Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample29.0ms (0.9%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	10	12

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series59.0ms (1.9%)

Counts

3 → 12

Calls

3 calls:

44.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
7.0ms	(sqrt.f64 (+.f64 x 1))

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`

Counts

3 → 82

Calls

3 calls:

7.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
6.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
2.0ms	(sqrt.f64 (+.f64 x 1))

simplify94.0ms (3%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-neg_binary64`
333×	`associate-/r*_binary64`
321×	`associate-/l/_binary64`
303×	`associate-*l/_binary64`
284×	`cancel-sign-sub-inv_binary64`

Counts

94 → 108

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	123	1335
1	263	1239
2	634	1227
3	1878	1212
4	4323	1211
5	4987	1211
6	4875	1211

prune81.0ms (2.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	105	4	109

Error

Counts

109 → 4

Alt Table

Status	Error	Program
	33.3b	(/.f64 x (/.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
▶	0.8b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
	25.7b	(fma.f64 1/2 x (.f64 (.f64 x x) (fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8)))

Compiler

Compiled 1643 to 1260 computations (23.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.1b	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.3b	(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.4b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series232.0ms (7.4%)

Counts

3 → 12

Calls

3 calls:

146.0ms

(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

50.0ms

(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

35.0ms

(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite114.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

597×	`*-un-lft-identity_binary64`
594×	`times-frac_binary64`
555×	`sqrt-prod_binary64`
397×	`add-sqr-sqrt_binary64`
276×	`distribute-lft-out_binary64`

Counts

3 → 439

Calls

3 calls:

20.0ms

(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

7.0ms

(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

5.0ms

(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify396.0ms (12.6%)

Algorithm

1×	egg-herbie

Rules

834×	`fma-def_binary64`
689×	`times-frac_binary64`
590×	`associate-/l/_binary64`
560×	`associate-/l*_binary64`
410×	`associate-/r*_binary64`

Counts

451 → 369

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	325	18146
1	742	16553
2	1782	15224
3	4539	15213
4	5089	15213

prune337.0ms (10.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	457	0	457
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	457	4	461

Error

Counts

461 → 4

Alt Table

Status	Error	Program
	33.3b	(/.f64 x (/.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.8b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	25.7b	(fma.f64 1/2 x (.f64 (.f64 x x) (fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8)))

Compiler

Compiled 14078 to 11509 computations (18.2% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 x x) (fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8))
✓	0.1b	(fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8)

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(.f64 (.f64 x x) (fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8))
2.0ms	(fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8)

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`

Counts

2 → 33

Calls

2 calls:

5.0ms	(.f64 (.f64 x x) (fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8))
0.0ms	(fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8)

simplify85.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

671×	`fma-def_binary64`
557×	`fma-neg_binary64`
549×	`associate-l_binary64`
446×	`exp-prod_binary64`
422×	`associate-r_binary64`

Counts

57 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	74	1059
1	179	872
2	515	755
3	1871	755
4	3945	755
5	4954	755
6	4930	755

prune54.0ms (1.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	71	4	75

Error

Counts

75 → 4

Alt Table

Status	Error	Program
▶	33.3b	(/.f64 x (/.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.8b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	25.7b	(fma.f64 1/2 x (.f64 (.f64 x x) (fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8)))

Compiler

Compiled 1468 to 960 computations (34.6% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.2b	(/.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.2b	(/.f64 x (/.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	4.0b	(-.f64 1 (sqrt.f64 (+.f64 x 1)))

series64.0ms (2%)

Counts

3 → 12

Calls

3 calls:

43.0ms	(/.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1))))
12.0ms	(/.f64 x (/.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
9.0ms	(-.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite131.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Rules

818×	`times-frac_binary64`
750×	`add-sqr-sqrt_binary64`
706×	`*-un-lft-identity_binary64`
334×	`add-cube-cbrt_binary64`
224×	`sqrt-prod_binary64`

Counts

3 → 633

Calls

3 calls:

19.0ms	(/.f64 x (/.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
10.0ms	(/.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(-.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify400.0ms (12.8%)

Algorithm

1×	egg-herbie

Rules

753×	`fma-def_binary64`
414×	`associate-/r/_binary64`
336×	`associate-/l/_binary64`
268×	`associate-*l/_binary64`
247×	`associate-/l*_binary64`

Counts

645 → 579

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	468	19323
1	1028	17718
2	4208	17634
3	4938	17634

prune325.0ms (10.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	608	0	608
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	608	4	612

Error

Counts

612 → 4

Alt Table

Status	Error	Program
✓	33.3b	(/.f64 x (/.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.8b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	25.7b	(fma.f64 1/2 x (.f64 (.f64 x x) (fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8)))

Compiler

Compiled 14557 to 9505 computations (34.7% saved)

regimes148.0ms (4.7%)

Accuracy

Total 0.2b remaining (99%)

Threshold costs 0.2b (99%)

Counts

77 → 1

Compiler

Compiled 2140 to 1642 computations (23.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	10	12

end2.0ms (0.1%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

sample516.0ms (16.4%)

Algorithm

1×

intervals

Results

293.0ms	7998×	body	128	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 75 to 58 computations (22.7% saved)

Details

analyze3.0ms (0.1%)

sample29.0ms (0.9%)

simplify6.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series59.0ms (1.9%)

rewrite19.0ms (0.6%)

simplify94.0ms (3%)

prune81.0ms (2.6%)

localize7.0ms (0.2%)

series232.0ms (7.4%)

rewrite114.0ms (3.6%)

simplify396.0ms (12.6%)

prune337.0ms (10.7%)

localize10.0ms (0.3%)

series6.0ms (0.2%)

rewrite6.0ms (0.2%)

simplify85.0ms (2.7%)

prune54.0ms (1.7%)

localize7.0ms (0.2%)

series64.0ms (2%)

rewrite131.0ms (4.2%)

simplify400.0ms (12.8%)

prune325.0ms (10.4%)

regimes148.0ms (4.7%)

simplify2.0ms (0.1%)

end2.0ms (0.1%)

sample516.0ms (16.4%)

Profiling