Details

analyze1.4s (15.5%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample148.0ms (1.6%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
9.0ms	92×	body	128	invalid
4.0ms	66×	body	128	nan

Compiler

Compiled 40 to 28 computations (30% saved)

simplify106.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

614×	`*-commutative_binary64`
613×	`associate-l_binary64`
526×	`sqr-pow_binary64`
394×	`associate-*r/_binary64`
380×	`cube-prod_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	27	18
2	55	17
3	104	17
4	225	17
5	591	17
6	1774	17
7	2466	17
8	2534	17
9	2692	17
10	2908	17
11	3166	17
12	3656	17
13	4497	17
14	5019	17

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

2.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 60 to 37 computations (38.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	2.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series307.0ms (3.3%)

Counts

2 → 48

Calls

2 calls:

305.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
2.0ms	(fma.f64 k (+.f64 k 10) 1)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 35

Calls

2 calls:

4.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
0.0ms	(fma.f64 k (+.f64 k 10) 1)

simplify79.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

828×	`associate-/l*_binary64`
641×	`times-frac_binary64`
418×	`fma-neg_binary64`
376×	`fma-def_binary64`
245×	`cancel-sign-sub-inv_binary64`

Counts

83 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	2074
1	443	1777
2	1567	1600
3	4891	1596
4	5106	1596

prune67.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	4	81

Error

2.4b

Counts

81 → 4

Alt Table

Status	Error	Program
✓	2.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
	11.8b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k 10 1))
▶	2.4b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
	2.5b	(.f64 (/.f64 a (.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))) (/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))

Compiler

Compiled 1977 to 1125 computations (43.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	0.2b	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))
✓	2.2b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))

series330.0ms (3.6%)

Counts

2 → 60

Calls

2 calls:

290.0ms	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
40.0ms	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`times-frac_binary64`
43×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
25×	`associate-r_binary64`

Counts

2 → 97

Calls

2 calls:

7.0ms	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
3.0ms	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))

simplify119.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

788×	`times-frac_binary64`
592×	`fma-def_binary64`
399×	`fma-neg_binary64`
388×	`cancel-sign-sub-inv_binary64`
218×	`associate-r_binary64`

Counts

157 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	4566
1	722	4205
2	2577	3821
3	4685	3821
4	4973	3821

prune200.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	208	2	210
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	211	3	214

Error

2.4b

Counts

214 → 3

Alt Table

Status	Error	Program
▶	2.9b	(*.f64 a (/.f64 (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	2.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
	11.8b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k 10 1)))

Compiler

Compiled 5282 to 3000 computations (43.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	0.0b	(/.f64 (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	2.2b	(*.f64 a (/.f64 (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	17.7b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series365.0ms (4%)

Counts

4 → 96

Calls

4 calls:

278.0ms	(*.f64 a (/.f64 (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
44.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
40.0ms	(/.f64 (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
2.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

rewrite234.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

1166×	`times-frac_binary64`
627×	`add-sqr-sqrt_binary64`
592×	`sqrt-prod_binary64`
574×	`*-un-lft-identity_binary64`
574×	`add-cube-cbrt_binary64`

Counts

4 → 751

Calls

4 calls:

51.0ms	(*.f64 a (/.f64 (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
12.0ms	(/.f64 (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
4.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
1.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

simplify637.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

536×	`associate-/l/_binary64`
493×	`associate-/l*_binary64`
389×	`fma-def_binary64`
319×	`associate-l_binary64`
287×	`associate-*r/_binary64`

Counts

847 → 907

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	747	34914
1	1756	32029
2	4808	31991
3	5032	31991

prune1.1s (11.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	944	1	945
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	945	3	948

Error

0.0b

Counts

948 → 3

Alt Table

Status	Error	Program
✓	2.9b	(*.f64 a (/.f64 (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	2.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
▶	35.6b	(fma.f64 (/.f64 (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k))))) k) (/.f64 a k) (.f64 (/.f64 (.f64 a (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k)))))) (pow.f64 k 3)) -10))

