Details

analyze3.1s (30.3%)

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

Compiler

Compiled 28 to 23 computations (17.9% saved)

sample4.2s (41.4%)

Results

2.2s	2053×	body	1024	valid
1.0s	4602×	body	128	valid
733.0ms	1086×	body	512	valid
224.0ms	511×	body	256	valid
8.0ms	4×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	2×	body	128	invalid

Compiler

Compiled 83 to 68 computations (18.1% saved)

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

667×	`associate-/l/_binary64`
443×	`associate-/l*_binary64`
398×	`times-frac_binary64`
330×	`unswap-sqr_binary64`
265×	`associate-*l/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	37	32
2	89	32
3	253	32
4	968	32
5	3686	32
6	3897	32
7	4521	32
8	4720	32
9	4865	32

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

5.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.3b	(.f64 -2 (.f64 (hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))) (*.f64 J (cos.f64 (/.f64 K 2)))))

Compiler

Compiled 96 to 76 computations (20.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2))))))
✓	0.1b	(*.f64 J (cos.f64 (/.f64 K 2)))
✓	0.1b	(/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))
✓	5.0b	(.f64 (hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))) (.f64 J (cos.f64 (/.f64 K 2))))

series184.0ms (1.8%)

Counts

4 → 132

Calls

4 calls:

81.0ms	(.f64 (hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))) (.f64 J (cos.f64 (/.f64 K 2))))
52.0ms	(hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2))))))
43.0ms	(/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))
8.0ms	(*.f64 J (cos.f64 (/.f64 K 2)))

rewrite59.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

237×	`expm1-udef_binary64`
237×	`log1p-udef_binary64`
210×	`log-pow_binary64`
137×	`prod-diff_binary64`
134×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	71
1	271	71
2	3455	71

Stop Event

1×	node limit

Counts

4 → 92

Calls

4 calls:

57.0ms	(hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2))))))
57.0ms	(*.f64 J (cos.f64 (/.f64 K 2)))
57.0ms	(/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))
57.0ms	(.f64 (hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))) (.f64 J (cos.f64 (/.f64 K 2))))

simplify73.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

494×	`cancel-sign-sub-inv_binary64`
288×	`associate-/r/_binary64`
230×	`fma-neg_binary64`
185×	`fma-def_binary64`
164×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	4466
1	764	4225
2	2824	4149

Stop Event

1×	node limit

Counts

224 → 180

prune176.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	198	5	203
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	199	5	204

Error

0.0b

Counts

204 → 5

Alt Table

Status	Error	Program
	49.3b	(.f64 -2 (.f64 -1/2 U))
	46.1b	(.f64 -2 (.f64 1/2 U))
▶	20.4b	(.f64 -2 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J)))) 3)) (.f64 J (cos.f64 (/.f64 K 2)))))
	45.7b	(.f64 -2 (cbrt.f64 (pow.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))))) 3)))
	39.7b	(.f64 -2 (pow.f64 (sqrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J))))))) 2))

Compiler

Compiled 7012 to 5263 computations (24.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))
✓	0.1b	(pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))) 3)
✓	5.0b	(.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J)))) 3)) (*.f64 J (cos.f64 (/.f64 K 2))))
✓	14.2b	(cbrt.f64 (pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))) 3))

series282.0ms (2.8%)

Counts

4 → 144

Calls

4 calls:

106.0ms	(pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))) 3)
81.0ms	(.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J)))) 3)) (*.f64 J (cos.f64 (/.f64 K 2))))
53.0ms	(cbrt.f64 (pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))) 3))
41.0ms	(/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))

rewrite69.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

296×	`log1p-udef_binary64`
190×	`prod-diff_binary64`
171×	`add-sqr-sqrt_binary64`
163×	`log1p-expm1-u_binary64`
163×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	83
1	416	83
2	4421	83

Stop Event

1×	node limit

Counts

4 → 103

Calls

4 calls:

67.0ms	(/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))
67.0ms	(pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))) 3)
67.0ms	(.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J)))) 3)) (*.f64 J (cos.f64 (/.f64 K 2))))
67.0ms	(cbrt.f64 (pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))) 3))

simplify102.0ms (1%)

Algorithm

1×	egg-herbie

Rules

603×	`cancel-sign-sub-inv_binary64`
292×	`fma-def_binary64`
292×	`fma-neg_binary64`
182×	`associate-*r/_binary64`
181×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	333	6291
1	1151	5848
2	4146	5759

