Details

analyze2.9s (16.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample2.3s (13.4%)

Symmetry

(sort m n)

Results

1.8s	8092×	body	128	valid
97.0ms	113×	body	1024	invalid
67.0ms	305×	body	128	invalid
57.0ms	20×	body	2048	invalid
55.0ms	67×	body	1024	valid
49.0ms	86×	body	512	invalid
32.0ms	58×	body	512	valid
16.0ms	44×	body	256	invalid
14.0ms	36×	body	256	valid
4.0ms	3×	body	2048	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify62.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

691×	`exp-prod_binary64`
507×	`exp-sum_binary64`
446×	`fma-neg_binary64`
375×	`associate-l_binary64`
251×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	58	45
2	129	43
3	384	43
4	1266	43
5	4023	43
6	4945	43
7	5019	43

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

15.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 128 to 80 computations (37.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	35.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series316.0ms (1.9%)

Counts

4 → 180

Calls

4 calls:

272.0ms	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
22.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
15.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
6.0ms	(*.f64 K (+.f64 m n))

rewrite68.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

252×	`log1p-expm1-u_binary64`
252×	`expm1-log1p-u_binary64`
243×	`add-log-exp_binary64`
241×	`add-cube-cbrt_binary64`
241×	`add-cbrt-cube_binary64`

Counts

4 → 67

Calls

4 calls:

66.0ms	(*.f64 K (+.f64 m n))
66.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
66.0ms	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
66.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	78
1	502	78
2	4831	78
3	5033	78

simplify171.0ms (1%)

Algorithm

1×	egg-herbie

Rules

897×	`fma-def_binary64`
368×	`associate-+l+_binary64`
365×	`*-commutative_binary64`
298×	`associate-r_binary64`
197×	`associate--r+_binary64`

Counts

247 → 172

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	624	13345
1	2180	12084
2	5164	12084

prune319.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	165	7	172
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	166	7	173

Error

1.5b

Counts

173 → 7

Alt Table

Status	Error	Program
	15.6b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 3) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	2.1b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	11.9b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	29.8b	(.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.f64 (.f64 K (+.f64 m n)))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	43.6b	(.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (pow.f64 (.f64 K (+.f64 m n)) 3) 1/3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(cbrt.f64 (pow.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 3))

Compiler

Compiled 16653 to 8256 computations (50.4% saved)

localize15.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

prune61.0ms (0.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	38	7	45

Error

1.5b

Counts

45 → 7

Alt Table

Status	Error	Program
	15.6b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 3) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	2.1b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	11.9b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	29.8b	(.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.f64 (.f64 K (+.f64 m n)))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	43.6b	(.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (pow.f64 (.f64 K (+.f64 m n)) 3) 1/3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(cbrt.f64 (pow.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 3))

Compiler

Compiled 1381 to 749 computations (45.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/2 (.f64 n K))
✓	0.0b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	26.0b	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

series241.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

227.0ms

(*.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

9.0ms

(cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))

4.0ms

(*.f64 1/2 (*.f64 n K))

rewrite64.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

255×	`log1p-expm1-u_binary64`
255×	`expm1-log1p-u_binary64`
246×	`add-log-exp_binary64`
244×	`add-cube-cbrt_binary64`
244×	`add-cbrt-cube_binary64`

Counts

3 → 48

Calls

3 calls:

63.0ms

(*.f64 1/2 (*.f64 n K))

63.0ms

(*.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

63.0ms

(cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	59
1	514	59
2	4818	59
3	5011	59

simplify125.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

719×	`associate-l_binary64`
637×	`fma-def_binary64`
389×	`associate-+r+_binary64`
260×	`associate-+l+_binary64`
257×	`*-commutative_binary64`

Counts

120 → 108

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	444	9097
1	1515	7965
2	5268	7965

prune305.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	1	4	5
Picked	1	0	1
Done	1	0	1
Total	145	8	153

