Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
99.8%	0%	0.2%	1

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample1.7s (22.5%)

Symmetry

(sort m n)

Results

1.5s	7888×	body	128	valid
97.0ms	131×	body	1024	valid
68.0ms	139×	body	512	valid
26.0ms	80×	body	256	valid
19.0ms	18×	body	2048	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify62.0ms (0.8%)

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 (0.1%)

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

15.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.1b	(.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)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	31.7b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series66.0ms (0.9%)

Counts

4 → 168

Calls

4 calls:

27.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
6.0ms	(*.f64 K (+.f64 m n))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64`
42×	`prod-diff_binary64`
38×	`add-cube-cbrt_binary64`
25×	`cos-sum_binary64`

Counts

4 → 129

Calls

4 calls:

10.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
4.0ms	(*.f64 K (+.f64 m n))

simplify172.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

528×	`fma-neg_binary64`
341×	`associate-r_binary64`
311×	`associate-l_binary64`
240×	`distribute-rgt-neg-in_binary64`
221×	`*-commutative_binary64`

Counts

297 → 254

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	431	7218
1	884	5740
2	3048	5550
3	4877	5550
4	5041	5550

prune523.0ms (6.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	248	6	254
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	249	6	255

Error

0.6b

Counts

255 → 6

Alt Table

Status	Error	Program
	15.1b	(.f64 (log.f64 (exp.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))))
	32.6b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 K (-.f64 (.f64 m m) (.f64 n n))) (-.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))))
	15.4b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (.f64 1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	28.4b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (fma.f64 1/2 (.f64 K (.f64 m (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)))) (.f64 1/8 (.f64 (.f64 K K) (.f64 (.f64 m m) (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))))
	27.3b	(.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))))
▶	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))))

Compiler

Compiled 11471 to 5404 computations (52.9% saved)

localize17.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series47.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

47.0ms

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

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`fma-def_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
6×	`unpow-prod-down_binary64`
3×	`add-log-exp_binary64`

Counts

1 → 25

Calls

1 calls:

38.0ms

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

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

737×	`distribute-rgt-in_binary64`
733×	`fma-neg_binary64`
455×	`fma-def_binary64`
381×	`associate--l+_binary64`
377×	`associate-+l+_binary64`

Counts

73 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	1735
1	293	1532
2	742	1518
3	2610	1516
4	4954	1516
5	5359	1516

prune225.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	127	6	133

Error

0.6b

Counts

133 → 6

Alt Table

Status	Error	Program
▶	15.1b	(.f64 (log.f64 (exp.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))))
	32.6b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 K (-.f64 (.f64 m m) (.f64 n n))) (-.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))))
	15.4b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (.f64 1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	28.4b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (fma.f64 1/2 (.f64 K (.f64 m (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)))) (.f64 1/8 (.f64 (.f64 K K) (.f64 (.f64 m m) (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))))
	27.3b	(.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))))
✓	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))))

Compiler

Compiled 3935 to 1983 computations (49.6% saved)

localize56.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.2b	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
✓	0.6b	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
	31.7b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series102.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

73.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
29.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`exp-diff_binary64`
50×	`cos-sum_binary64`
42×	`prod-diff_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`

Counts

2 → 82

Calls

2 calls:

14.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
10.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))

simplify169.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

631×	`associate-l_binary64`
451×	`*-commutative_binary64`
382×	`fma-def_binary64`
256×	`sub-neg_binary64`
255×	`unswap-sqr_binary64`

Counts

178 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	631	9371
1	1373	7245
2	4100	6992
3	5264	6992

prune669.0ms (8.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	317	3	320
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	320	6	326

Error

0.6b

Counts

326 → 6

Alt Table

Status	Error	Program
	32.6b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 K (-.f64 (.f64 m m) (.f64 n n))) (-.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))))
	15.3b	(.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (exp.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))))
	24.4b	(.f64 (log.f64 (-.f64 (exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))) (.f64 1/2 (.f64 n (.f64 K (.f64 (exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))) (sin.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	27.3b	(.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))))
▶	14.6b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 1/2 (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m)))) (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))))

Compiler

Compiled 19950 to 9736 computations (51.2% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m))
✓	8.1b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 1/2 (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	21.1b	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
✓	21.2b	(sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

series627.0ms (8.1%)

Counts

4 → 96

Calls

4 calls:

559.0ms	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 1/2 (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
43.0ms	(.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m))
12.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
12.0ms	(sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

rewrite74.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64`
45×	`associate-r_binary64`
43×	`add-sqr-sqrt_binary64`
42×	`prod-diff_binary64`
41×	`exp-sum_binary64`

Counts

4 → 120

Calls

4 calls:

32.0ms	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 1/2 (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
11.0ms	(.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m))
5.0ms	(sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
5.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

simplify455.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

635×	`*-commutative_binary64`
499×	`associate-r_binary64`
218×	`+-commutative_binary64`
200×	`fma-def_binary64`
169×	`associate-+r+_binary64`

Counts

216 → 261

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1133	23320
1	3281	22184
2	4871	22184
3	4986	22184

prune643.0ms (8.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	262	5	267

Error

0.6b

Counts

267 → 5

Alt Table

Status	Error	Program
	32.6b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 K (-.f64 (.f64 m m) (.f64 n n))) (-.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))))
	24.4b	(.f64 (log.f64 (-.f64 (exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))) (.f64 1/2 (.f64 n (.f64 K (.f64 (exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))) (sin.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	27.3b	(.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))))
	18.8b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 1/2 (.f64 K (.f64 (fma.f64 1/2 (.f64 n (.f64 K (cos.f64 M))) (sin.f64 (neg.f64 M))) m)))) (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))))

Compiler

Compiled 31465 to 15984 computations (49.2% saved)

regimes1.7s (21.6%)

Accuracy

Total 0.8b remaining (39.6%)

Threshold costs 0.8b (39.6%)

Counts

205 → 1

Compiler

Compiled 48380 to 33222 computations (31.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`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	17	31
1	28	31
2	45	31
3	60	31
4	69	31
5	72	31
6	72	31

end144.0ms (1.9%)

Remove: (sort m n)
Compiler: Compiled 308 to 213 computations (30.8% saved)

Details

analyze3.0ms (0%)

sample1.7s (22.5%)

simplify62.0ms (0.8%)

prune4.0ms (0.1%)

localize17.0ms (0.2%)

series66.0ms (0.9%)

rewrite39.0ms (0.5%)

simplify172.0ms (2.2%)

prune523.0ms (6.8%)

localize17.0ms (0.2%)

series47.0ms (0.6%)

rewrite39.0ms (0.5%)

simplify82.0ms (1.1%)

prune225.0ms (2.9%)

localize56.0ms (0.7%)

series102.0ms (1.3%)

rewrite40.0ms (0.5%)

simplify169.0ms (2.2%)

prune669.0ms (8.7%)

localize25.0ms (0.3%)

series627.0ms (8.1%)

rewrite74.0ms (1%)

simplify455.0ms (5.9%)

prune643.0ms (8.3%)

regimes1.7s (21.6%)

simplify3.0ms (0%)

end144.0ms (1.9%)

Profiling