Stop Event

1×	node limit

Counts

247 → 226

prune230.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	226	5	231

Error

0.0b

Counts

231 → 5

Alt Table

Status	Error	Program
	49.3b	(.f64 -2 (.f64 -1/2 U))
	46.1b	(.f64 -2 (.f64 1/2 U))
✓	20.4b	(.f64 -2 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J)))) 3)) (.f64 J (cos.f64 (/.f64 K 2)))))
	45.7b	(.f64 -2 (cbrt.f64 (pow.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))))) 3)))
▶	39.7b	(.f64 -2 (pow.f64 (sqrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J))))))) 2))

Compiler

Compiled 9331 to 6994 computations (25% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J))))))
	0.1b	(/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))
✓	0.2b	(pow.f64 (sqrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J))))))) 2)
✓	5.0b	(.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J)))))

series285.0ms (2.8%)

Counts

3 → 92

Calls

3 calls:

132.0ms

(pow.f64 (sqrt.f64 (*.f64 (cos.f64 (*.f64 K 1/2)) (*.f64 J (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (*.f64 K 1/2)) (*.f64 2 J))))))) 2)

86.0ms

(*.f64 (cos.f64 (*.f64 K 1/2)) (*.f64 J (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (*.f64 K 1/2)) (*.f64 2 J))))))

66.0ms

(*.f64 J (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (*.f64 K 1/2)) (*.f64 2 J)))))

rewrite61.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

276×	`expm1-udef_binary64`
276×	`log1p-udef_binary64`
158×	`prod-diff_binary64`
155×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	79
1	345	79
2	4031	79

Stop Event

1×	node limit

Counts

3 → 70

Calls

3 calls:

58.0ms

(*.f64 (cos.f64 (*.f64 K 1/2)) (*.f64 J (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (*.f64 K 1/2)) (*.f64 2 J))))))

58.0ms

(pow.f64 (sqrt.f64 (*.f64 (cos.f64 (*.f64 K 1/2)) (*.f64 J (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (*.f64 K 1/2)) (*.f64 2 J))))))) 2)

58.0ms

(*.f64 J (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (*.f64 K 1/2)) (*.f64 2 J)))))

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

402×	`cancel-sign-sub-inv_binary64`
210×	`associate-/r/_binary64`
209×	`fma-neg_binary64`
195×	`fma-def_binary64`
162×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	237	5146
1	747	4636
2	2773	4511

Stop Event

1×	node limit

Counts

162 → 135

prune183.0ms (1.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	183	3	186
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	184	7	191

Error

0.0b

Counts

191 → 7

Alt Table

Status	Error	Program
✓	20.4b	(.f64 -2 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J)))) 3)) (.f64 J (cos.f64 (/.f64 K 2)))))
▶	31.5b	(.f64 -2 (+.f64 (.f64 1/16 (/.f64 (pow.f64 U 2) (.f64 J (cos.f64 (.f64 1/2 K))))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 U 2) (.f64 (cos.f64 (.f64 1/2 K)) J))) (.f64 J (cos.f64 (*.f64 1/2 K))))))
	39.7b	(.f64 -2 (.f64 (pow.f64 (.f64 J (.f64 (hypot.f64 1 (/.f64 (/.f64 U (cos.f64 (.f64 K 1/2))) (.f64 J 2))) (cos.f64 (.f64 K 1/2)))) 1/4) (.f64 (pow.f64 (.f64 J (.f64 (hypot.f64 1 (/.f64 (/.f64 U (cos.f64 (.f64 K 1/2))) (.f64 J 2))) (cos.f64 (.f64 K 1/2)))) 1/4) (sqrt.f64 (.f64 J (.f64 (hypot.f64 1 (/.f64 (/.f64 U (cos.f64 (.f64 K 1/2))) (.f64 J 2))) (cos.f64 (.f64 K 1/2))))))))
	46.4b	(.f64 -2 (.f64 (sqrt.f64 (cos.f64 (.f64 K 1/2))) (.f64 (sqrt.f64 (.f64 J (hypot.f64 1 (/.f64 (/.f64 U (cos.f64 (.f64 K 1/2))) (.f64 J 2))))) (sqrt.f64 (.f64 J (.f64 (hypot.f64 1 (/.f64 (/.f64 U (cos.f64 (.f64 K 1/2))) (.f64 J 2))) (cos.f64 (.f64 K 1/2))))))))
	49.3b	(.f64 -2 (.f64 -1/2 U))
	46.1b	(.f64 -2 (.f64 1/2 U))
✓	39.7b	(.f64 -2 (pow.f64 (sqrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J))))))) 2))

Compiler

Compiled 7573 to 5793 computations (23.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 (.f64 1/2 K)) J)
✓	0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))
✓	8.1b	(/.f64 (pow.f64 U 2) (.f64 J (cos.f64 (.f64 1/2 K))))
✓	8.1b	(/.f64 (pow.f64 U 2) (.f64 (cos.f64 (.f64 1/2 K)) J))

series110.0ms (1.1%)

