Details

analyze2.9s (35.2%)

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)

sample105.0ms (1.3%)

Algorithm

1×

intervals

Symmetry

(sort m n)

Results

32.0ms	249×	body	128	valid
2.0ms	3×	body	512	valid
1.0ms	11×	body	128	invalid
1.0ms	2×	body	1024	valid
1.0ms	1×	body	2048	invalid
1.0ms	2×	body	1024	invalid
1.0ms	2×	body	512	invalid
1.0ms	2×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify72.0ms (0.9%)

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

17.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.6b	(.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)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
✓	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	35.1b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series101.0ms (1.2%)

Counts

4 → 168

Calls

4 calls:

52.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
25.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
18.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
6.0ms	(*.f64 K (+.f64 m n))

rewrite106.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64`
70×	`add-sqr-sqrt_binary64`
57×	`prod-diff_binary64`
42×	`add-cube-cbrt_binary64`
26×	`fabs-mul_binary64`

Counts

4 → 156

Calls

4 calls:

69.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
5.0ms	(*.f64 K (+.f64 m n))

simplify259.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
385×	`associate-r_binary64`
362×	`associate-l_binary64`
329×	`fma-def_binary64`
268×	`*-commutative_binary64`

Counts

324 → 305

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	575	11388
1	1288	8942
2	4458	8942
3	5047	8942

prune536.0ms (6.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	300	5	305
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	301	5	306

Error

1.4b

Counts

306 → 5

Alt Table

Status	Error	Program
	17.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.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))))
▶	1.7b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	17.6b	(.f64 (-.f64 (.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (neg.f64 (.f64 M 1)))) (cos.f64 (fma.f64 (neg.f64 M) 1 (.f64 M 1)))) (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (neg.f64 (.f64 M 1)))) (sin.f64 (fma.f64 (neg.f64 M) 1 (*.f64 M 1))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	12.3b	(.f64 (cos.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))))
	17.7b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (.f64 (cbrt.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 15236 to 7403 computations (51.4% saved)

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.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)

prune281.0ms (3.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	183	5	188

Error

1.4b

Counts

188 → 5

Alt Table

Status	Error	Program
	17.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.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))))
✓	1.7b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	17.6b	(.f64 (-.f64 (.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (neg.f64 (.f64 M 1)))) (cos.f64 (fma.f64 (neg.f64 M) 1 (.f64 M 1)))) (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (neg.f64 (.f64 M 1)))) (sin.f64 (fma.f64 (neg.f64 M) 1 (*.f64 M 1))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	12.3b	(.f64 (cos.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))))
	17.7b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (.f64 (cbrt.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 7641 to 3852 computations (49.6% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.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)
✓	26.6b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

series13.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

12.0ms

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

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`cos-sum_binary64`
3×	`cancel-sign-sub-inv_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`prod-diff_binary64`

Counts

1 → 17

Calls

1 calls:

5.0ms

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

simplify133.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-neg_binary64`
649×	`distribute-rgt-neg-in_binary64`
527×	`associate-r_binary64`
509×	`associate-l_binary64`
230×	`distribute-lft-neg-out_binary64`

Counts

29 → 36

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	810
1	202	773
2	626	723
3	2646	701
4	4956	701
5	4976	701
6	4888	701

prune416.0ms (5.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	218	1	219
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	219	5	224

Error

1.4b

Counts

224 → 5

Alt Table

Status	Error	Program
▶	12.3b	(.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	17.6b	(.f64 (-.f64 (.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (neg.f64 (.f64 M 1)))) (cos.f64 (fma.f64 (neg.f64 M) 1 (.f64 M 1)))) (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (neg.f64 (.f64 M 1)))) (sin.f64 (fma.f64 (neg.f64 M) 1 (*.f64 M 1))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	17.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.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))))
✓	1.7b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	17.7b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (.f64 (cbrt.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 10199 to 5312 computations (47.9% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.5b	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 3))
✓	0.6b	(pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 3)
	26.6b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

series107.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

95.0ms	(pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 3)
12.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 3))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

2 → 48

Calls

2 calls:

4.0ms	(pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 3))

simplify115.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

574×	`cancel-sign-sub-inv_binary64`
445×	`fma-neg_binary64`
411×	`neg-mul-1_binary64`
374×	`unswap-sqr_binary64`
267×	`associate-r_binary64`

Counts

96 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	2633
1	473	2494
2	1876	2317
3	4066	2311
4	4856	2311
5	4965	2311

prune371.0ms (4.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	184	5	189

Error

1.4b

Counts

189 → 5

Alt Table

Status	Error	Program
	17.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.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))))
✓	1.7b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	12.3b	(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))) (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))) 3)) (cbrt.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M))) 3))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	17.6b	(.f64 (-.f64 (.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (neg.f64 (.f64 M 1)))) (cos.f64 (fma.f64 (neg.f64 M) 1 (.f64 M 1)))) (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (neg.f64 (.f64 M 1)))) (sin.f64 (fma.f64 (neg.f64 M) 1 (*.f64 M 1))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	17.7b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (.f64 (cbrt.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 7874 to 4420 computations (43.9% saved)

regimes599.0ms (7.4%)

Accuracy

Total 0.2b remaining (14.5%)

Threshold costs 0.2b (14.5%)

Counts

76 → 1

Compiler

Compiled 15590 to 10098 computations (35.2% 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

end7.0ms (0.1%)

Remove: (sort m n)
Compiler: Compiled 75 to 54 computations (28% saved)

sample2.0s (24.1%)

Algorithm

1×

intervals

Results

1.1s	7847×	body	128	valid
63.0ms	101×	body	1024	invalid
40.0ms	62×	body	1024	valid
36.0ms	267×	body	128	invalid
30.0ms	77×	body	512	invalid
23.0ms	59×	body	512	valid
16.0ms	63×	body	256	invalid
16.0ms	18×	body	2048	invalid
9.0ms	30×	body	256	valid
2.0ms	2×	body	2048	valid

Compiler

Compiled 340 to 218 computations (35.9% saved)

Details

analyze2.9s (35.2%)

sample105.0ms (1.3%)

simplify72.0ms (0.9%)

prune4.0ms (0%)

localize17.0ms (0.2%)

series101.0ms (1.2%)

rewrite106.0ms (1.3%)

simplify259.0ms (3.2%)

prune536.0ms (6.6%)

localize15.0ms (0.2%)

prune281.0ms (3.5%)

localize17.0ms (0.2%)

series13.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify133.0ms (1.6%)

prune416.0ms (5.1%)

localize23.0ms (0.3%)

series107.0ms (1.3%)

rewrite8.0ms (0.1%)

simplify115.0ms (1.4%)

prune371.0ms (4.6%)

regimes599.0ms (7.4%)

simplify3.0ms (0%)

end7.0ms (0.1%)

sample2.0s (24.1%)

Profiling