 2) (.f64 (cbrt.f64 (.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 1/2)) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))))

Compiler

Compiled 7473 to 3184 computations (57.4% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
✓	0.2b	(*.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a)) (/.f64 1/2 (-.f64 b a)))
✓	0.2b	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a))
	0.3b	(/.f64 (PI.f64) a)

series28.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

18.0ms	(*.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a)) (/.f64 1/2 (-.f64 b a)))
11.0ms	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a))

rewrite75.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

795×	`prod-diff_binary64`
164×	`add-sqr-sqrt_binary64`
154×	`add-cbrt-cube_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	47
1	321	47
2	4712	47

Stop Event

1×	node limit

Counts

2 → 89

Calls

2 calls:

73.0ms	(*.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a)) (/.f64 1/2 (-.f64 b a)))
73.0ms	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a))

simplify49.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

382×	`times-frac_binary64`
339×	`distribute-neg-frac_binary64`
297×	`distribute-rgt-neg-in_binary64`
283×	`associate-/l*_binary64`
253×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	1512
1	293	1458
2	953	1341
3	3868	1341

Stop Event

1×	node limit

Counts

137 → 122

prune248.0ms (6.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	178	5	183
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	185	8	193

Error

Counts

193 → 8

Alt Table

Status	Error	Program
	13.2b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
	0.7b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 1/2)) 2) (+.f64 b a)) (/.f64 (cbrt.f64 (*.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 1/2)) (-.f64 b a)))
	0.3b	(*.f64 (pow.f64 (/.f64 (+.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) -1) (/.f64 1/2 (-.f64 b a)))
	0.3b	(*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (+.f64 b a)) (/.f64 1/2 (-.f64 b a)))
	18.4b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a)) 3)) (/.f64 1/2 (-.f64 b a)))
	0.8b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a)) (/.f64 1/2 (-.f64 b a)))) 3)
	0.5b	(/.f64 1/2 (*.f64 (/.f64 (+.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (-.f64 b a)))
▶	0.2b	(/.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a)) (*.f64 (-.f64 b a) 2))

Compiler

Compiled 4500 to 2174 computations (51.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a)) (*.f64 (-.f64 b a) 2))
	0.2b	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
	0.2b	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a))
	0.3b	(/.f64 (PI.f64) a)

series14.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

14.0ms

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

rewrite70.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

813×	`prod-diff_binary64`
162×	`add-sqr-sqrt_binary64`
152×	`add-cbrt-cube_binary64`
152×	`log1p-expm1-u_binary64`
152×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	317	28
2	4731	28

Stop Event

1×	node limit

Counts

1 → 49

Calls

1 calls:

68.0ms

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

simplify33.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

634×	`cancel-sign-sub-inv_binary64`
564×	`fma-neg_binary64`
292×	`associate-/l/_binary64`
183×	`distribute-neg-frac_binary64`
170×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	804
1	182	768
2	563	702
3	2234	684

Stop Event

1×	node limit

Counts

73 → 65

prune214.0ms (5.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	178	8	186

Error

Counts

186 → 8

Alt Table

Status	Error	Program
	13.2b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
	0.7b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 1/2)) 2) (+.f64 b a)) (/.f64 (cbrt.f64 (*.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 1/2)) (-.f64 b a)))
	0.3b	(*.f64 (pow.f64 (/.f64 (+.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) -1) (/.f64 1/2 (-.f64 b a)))
▶	0.3b	(*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (+.f64 b a)) (/.f64 1/2 (-.f64 b a)))
	18.4b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a)) 3)) (/.f64 1/2 (-.f64 b a)))
	0.5b	(/.f64 1/2 (*.f64 (/.f64 (+.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (-.f64 b a)))
✓	0.2b	(/.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a)) (*.f64 (-.f64 b a) 2))
	17.7b	(/.f64 (.f64 -1 (/.f64 (PI.f64) (.f64 a b))) (*.f64 (-.f64 b a) 2))