Error

1.5b

Counts

153 → 8

Alt Table

Status	Error	Program
	34.0b	(.f64 (cos.f64 (-.f64 (pow.f64 (.f64 1/8 (pow.f64 (*.f64 n K) 3)) 1/3) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 3) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	1.9b	(log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 n m) 1/2) M) 2) l)))))
	43.6b	(.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (pow.f64 (.f64 K (+.f64 m n)) 3) 1/3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	23.3b	(.f64 (cos.f64 (-.f64 (expm1.f64 (log1p.f64 (.f64 1/2 (*.f64 n K)))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(cbrt.f64 (pow.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 3))
	12.0b	(.f64 (cos.f64 (-.f64 (pow.f64 (cbrt.f64 (.f64 1/2 (*.f64 n K))) 3) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 12111 to 6073 computations (49.9% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (-.f64 (*.f64 (+.f64 n m) 1/2) M) 2)
✓	0.0b	(log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 n m) 1/2) M) 2) l)))))
✓	0.1b	(exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)))
	26.0b	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

series8.1s (47.8%)

Counts

3 → 108

Calls

3 calls:

8.1s

(log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 n m) 1/2) M) 2) l)))))

36.0ms

(pow.f64 (-.f64 (*.f64 (+.f64 n m) 1/2) M) 2)

21.0ms

(exp.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)))

rewrite39.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

271×	`log1p-expm1-u_binary64`
271×	`expm1-log1p-u_binary64`
263×	`add-log-exp_binary64`
260×	`add-exp-log_binary64`
259×	`add-cube-cbrt_binary64`

Counts

3 → 52

Calls

3 calls:

38.0ms

(pow.f64 (-.f64 (*.f64 (+.f64 n m) 1/2) M) 2)

38.0ms

(log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 n m) 1/2) M) 2) l)))))

38.0ms

(exp.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	67
1	547	67
2	5057	67

simplify295.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

632×	`*-commutative_binary64`
560×	`associate-r_binary64`
218×	`+-commutative_binary64`
213×	`fma-neg_binary64`
203×	`fma-def_binary64`

Counts

160 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	979	16368
1	3105	15619
2	4964	15617
3	5120	15617

prune531.0ms (3.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	179	8	187

Error

1.5b

Counts

187 → 8

Alt Table

Status	Error	Program
	34.0b	(.f64 (cos.f64 (-.f64 (pow.f64 (.f64 1/8 (pow.f64 (*.f64 n K) 3)) 1/3) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 3) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	43.6b	(.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (pow.f64 (.f64 K (+.f64 m n)) 3) 1/3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	1.9b	(log.f64 (pow.f64 (expm1.f64 (log1p.f64 (exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 n m) 1/2) M) 2) l)))))
	23.3b	(.f64 (cos.f64 (-.f64 (expm1.f64 (log1p.f64 (.f64 1/2 (*.f64 n K)))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(cbrt.f64 (pow.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 3))
	12.0b	(.f64 (cos.f64 (-.f64 (pow.f64 (cbrt.f64 (.f64 1/2 (*.f64 n K))) 3) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 22300 to 11480 computations (48.5% saved)

regimes795.0ms (4.7%)

Accuracy

Total 0.1b remaining (9.5%)

Threshold costs 0.1b (9.5%)

Counts

112 → 1

Compiler

Compiled 21110 to 15120 computations (28.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
11×	`sub-neg_binary64`
7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	47
1	35	47
2	53	47
3	68	47
4	77	47
5	80	47
6	80	47

end255.0ms (1.5%)

Remove: (sort m n)
Compiler: Compiled 423 to 299 computations (29.3% saved)

Details

analyze2.9s (16.8%)

sample2.3s (13.4%)

simplify62.0ms (0.4%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series316.0ms (1.9%)

rewrite68.0ms (0.4%)

simplify171.0ms (1%)

prune319.0ms (1.9%)

localize15.0ms (0.1%)

prune61.0ms (0.4%)

localize19.0ms (0.1%)

series241.0ms (1.4%)

rewrite64.0ms (0.4%)

simplify125.0ms (0.7%)

prune305.0ms (1.8%)

localize19.0ms (0.1%)

series8.1s (47.8%)

rewrite39.0ms (0.2%)

simplify295.0ms (1.7%)

prune531.0ms (3.1%)

regimes795.0ms (4.7%)

simplify3.0ms (0%)

end255.0ms (1.5%)

Profiling