Details

analyze34.0ms (1.7%)

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)

sample80.0ms (3.9%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true
0.0ms	10×	pre	128	false

Compiler

Compiled 43 to 25 computations (41.9% saved)

simplify44.0ms (2.2%)

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

15.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.3b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 49 to 29 computations (40.8% saved)

localize7.0ms (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)))
✓	15.2b	(/.f64 b (*.f64 a a))

series64.0ms (3.1%)

Counts

3 → 72

Calls

3 calls:

28.0ms	(/.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))
1.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
0.0ms	(fma.f64 b (/.f64 b (*.f64 a a)) -1)

simplify76.0ms (3.7%)

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

prune42.0ms (2.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	1	71

Error

0.0b

Counts

71 → 1

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

Compiler

Compiled 1103 to 531 computations (51.9% saved)

localize7.0ms (0.4%)

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)))
✓	0.3b	(/.f64 (/.f64 b a) a)

series64.0ms (3.1%)

Counts

3 → 72

Calls

3 calls:

27.0ms	(/.f64 (/.f64 b a) a)
24.0ms	(fma.f64 b (/.f64 (/.f64 b a) a) -1)
13.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

rewrite13.0ms (0.7%)

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:

5.0ms	(/.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 (5.9%)

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

prune80.0ms (3.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	162	2	164

Error

0.0b

Counts

164 → 2

Alt Table

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

Compiler

Compiled 2911 to 1271 computations (56.3% saved)

localize9.0ms (0.5%)

Local error

Found 4 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)))
✓	0.0b	(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
	0.3b	(/.f64 (/.f64 b a) a)

series14.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

14.0ms

(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

simplify130.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

1120×	`fma-def_binary64`
494×	`associate-/r/_binary64`
446×	`unswap-sqr_binary64`
376×	`fma-neg_binary64`
374×	`div-sub_binary64`

Counts

35 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	583
1	31	552
2	47	552
3	76	552
4	155	552
5	407	552
6	1342	552
7	2141	552
8	2450	552
9	2868	552
10	3692	552
11	4203	552
12	4876	552
13	4988	552
14	4790	552

prune220.0ms (10.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	184	2	186

Error

0.0b

Counts

186 → 2

Alt Table

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

Compiler

Compiled 3591 to 1784 computations (50.3% saved)

regimes119.0ms (5.8%)

Accuracy

Total 0.0b remaining (47.1%)

Threshold costs 0.0b (47.1%)

Counts

15 → 1

Compiler

Compiled 1795 to 1213 computations (32.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	13	18
2	12	18

end0.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

sample897.0ms (44.1%)

Algorithm

1×

intervals

Results

367.0ms	8000×	body	128	valid
179.0ms	8000×	pre	128	true
9.0ms	391×	pre	128	false

Compiler

Compiled 68 to 45 computations (33.8% saved)

Details

analyze34.0ms (1.7%)

sample80.0ms (3.9%)

simplify44.0ms (2.2%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series64.0ms (3.1%)

rewrite7.0ms (0.3%)

simplify76.0ms (3.7%)

prune42.0ms (2.1%)

localize7.0ms (0.4%)

series64.0ms (3.1%)

rewrite13.0ms (0.7%)

simplify120.0ms (5.9%)

prune80.0ms (3.9%)

localize9.0ms (0.5%)

series14.0ms (0.7%)

rewrite1.0ms (0%)

simplify130.0ms (6.4%)

prune220.0ms (10.8%)

regimes119.0ms (5.8%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample897.0ms (44.1%)

Profiling