Compiler

Compiled 4659 to 2286 computations (50.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (+.f64 b a)) (/.f64 1/2 (-.f64 b a)))
✓	0.2b	(/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (+.f64 b a))
✓	0.2b	(/.f64 (PI.f64) b)
	0.3b	(/.f64 (PI.f64) a)

series28.0ms (0.7%)

Counts

3 → 48

Calls

3 calls:

16.0ms	(*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (+.f64 b a)) (/.f64 1/2 (-.f64 b a)))
10.0ms	(/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (+.f64 b a))
2.0ms	(/.f64 (PI.f64) b)

rewrite40.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

170×	`add-sqr-sqrt_binary64`
163×	`log1p-expm1-u_binary64`
163×	`expm1-log1p-u_binary64`
162×	`add-cbrt-cube_binary64`
159×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	50
1	323	50

Stop Event

1×	node limit

Counts

3 → 120

Calls

3 calls:

38.0ms	(*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (+.f64 b a)) (/.f64 1/2 (-.f64 b a)))
38.0ms	(/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (+.f64 b a))
38.0ms	(/.f64 (PI.f64) b)

simplify52.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

382×	`times-frac_binary64`
339×	`distribute-neg-frac_binary64`
297×	`distribute-rgt-neg-in_binary64`
285×	`associate-/l*_binary64`
255×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	1512
1	293	1458
2	953	1341
3	3873	1341

Stop Event

1×	node limit

Counts

168 → 153

prune193.0ms (5.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	187	7	194

Error

Counts

194 → 7

Alt Table

Status	Error	Program
	13.2b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
	0.7b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 1/2)) 2) (+.f64 b a)) (/.f64 (cbrt.f64 (*.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) 1/2)) (-.f64 b a)))
✓	0.3b	(*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (+.f64 b a)) (/.f64 1/2 (-.f64 b a)))
	0.3b	(/.f64 (/.f64 1/2 (-.f64 b a)) (/.f64 (+.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))
	18.4b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (+.f64 b a)) 3)) (/.f64 1/2 (-.f64 b a)))
	17.7b	(/.f64 (.f64 -1 (/.f64 (PI.f64) (.f64 a b))) (*.f64 (-.f64 b a) 2))
	0.3b	(*.f64 (pow.f64 (/.f64 (+.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) -1) (/.f64 1/2 (-.f64 b a)))

Compiler

Compiled 4158 to 1558 computations (62.5% saved)

regimes556.0ms (14.6%)

Accuracy

Total 0.2b remaining (74.9%)

Threshold costs 0.2b (74.9%)

Counts

185 → 1

Compiler

Compiled 11962 to 8010 computations (33% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`*-commutative_binary64`
6×	`cancel-sign-sub-inv_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	29
1	24	29
2	37	29
3	54	27
4	75	27
5	82	27

Stop Event

1×

saturated

end110.0ms (2.9%)

Compiler: Compiled 193 to 129 computations (33.2% saved)

Details

analyze337.0ms (8.8%)

sample1.2s (32.8%)

simplify19.0ms (0.5%)

prune4.0ms (0.1%)

localize11.0ms (0.3%)

series39.0ms (1%)

rewrite94.0ms (2.5%)

simplify46.0ms (1.2%)

prune262.0ms (6.9%)

localize14.0ms (0.4%)

series28.0ms (0.7%)

rewrite75.0ms (2%)

simplify49.0ms (1.3%)

prune248.0ms (6.5%)

localize11.0ms (0.3%)

series14.0ms (0.4%)

rewrite70.0ms (1.8%)

simplify33.0ms (0.9%)

prune214.0ms (5.6%)

localize11.0ms (0.3%)

series28.0ms (0.7%)

rewrite40.0ms (1.1%)

simplify52.0ms (1.4%)

prune193.0ms (5.1%)

regimes556.0ms (14.6%)

simplify3.0ms (0.1%)

end110.0ms (2.9%)

Profiling