Counts

4 → 56

Calls

4 calls:

46.0ms	(/.f64 (pow.f64 U 2) (.f64 J (cos.f64 (.f64 1/2 K))))
46.0ms	(/.f64 (pow.f64 U 2) (.f64 (cos.f64 (.f64 1/2 K)) J))
10.0ms	(.f64 (cos.f64 (.f64 1/2 K)) J)
8.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))

rewrite58.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

558×	`log-prod_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
181×	`prod-diff_binary64`
176×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	277	48
2	2941	48

Stop Event

1×	node limit

Counts

4 → 124

Calls

4 calls:

55.0ms	(.f64 (cos.f64 (.f64 1/2 K)) J)
55.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
55.0ms	(/.f64 (pow.f64 U 2) (.f64 J (cos.f64 (.f64 1/2 K))))
55.0ms	(/.f64 (pow.f64 U 2) (.f64 (cos.f64 (.f64 1/2 K)) J))

simplify31.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

556×	`fma-def_binary64`
396×	`associate-/l*_binary64`
294×	`*-commutative_binary64`
275×	`cancel-sign-sub-inv_binary64`
269×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	872
1	126	866
2	380	850
3	1476	820

Stop Event

1×	node limit

Counts

180 → 82

prune118.0ms (1.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	109	7	116

Error

0.0b

Counts

116 → 7

Alt Table

Status	Error	Program
✓	20.4b	(.f64 -2 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J)))) 3)) (.f64 J (cos.f64 (/.f64 K 2)))))
✓	31.5b	(.f64 -2 (+.f64 (.f64 1/16 (/.f64 (pow.f64 U 2) (.f64 J (cos.f64 (.f64 1/2 K))))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 U 2) (.f64 (cos.f64 (.f64 1/2 K)) J))) (.f64 J (cos.f64 (*.f64 1/2 K))))))
	39.7b	(.f64 -2 (.f64 (pow.f64 (.f64 J (.f64 (hypot.f64 1 (/.f64 (/.f64 U (cos.f64 (.f64 K 1/2))) (.f64 J 2))) (cos.f64 (.f64 K 1/2)))) 1/4) (.f64 (pow.f64 (.f64 J (.f64 (hypot.f64 1 (/.f64 (/.f64 U (cos.f64 (.f64 K 1/2))) (.f64 J 2))) (cos.f64 (.f64 K 1/2)))) 1/4) (sqrt.f64 (.f64 J (.f64 (hypot.f64 1 (/.f64 (/.f64 U (cos.f64 (.f64 K 1/2))) (.f64 J 2))) (cos.f64 (.f64 K 1/2))))))))
	46.4b	(.f64 -2 (.f64 (sqrt.f64 (cos.f64 (.f64 K 1/2))) (.f64 (sqrt.f64 (.f64 J (hypot.f64 1 (/.f64 (/.f64 U (cos.f64 (.f64 K 1/2))) (.f64 J 2))))) (sqrt.f64 (.f64 J (.f64 (hypot.f64 1 (/.f64 (/.f64 U (cos.f64 (.f64 K 1/2))) (.f64 J 2))) (cos.f64 (.f64 K 1/2))))))))
	49.3b	(.f64 -2 (.f64 -1/2 U))
	46.1b	(.f64 -2 (.f64 1/2 U))
✓	39.7b	(.f64 -2 (pow.f64 (sqrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J))))))) 2))

Compiler

Compiled 4542 to 3365 computations (25.9% saved)

regimes490.0ms (4.8%)

Accuracy

Total 8.4b remaining (99.4%)

Threshold costs 0b (0%)

Counts

62 → 1

Compiler

Compiled 9662 to 7680 computations (20.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	21	32

Stop Event

1×

saturated

end190.0ms (1.9%)

Compiler: Compiled 271 to 216 computations (20.3% saved)

Details

analyze3.1s (30.3%)

sample4.2s (41.4%)

simplify40.0ms (0.4%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series184.0ms (1.8%)

rewrite59.0ms (0.6%)

simplify73.0ms (0.7%)

prune176.0ms (1.7%)

localize19.0ms (0.2%)

series282.0ms (2.8%)

rewrite69.0ms (0.7%)

simplify102.0ms (1%)

prune230.0ms (2.3%)

localize14.0ms (0.1%)

series285.0ms (2.8%)

rewrite61.0ms (0.6%)

simplify81.0ms (0.8%)

prune183.0ms (1.8%)

localize14.0ms (0.1%)

series110.0ms (1.1%)

rewrite58.0ms (0.6%)

simplify31.0ms (0.3%)

prune118.0ms (1.2%)

regimes490.0ms (4.8%)

simplify2.0ms (0%)

end190.0ms (1.9%)

Profiling