Details

analyze1.1s (9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0.1%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample257.0ms (2.2%)

Algorithm

1×

intervals

Results

119.0ms	45×	body	8192	exit
59.0ms	128×	body	1024	valid
23.0ms	51×	body	1024	nan
17.0ms	55×	body	512	valid
8.0ms	8×	body	2048	valid
7.0ms	28×	body	512	nan
6.0ms	32×	body	256	valid
3.0ms	33×	body	128	valid
1.0ms	9×	body	256	nan
1.0ms	9×	body	128	nan

Compiler

Compiled 24 to 18 computations (25% saved)

simplify94.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

924×	`unswap-sqr_binary64`
493×	`fma-neg_binary64`
430×	`associate-/l*_binary64`
379×	`fma-def_binary64`
296×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	16	17
2	25	15
3	36	15
4	59	15
5	103	15
6	204	15
7	435	15
8	703	15
9	1995	15
10	2934	15
11	3478	15
12	4158	15
13	4980	15
14	4913	15

prune3.0ms (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

59.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	59.0b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

Compiler

Compiled 40 to 21 computations (47.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (cos.f64 x))
✓	0.3b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
✓	6.1b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 53

Calls

3 calls:

3.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
1.0ms	(sqrt.f64 (cos.f64 x))
0.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series19.0ms (0.2%)

Counts

3 → 8

Calls

3 calls:

13.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
4.0ms	(sqrt.f64 (cos.f64 x))
2.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify107.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

599×	`cancel-sign-sub-inv_binary64`
541×	`fma-def_binary64`
463×	`times-frac_binary64`
381×	`div-sub_binary64`
282×	`fma-neg_binary64`

Counts

61 → 80

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	1190
1	212	1105
2	477	1069
3	1265	1049
4	3482	1048
5	4641	1048
6	5116	1048

prune51.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Error

59.0b

Counts

81 → 4

Alt Table

Status	Error	Program
	59.0b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.5b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
	59.0b	(/.f64 (fmod.f64 (exp.f64 x) (fabs.f64 (sqrt.f64 (cos.f64 x)))) (exp.f64 x))
▶	59.0b	(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 1301 to 367 computations (71.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(cbrt.f64 (cos.f64 x))
✓	0.1b	(cbrt.f64 (cos.f64 x))
✓	0.3b	(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))) (exp.f64 x))
✓	6.1b	(fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 51

Calls

3 calls:

3.0ms

(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))) (exp.f64 x))

1.0ms

(cbrt.f64 (cos.f64 x))

0.0ms

(fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))

series244.0ms (2.1%)

Counts

3 → 36

Calls

3 calls:

227.0ms

(cbrt.f64 (cos.f64 x))

15.0ms

(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))) (exp.f64 x))

2.0ms

(fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))

simplify128.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

576×	`cancel-sign-sub-inv_binary64`
553×	`fma-def_binary64`
496×	`unswap-sqr_binary64`
407×	`log-prod_binary64`
289×	`*-commutative_binary64`

Counts

87 → 161

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	110	2361
1	224	2050
2	515	1640
3	1339	1325
4	3467	1320
5	4917	1320
6	5331	1320

prune166.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	203	3	206

Error

59.0b

Counts

206 → 3

Alt Table

Status	Error	Program
▶	59.0b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))) x))
	59.0b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.5b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 2807 to 714 computations (74.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))) x))
✓	2.7b	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))) x)
✓	4.1b	(log.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))))
	6.1b	(fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
24×	`add-cube-cbrt_binary64`
19×	`exp-sum_binary64`

Counts

3 → 89

Calls

3 calls:

5.0ms

(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))) x))

4.0ms

(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))) x)

1.0ms

(log.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))))

series749.0ms (6.3%)

Counts

3 → 36

Calls

3 calls:

622.0ms

(log.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))))

114.0ms

(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))) x)

13.0ms

(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))) x))

simplify175.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

915×	`fma-neg_binary64`
407×	`associate-l_binary64`
383×	`associate-r_binary64`
301×	`distribute-rgt-neg-in_binary64`
299×	`fma-def_binary64`

Counts

125 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	141	3597
1	236	3161
2	632	2465
3	2443	2446
4	4394	2446
5	4991	2446
6	4842	2446

prune92.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	273	3	276
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	274	5	279

Error

24.1b

Counts

279 → 5

Alt Table

Status	Error	Program
▶	26.3b	(exp.f64 (neg.f64 x))
✓	59.0b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))) x))
	59.0b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.0b	(exp.f64 (log1p.f64 (expm1.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (pow.f64 (pow.f64 (cos.f64 x) 1/6) 3))) x))))
	59.0b	(exp.f64 (-.f64 (cbrt.f64 (pow.f64 (log.f64 (fmod.f64 (exp.f64 x) (pow.f64 (pow.f64 (cos.f64 x) 1/6) 3))) 3)) x))

Compiler

Compiled 4198 to 1187 computations (71.7% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune4.0ms (0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	1	1
Total	5	5

Error

24.1b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	26.3b	(exp.f64 (neg.f64 x))
✓	59.0b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))) x))
	59.0b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.0b	(exp.f64 (log1p.f64 (expm1.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (pow.f64 (pow.f64 (cos.f64 x) 1/6) 3))) x))))
	59.0b	(exp.f64 (-.f64 (cbrt.f64 (pow.f64 (log.f64 (fmod.f64 (exp.f64 x) (pow.f64 (pow.f64 (cos.f64 x) 1/6) 3))) 3)) x))

Compiler

Compiled 66 to 49 computations (25.8% saved)

regimes117.0ms (1%)

Accuracy

Total 0.5b remaining (1.9%)

Threshold costs 0.5b (1.9%)

Compiler

Compiled 1234 to 846 computations (31.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	79
1	34	79
2	37	79
3	38	79
4	37	79

end1.0ms (0%)

Compiler: Compiled 47 to 23 computations (51.1% saved)

sample8.5s (71.7%)

Algorithm

1×

intervals

Results

4.2s	1605×	body	8192	exit
2.0s	3988×	body	1024	valid
615.0ms	1524×	body	1024	nan
578.0ms	1984×	body	512	valid
192.0ms	788×	body	512	nan
188.0ms	988×	body	256	valid
131.0ms	185×	body	2048	valid
91.0ms	855×	body	128	valid
63.0ms	376×	body	256	nan
39.0ms	395×	body	128	nan

Compiler

Compiled 126 to 82 computations (34.9% saved)

Details

analyze1.1s (9%)

sample257.0ms (2.2%)

simplify94.0ms (0.8%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite7.0ms (0.1%)

series19.0ms (0.2%)

simplify107.0ms (0.9%)

prune51.0ms (0.4%)

localize12.0ms (0.1%)

rewrite7.0ms (0.1%)

series244.0ms (2.1%)

simplify128.0ms (1.1%)

prune166.0ms (1.4%)

localize13.0ms (0.1%)

rewrite18.0ms (0.2%)

series749.0ms (6.3%)

simplify175.0ms (1.5%)

prune92.0ms (0.8%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify9.0ms (0.1%)

prune4.0ms (0%)

regimes117.0ms (1%)

bsearch1.0ms (0%)

simplify5.0ms (0%)

end1.0ms (0%)

sample8.5s (71.7%)

Profiling