Compiler

Compiled 38355 to 24767 computations (35.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (/.f64 (.f64 a (exp.f64 (neg.f64 (*.f64 m (neg.f64 (log.f64 k)))))) (pow.f64 k 3)) -10)
✓	0.2b	(*.f64 m (neg.f64 (log.f64 k)))
✓	4.7b	(fma.f64 (/.f64 (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k))))) k) (/.f64 a k) (.f64 (/.f64 (.f64 a (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k)))))) (pow.f64 k 3)) -10))
✓	9.4b	(/.f64 (.f64 a (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k)))))) (pow.f64 k 3))

series1.3s (13.8%)

Counts

4 → 132

Calls

4 calls:

495.0ms	(fma.f64 (/.f64 (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k))))) k) (/.f64 a k) (.f64 (/.f64 (.f64 a (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k)))))) (pow.f64 k 3)) -10))
281.0ms	(.f64 (/.f64 (.f64 a (exp.f64 (neg.f64 (*.f64 m (neg.f64 (log.f64 k)))))) (pow.f64 k 3)) -10)
275.0ms	(/.f64 (.f64 a (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k)))))) (pow.f64 k 3))
221.0ms	(*.f64 m (neg.f64 (log.f64 k)))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`

Counts

4 → 136

Calls

4 calls:

10.0ms	(.f64 (/.f64 (.f64 a (exp.f64 (neg.f64 (*.f64 m (neg.f64 (log.f64 k)))))) (pow.f64 k 3)) -10)
8.0ms	(/.f64 (.f64 a (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k)))))) (pow.f64 k 3))
7.0ms	(*.f64 m (neg.f64 (log.f64 k)))
0.0ms	(fma.f64 (/.f64 (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k))))) k) (/.f64 a k) (.f64 (/.f64 (.f64 a (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k)))))) (pow.f64 k 3)) -10))

simplify159.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-def_binary64`
327×	`times-frac_binary64`
302×	`fma-neg_binary64`
236×	`associate-/r*_binary64`
200×	`associate-l_binary64`

Counts

268 → 230

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	302	6060
1	734	4738
2	3176	4661
3	4806	4661
4	4905	4661

prune196.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

0.0b

Counts

276 → 3

Alt Table

Status	Error	Program
✓	2.9b	(*.f64 a (/.f64 (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	2.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
✓	35.6b	(fma.f64 (/.f64 (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k))))) k) (/.f64 a k) (.f64 (/.f64 (.f64 a (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k)))))) (pow.f64 k 3)) -10))

Compiler

Compiled 9346 to 3097 computations (66.9% saved)

regimes664.0ms (7.2%)

Accuracy

Total 0.0b remaining (41.8%)

Threshold costs 0.0b (41.8%)

Counts

109 → 2

Compiler

Compiled 9180 to 6186 computations (32.6% saved)

bsearch6.0ms (0.1%)

Steps

Iters	Range		Point
1	9.104138716827185e+94	1.0445711930009297e+95	9.77492532341824e+94

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`cancel-sign-sub-inv_binary64`
12×	`distribute-lft-neg-in_binary64`
12×	`distribute-rgt-neg-in_binary64`
7×	`*-commutative_binary64`
7×	`distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	60
1	48	56
2	62	56
3	82	56
4	90	56
5	93	56
6	89	56

end1.0ms (0%)

Compiler: Compiled 41 to 25 computations (39% saved)

sample1.7s (18.4%)

Algorithm

1×

intervals

Results

655.0ms	8000×	body	128	valid
367.0ms	3144×	body	128	invalid
125.0ms	2020×	body	128	nan

Compiler

Compiled 133 to 85 computations (36.1% saved)

Details

analyze1.4s (15.5%)

sample148.0ms (1.6%)

simplify106.0ms (1.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series307.0ms (3.3%)

rewrite6.0ms (0.1%)

simplify79.0ms (0.9%)

prune67.0ms (0.7%)

localize9.0ms (0.1%)

series330.0ms (3.6%)

rewrite36.0ms (0.4%)

simplify119.0ms (1.3%)

prune200.0ms (2.2%)

localize9.0ms (0.1%)

series365.0ms (4%)

rewrite234.0ms (2.5%)

simplify637.0ms (6.9%)

prune1.1s (11.7%)

localize16.0ms (0.2%)

series1.3s (13.8%)

rewrite32.0ms (0.3%)

simplify159.0ms (1.7%)

prune196.0ms (2.1%)

regimes664.0ms (7.2%)

bsearch6.0ms (0.1%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.7s (18.4%)

Profiling