Details

analyze4.7s (16.5%)

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)

sample7.9s (27.8%)

Results

4.1s	2046×	body	1024	valid
1.9s	4678×	body	128	valid
1.3s	1018×	body	512	valid
489.0ms	513×	body	256	valid
4.0ms	2×	body	1024	invalid
3.0ms	1×	body	2048	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 83 to 68 computations (18.1% saved)

simplify87.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1043×	`associate-*l/_binary64`
692×	`associate-/l/_binary64`
651×	`associate-/r/_binary64`
474×	`associate-/l*_binary64`
398×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	37	32
2	83	32
3	208	32
4	742	32
5	2273	32
6	2474	32
7	2875	32
8	3015	32
9	3126	32
10	3234	32
11	4835	32
12	4953	32
13	4880	32

prune7.0ms (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

8.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 96 to 76 computations (20.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
✓	0.1b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
✓	0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
✓	7.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series393.0ms (1.4%)

Counts

4 → 120

Calls

4 calls:

255.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
95.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
22.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
21.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))

rewrite172.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

258×	`prod-diff_binary64`
250×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
219×	`log-pow_binary64`
161×	`add-sqr-sqrt_binary64`

Counts

4 → 100

Calls

4 calls:

168.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
168.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
168.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
168.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	71
1	332	71
2	3564	71
3	4970	71
4	5134	71
0	0	0
1	0	0

simplify174.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-def_binary64`
616×	`fma-neg_binary64`
345×	`cancel-sign-sub-inv_binary64`
218×	`neg-mul-1_binary64`
192×	`associate-/r/_binary64`

Counts

220 → 141

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	196	3231
1	559	3137
2	2104	3011
3	4617	3003
4	5065	3003

prune247.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	137	5	142

Error

0.0b

Counts

142 → 5

Alt Table

Status	Error	Program
	50.3b	U
▶	9.4b	(pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 3)
✓	8.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	30.2b	(fma.f64 J (.f64 (cos.f64 (.f64 1/2 K)) -2) (.f64 (/.f64 (.f64 U U) (.f64 J (cos.f64 (.f64 1/2 K)))) -1/4))
	46.8b	(neg.f64 U)

Compiler

Compiled 4576 to 3427 computations (25.1% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
✓	0.6b	(cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))))))
✓	0.7b	(pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 3)
✓	7.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))

series5.9s (20.9%)

Counts

3 → 108

Calls

3 calls:

3.3s

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

2.3s

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

255.0ms

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

rewrite129.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

275×	`expm1-udef_binary64`
275×	`log1p-udef_binary64`
157×	`add-sqr-sqrt_binary64`
151×	`log1p-expm1-u_binary64`
151×	`expm1-log1p-u_binary64`

Counts

3 → 87

Calls

3 calls:

124.0ms

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

124.0ms

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

124.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	98
1	338	98
2	3911	98
3	4899	98
0	0	0
1	0	0

simplify238.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

437×	`fma-def_binary64`
387×	`times-frac_binary64`
331×	`associate-/l*_binary64`
295×	`associate-/r*_binary64`
250×	`*-commutative_binary64`

Counts

195 → 215

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	614	9058
1	1848	8304
2	4960	8304

prune698.0ms (2.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	268	3	271
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	271	5	276

Error

0.0b

Counts

276 → 5

Alt Table

Status	Error	Program
	46.8b	(neg.f64 U)
	33.3b	(.f64 (sqrt.f64 (.f64 -2 J)) (.f64 (sqrt.f64 (.f64 -2 J)) (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))))
	9.7b	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 3)) 3)
	50.3b	U
▶	8.4b	(.f64 -2 (.f64 J (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))))

Compiler

Compiled 13375 to 10750 computations (19.6% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 U (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))
✓	0.1b	(.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))
	0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
✓	7.8b	(.f64 J (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))))))

series435.0ms (1.5%)

Counts

3 → 108

Calls

3 calls:

178.0ms

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

175.0ms

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

81.0ms

(/.f64 U (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))

rewrite153.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

264×	`expm1-udef_binary64`
264×	`log1p-udef_binary64`
209×	`fma-neg_binary64`
149×	`add-sqr-sqrt_binary64`
146×	`prod-diff_binary64`

