Details

analyze119.0ms (4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 20 to 11 computations (45% saved)

sample30.0ms (1%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true
0.0ms	4×	pre	128	false

Compiler

Compiled 37 to 21 computations (43.2% saved)

simplify52.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

603×	`associate-/r*_binary64`
566×	`associate-l_binary64`
494×	`associate-r_binary64`
376×	`fabs-div_binary64`
362×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	25	17
2	68	17
3	187	17
4	441	17
5	1424	17
6	4841	17
7	5086	17

prune3.0ms (0.1%)

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

15.1b

Counts

2 → 2

Alt Table

Status	Error	Program
	15.1b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
▶	15.1b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))

Compiler

Compiled 69 to 43 computations (37.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
28.7b	(/.f64 (.f64 b b) (.f64 a a))

rewrite56.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
12×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`fabs-mul_binary64`

Counts

2 → 47

Calls

2 calls:

9.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
5.0ms	(/.f64 (.f64 b b) (.f64 a a))

Compiler

Compiled 903 to 378 computations (58.1% saved)

series39.0ms (1.3%)

Error

15.1b

Counts

2 → 12

Calls

2 calls:

23.0ms	(/.f64 (.f64 b b) (.f64 a a))
15.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))

Compiler

Compiled 325 to 275 computations (15.4% saved)

simplify103.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
516×	`distribute-neg-frac_binary64`
385×	`associate-/l*_binary64`
363×	`unswap-sqr_binary64`
337×	`cancel-sign-sub-inv_binary64`

Counts

59 → 39

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1103
1	222	980
2	622	931
3	2953	904
4	4859	904
5	4994	904
6	4950	904

prune17.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Error

Counts

41 → 3

Alt Table

Status	Error	Program
	0.1b	(*.f64 (sqrt.f64 (fabs.f64 (+.f64 1 (/.f64 b a)))) (sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 b a)))))
	15.1b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
▶	0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 b a) 6)))))

Compiler

Compiled 336 to 190 computations (43.5% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 b a) 6)))))
0.4b	(pow.f64 (/.f64 b a) 6)
27.1b	(cbrt.f64 (pow.f64 (/.f64 b a) 6))

rewrite104.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

40×	`add-sqr-sqrt_binary64`
30×	`unpow-prod-down_binary64`
28×	`*-un-lft-identity_binary64`
25×	`cbrt-prod_binary64`
21×	`add-cube-cbrt_binary64`

Counts

3 → 85

Calls

3 calls:

12.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 b a) 6)))))
3.0ms	(pow.f64 (/.f64 b a) 6)
3.0ms	(cbrt.f64 (pow.f64 (/.f64 b a) 6))

Compiler

Compiled 1577 to 1083 computations (31.3% saved)

series54.0ms (1.8%)

Error

Counts

3 → 18

Calls

3 calls:

20.0ms	(pow.f64 (/.f64 b a) 6)
16.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 b a) 6)))))
16.0ms	(cbrt.f64 (pow.f64 (/.f64 b a) 6))

Compiler

Compiled 505 to 429 computations (15% saved)

simplify120.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

360×	`log-prod_binary64`
356×	`log-div_binary64`
315×	`associate-l_binary64`
292×	`cube-prod_binary64`
290×	`associate-r_binary64`

Counts

103 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	1955
1	333	1633
2	716	1567
3	2747	1447
4	4740	1447
5	5087	1447

prune35.0ms (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	82	2	84

Error

Counts

84 → 2

Alt Table

Status	Error	Program
	0.0b	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))))
▶	0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))

Compiler

Compiled 609 to 429 computations (29.6% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (pow.f64 (/.f64 b a) 2))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))
0.4b	(pow.f64 (/.f64 b a) 2)
7.0b	(log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2)))

rewrite117.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

39×	`unpow-prod-down_binary64`
38×	`add-sqr-sqrt_binary64`
36×	`exp-prod_binary64`
35×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`

Counts

4 → 110

Calls

4 calls:

