Details

analyze35.0ms (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	37.5%	62.5%	0
0%	37.5%	62.5%	1
0%	18.7%	81.3%	2
0%	9.4%	90.6%	3
0%	9.4%	90.6%	4
0%	7%	93%	5
1.2%	4.7%	94.1%	6
1.2%	3.5%	95.3%	7
1.8%	2.6%	95.6%	8
2%	1.9%	96%	9
2.4%	1.3%	96.3%	10
2.6%	1%	96.5%	11
2.7%	0.7%	96.6%	12
2.8%	0.5%	96.7%	13
2.9%	0.3%	96.7%	14

Compiler

Compiled 26 to 15 computations (42.3% saved)

sample77.0ms (3%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true
0.0ms	19×	pre	128	false

Compiler

Compiled 43 to 25 computations (41.9% saved)

simplify47.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
643×	`fma-neg_binary64`
603×	`associate-/r*_binary64`
566×	`associate-l_binary64`
362×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	26	17
2	69	15
3	194	15
4	464	15
5	1521	15
6	4781	15
7	5160	15

prune3.0ms (0.1%)

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

13.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.3b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 49 to 29 computations (40.8% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 b (/.f64 b (*.f64 a a)) -1)
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
✓	13.2b	(/.f64 b (*.f64 a a))

series89.0ms (3.5%)

Counts

3 → 72

Calls

3 calls:

53.0ms	(/.f64 b (*.f64 a a))
23.0ms	(fma.f64 b (/.f64 b (*.f64 a a)) -1)
13.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
7×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64`

Counts

3 → 54

Calls

3 calls:

3.0ms	(/.f64 b (*.f64 a a))
2.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
0.0ms	(fma.f64 b (/.f64 b (*.f64 a a)) -1)

simplify74.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

661×	`associate-/l*_binary64`
603×	`fma-def_binary64`
491×	`associate-l_binary64`
486×	`associate-/l/_binary64`
431×	`associate-/r*_binary64`

Counts

126 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	1587
1	143	1492
2	293	1492
3	866	1490
4	4508	1490
5	5063	1490

prune47.0ms (1.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	3	71

Error

0.0b

Counts

71 → 3

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
	13.3b	(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))
	2.2b	(sqrt.f64 (fabs.f64 -1))

Compiler

Compiled 1141 to 561 computations (50.8% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 b (/.f64 (/.f64 b a) a) -1)
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
✓	0.2b	(/.f64 (/.f64 b a) a)

series65.0ms (2.5%)

Counts

3 → 72

Calls

3 calls:

29.0ms	(/.f64 (/.f64 b a) a)
23.0ms	(fma.f64 b (/.f64 (/.f64 b a) a) -1)
13.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

rewrite26.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
51×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64`
47×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

3 → 103

Calls

3 calls:

17.0ms	(/.f64 (/.f64 b a) a)
2.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
0.0ms	(fma.f64 b (/.f64 (/.f64 b a) a) -1)

simplify120.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary64`
423×	`unswap-sqr_binary64`
394×	`fma-neg_binary64`
337×	`associate-/l/_binary64`
324×	`times-frac_binary64`

Counts

175 → 163

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	184	2634
1	347	2461
2	650	2389
3	1692	2365
4	2633	2345
5	4642	2345
6	4955	2345

prune99.0ms (3.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	163	3	166

Error

Counts

166 → 3

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
▶	0.0b	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
	13.3b	(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))

Compiler

Compiled 2939 to 1291 computations (56.1% saved)

localize57.0ms (2.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
✓	0.0b	(exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))
✓	0.0b	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
	0.2b	(/.f64 (/.f64 b a) a)

series32.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

20.0ms	(exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))
12.0ms	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`exp-prod_binary64`
14×	`sqrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`log-pow_binary64`
9×	`*-un-lft-identity_binary64`

Counts

2 → 44

Calls

2 calls:

3.0ms	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
2.0ms	(exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))

simplify148.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

554×	`unswap-sqr_binary64`
524×	`associate-/r/_binary64`
500×	`fma-def_binary64`
366×	`exp-sum_binary64`
353×	`log-prod_binary64`

Counts

92 → 76

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	71	1651
1	81	1539
2	108	1539
3	151	1539
4	265	1539
5	602	1539
6	1750	1539
7	2926	1533
8	4392	1533
9	4784	1533
10	4986	1533
11	4916	1533

prune251.0ms (9.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	216	3	219

Error

Counts

219 → 3

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
✓	0.0b	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
▶	13.3b	(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))

Compiler

Compiled 4502 to 2263 computations (49.7% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 b (/.f64 b (*.f64 a a)) -1)
✓	0.0b	(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))
✓	0.1b	(log1p.f64 (expm1.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
	13.2b	(/.f64 b (*.f64 a a))

series38.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

23.0ms	(log1p.f64 (expm1.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
15.0ms	(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
7×	`sqrt-prod_binary64`
4×	`fabs-mul_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 32

Calls

2 calls:

1.0ms	(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))
0.0ms	(log1p.f64 (expm1.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

simplify72.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

549×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
528×	`fma-def_binary64`
348×	`fma-neg_binary64`
265×	`associate-/l/_binary64`

Counts

80 → 56

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	1196
1	71	1110
2	102	1110
3	251	1110
4	1238	1110
5	4871	1110
6	5120	1110

prune62.0ms (2.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	101	3	104

Error

Counts

104 → 3

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
✓	0.0b	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
✓	13.3b	(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))

Compiler

Compiled 1783 to 957 computations (46.3% saved)

regimes135.0ms (5.3%)

Accuracy

Total 0.0b remaining (44%)

Threshold costs 0.0b (44%)

Counts

17 → 1

Compiler

Compiled 2254 to 1490 computations (33.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	9	15

end0.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample1.0s (40.2%)

Algorithm

1×

intervals

Results

486.0ms	8000×	body	128	valid
193.0ms	8000×	pre	128	true
10.0ms	400×	pre	128	false

Compiler

Compiled 80 to 53 computations (33.8% saved)

Details

analyze35.0ms (1.4%)

sample77.0ms (3%)

simplify47.0ms (1.9%)

prune3.0ms (0.1%)

localize6.0ms (0.3%)

series89.0ms (3.5%)

rewrite7.0ms (0.3%)

simplify74.0ms (2.9%)

prune47.0ms (1.8%)

localize6.0ms (0.3%)

series65.0ms (2.5%)

rewrite26.0ms (1%)

simplify120.0ms (4.7%)

prune99.0ms (3.9%)

localize57.0ms (2.2%)

series32.0ms (1.3%)

rewrite9.0ms (0.4%)

simplify148.0ms (5.8%)

prune251.0ms (9.9%)

localize10.0ms (0.4%)

series38.0ms (1.5%)

rewrite3.0ms (0.1%)

simplify72.0ms (2.8%)

prune62.0ms (2.5%)

regimes135.0ms (5.3%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.0s (40.2%)

Profiling