Counts

3 → 73

Calls

3 calls:

150.0ms

(/.f64 U (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))

149.0ms

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

149.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	70
1	309	70
2	3701	70
3	4914	70
4	4976	70
5	5008	70
0	0	0
1	0	0

simplify197.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

455×	`cancel-sign-sub-inv_binary64`
388×	`fma-neg_binary64`
212×	`fma-def_binary64`
190×	`associate-/l/_binary64`
170×	`distribute-rgt-neg-in_binary64`

Counts

181 → 157

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	284	4396
1	787	4218
2	2892	4090
3	4806	4086
4	4971	4086

prune342.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	183	2	185
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	184	6	190

Error

0.0b

Counts

190 → 6

Alt Table

Status	Error	Program
▶	9.7b	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 3)) 3)
	28.4b	(.f64 -2 (.f64 J (log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2))))))))))
	50.3b	U
	46.8b	(neg.f64 U)
✓	8.4b	(.f64 -2 (.f64 J (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))))
	14.0b	(.f64 -2 (.f64 J (-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2))))))) 1)))

Compiler

Compiled 6630 to 4926 computations (25.7% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 3))
	0.7b	(pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 3)
✓	0.7b	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 3)) 3)
	7.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))

series5.1s (17.9%)

Counts

2 → 72

Calls

2 calls:

3.0s

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

2.1s

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

rewrite72.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

275×	`expm1-udef_binary64`
275×	`log1p-udef_binary64`
157×	`add-sqr-sqrt_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`

Counts

2 → 71

Calls

2 calls:

69.0ms

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

69.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	66
1	340	66
2	3911	66
3	4899	66
0	0	0
1	0	0

simplify101.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

416×	`fma-def_binary64`
376×	`times-frac_binary64`
323×	`associate-/l*_binary64`
284×	`associate-/r*_binary64`
243×	`*-commutative_binary64`

Counts

143 → 182

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	588	7215
1	1764	6437
2	4955	6437

prune396.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	315	0	315
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	315	6	321

Error

0.0b

Counts

321 → 6

Alt Table

Status	Error	Program
✓	9.7b	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 3)) 3)
	28.4b	(.f64 -2 (.f64 J (log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2))))))))))
	50.3b	U
	46.8b	(neg.f64 U)
✓	8.4b	(.f64 -2 (.f64 J (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))))
	14.0b	(.f64 -2 (.f64 J (-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2))))))) 1)))

Compiler

Compiled 17710 to 14251 computations (19.5% saved)

regimes698.0ms (2.5%)

Accuracy

Total 8.3b remaining (99.4%)

Threshold costs 0b (0%)

Counts

74 → 2

Compiler

Compiled 10550 to 8664 computations (17.9% saved)

bsearch3.0ms (0%)

Compiler: Compiled 27 to 22 computations (18.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	77
1	37	77
2	39	77
3	40	77
4	39	77

end126.0ms (0.4%)

Compiler: Compiled 225 to 181 computations (19.6% saved)

Details

analyze4.7s (16.5%)

sample7.9s (27.8%)

simplify87.0ms (0.3%)

prune7.0ms (0%)

localize23.0ms (0.1%)

series393.0ms (1.4%)

rewrite172.0ms (0.6%)

simplify174.0ms (0.6%)

prune247.0ms (0.9%)

localize24.0ms (0.1%)

series5.9s (20.9%)

rewrite129.0ms (0.5%)

simplify238.0ms (0.8%)

prune698.0ms (2.5%)

localize23.0ms (0.1%)

series435.0ms (1.5%)

rewrite153.0ms (0.5%)

simplify197.0ms (0.7%)

prune342.0ms (1.2%)

localize26.0ms (0.1%)

series5.1s (17.9%)

rewrite72.0ms (0.3%)

simplify101.0ms (0.4%)

prune396.0ms (1.4%)

regimes698.0ms (2.5%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end126.0ms (0.4%)

Profiling