12.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))
7.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2)))
4.0ms	(exp.f64 (pow.f64 (/.f64 b a) 2))
4.0ms	(pow.f64 (/.f64 b a) 2)

Compiler

Compiled 2040 to 1392 computations (31.8% saved)

series88.0ms (3%)

Error

Counts

4 → 33

Calls

4 calls:

35.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2)))
20.0ms	(exp.f64 (pow.f64 (/.f64 b a) 2))
15.0ms	(pow.f64 (/.f64 b a) 2)
13.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))

Compiler

Compiled 943 to 805 computations (14.6% saved)

simplify88.0ms (3%)

Algorithm

1×	egg-herbie

Rules

530×	`associate-/l/_binary64`
223×	`exp-prod_binary64`
192×	`sqr-pow_binary64`
177×	`associate-l_binary64`
166×	`associate-*l/_binary64`

Counts

143 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	196	2028
1	339	1730
2	707	1649
3	2378	1643
4	5018	1643

prune47.0ms (1.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	111	2	113

Error

Counts

113 → 2

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))))
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))

Compiler

Compiled 1163 to 748 computations (35.7% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))
0.0b	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))))
0.4b	(pow.f64 (/.f64 b a) 2)

rewrite143.0ms (4.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

66×	`add-sqr-sqrt_binary64`
54×	`sqrt-prod_binary64`
43×	`fabs-mul_binary64`
42×	`exp-prod_binary64`
42×	`*-un-lft-identity_binary64`

Counts

4 → 123

Calls

4 calls:

12.0ms	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))))
12.0ms	(exp.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))))
11.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))
4.0ms	(pow.f64 (/.f64 b a) 2)

Compiler

Compiled 2412 to 1735 computations (28.1% saved)

series98.0ms (3.3%)

Error

Counts

4 → 24

Calls

4 calls:

46.0ms	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))))
19.0ms	(exp.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))))
17.0ms	(pow.f64 (/.f64 b a) 2)
15.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))

Compiler

Compiled 735 to 637 computations (13.3% saved)

simplify122.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

455×	`associate-/r*_binary64`
390×	`associate-/l/_binary64`
268×	`log-div_binary64`
194×	`associate-/r/_binary64`
155×	`associate-l_binary64`

Counts

147 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	2635
1	334	2165
2	620	2138
3	1829	2136
4	4666	2136
5	5007	2136

prune50.0ms (1.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	112	2	114

Error

Counts

114 → 2

Alt Table

Status	Error	Program
	0.0b	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))))
	0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))

Compiler

Compiled 1142 to 784 computations (31.3% saved)

regimes374.0ms (12.6%)

Accuracy

Total 0.0b remaining (69.6%)

Threshold costs 0.0b (69.6%)

Compiler

Compiled 5327 to 4010 computations (24.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	20	17
2	26	17
3	29	17
4	30	17
5	27	17

end1.0ms (0%)

Compiler: Compiled 13 to 11 computations (15.4% saved)

sample1.1s (35.9%)

Algorithm

1×

intervals

Results

385.0ms	8000×	body	128	valid
186.0ms	8000×	pre	128	true
3.0ms	150×	pre	128	false

Compiler

Compiled 61 to 46 computations (24.6% saved)

Details

analyze119.0ms (4%)

sample30.0ms (1%)

simplify52.0ms (1.7%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

rewrite56.0ms (1.9%)

series39.0ms (1.3%)

simplify103.0ms (3.5%)

prune17.0ms (0.6%)

localize9.0ms (0.3%)

rewrite104.0ms (3.5%)

series54.0ms (1.8%)

simplify120.0ms (4.1%)

prune35.0ms (1.2%)

localize8.0ms (0.3%)

rewrite117.0ms (4%)

series88.0ms (3%)

simplify88.0ms (3%)

prune47.0ms (1.6%)

localize9.0ms (0.3%)

rewrite143.0ms (4.8%)

series98.0ms (3.3%)

simplify122.0ms (4.1%)

prune50.0ms (1.7%)

regimes374.0ms (12.6%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.1s (35.9%)

Profiling