Details

analyze844.0ms (11.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample141.0ms (1.9%)

Algorithm

1×

intervals

Results

61.0ms	75×	body	1024	valid
33.0ms	45×	body	2048	valid
19.0ms	42×	body	512	valid
8.0ms	74×	body	128	valid
5.0ms	19×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify20.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9
3	13	9

prune5.0ms (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

45.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	45.1b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.2b	(+.f64 x (hypot.f64 1 x))
✓	2.4b	(log.f64 (+.f64 x (hypot.f64 1 x)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`log-prod_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 34

Calls

2 calls:

6.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
4.0ms	(+.f64 x (hypot.f64 1 x))

series32.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

20.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
12.0ms	(+.f64 x (hypot.f64 1 x))

simplify142.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-neg_binary64`
426×	`associate-/r*_binary64`
386×	`cancel-sign-sub-inv_binary64`
299×	`sub-neg_binary64`
286×	`fma-def_binary64`

Counts

58 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	861
1	334	805
2	827	799
3	2288	799
4	4460	799
5	4998	799
6	4887	799

prune86.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	3	88

Error

Counts

88 → 3

Alt Table

Status	Error	Program
✓	45.1b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	33.6b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
	46.3b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 1163 to 882 computations (24.2% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 5/112 (pow.f64 x 7))
✓	0.1b	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
✓	0.2b	(fma.f64 3/40 (pow.f64 x 5) x)
✓	22.5b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`
9×	`prod-diff_binary64`

Counts

4 → 79

Calls

4 calls:

8.0ms	(*.f64 5/112 (pow.f64 x 7))
7.0ms	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
1.0ms	(fma.f64 3/40 (pow.f64 x 5) x)
1.0ms	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))

series146.0ms (2%)

Counts

4 → 36

Calls

4 calls:

50.0ms	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
46.0ms	(*.f64 5/112 (pow.f64 x 7))
35.0ms	(fma.f64 3/40 (pow.f64 x 5) x)
13.0ms	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))

simplify197.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-neg_binary64`
633×	`times-frac_binary64`
600×	`associate-r_binary64`
389×	`fma-def_binary64`
339×	`distribute-lft-in_binary64`

Counts

115 → 190

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	142	2229
1	264	2018
2	793	1831
3	3426	1774
4	4426	1759
5	5632	1759

prune209.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	190	3	193

Error

Counts

193 → 3

Alt Table

Status	Error	Program
✓	45.1b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	33.6b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
▶	46.3b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 3476 to 2758 computations (20.7% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
✓	0.1b	(/.f64 1/8 (pow.f64 x 3))
✓	8.3b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

rewrite132.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64`
63×	`*-un-lft-identity_binary64`
51×	`add-sqr-sqrt_binary64`
51×	`add-cube-cbrt_binary64`
40×	`fma-def_binary64`

Counts

3 → 142

Calls

3 calls:

57.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
49.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
8.0ms	(/.f64 1/8 (pow.f64 x 3))

series70.0ms (0.9%)

Counts

3 → 24

Calls

3 calls:

30.0ms	(/.f64 1/8 (pow.f64 x 3))
25.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
14.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

simplify179.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

409×	`fma-def_binary64`
378×	`associate-/l*_binary64`
347×	`cancel-sign-sub-inv_binary64`
334×	`associate-*l/_binary64`
284×	`associate-/l/_binary64`

Counts

166 → 262

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	2065
1	402	1967
2	1395	1913
3	4765	1912
4	5079	1912

prune186.0ms (2.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	262	3	265

Error

Counts

265 → 3

Alt Table

Status	Error	Program
✓	45.1b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	33.6b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
✓	46.3b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 3303 to 2623 computations (20.6% saved)

regimes189.0ms (2.6%)

Accuracy

Total 0.0b remaining (59.8%)

Threshold costs 0.0b (59.8%)

Compiler

Compiled 759 to 592 computations (22% saved)

bsearch61.0ms (0.8%)

Steps

Iters	Range		Point
9	4.2976498015271836e-7	3.2660511204486466	0.02445926160054447
9	-112385.69704575694	-0.008954988478185967	-1.1201596475277218

Compiler

Compiled 2 to 1 computations (50% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
8×	`*-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	64
1	45	64
2	53	64
3	75	64
4	84	64
5	90	64
6	92	64
7	89	64

end4.0ms (0.1%)

Compiler: Compiled 44 to 34 computations (22.7% saved)

sample4.6s (62.8%)

Algorithm

1×

intervals

Results

2.1s	2480×	body	1024	valid
917.0ms	1190×	body	2048	valid
570.0ms	1213×	body	512	valid
292.0ms	2439×	body	128	valid
172.0ms	617×	body	256	valid
59.0ms	61×	body	4096	valid

Compiler

Compiled 92 to 71 computations (22.8% saved)

Details

analyze844.0ms (11.5%)

sample141.0ms (1.9%)

simplify20.0ms (0.3%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

rewrite13.0ms (0.2%)

series32.0ms (0.4%)

simplify142.0ms (1.9%)

prune86.0ms (1.2%)

localize22.0ms (0.3%)

rewrite27.0ms (0.4%)

series146.0ms (2%)

simplify197.0ms (2.7%)

prune209.0ms (2.8%)

localize13.0ms (0.2%)

rewrite132.0ms (1.8%)

series70.0ms (0.9%)

simplify179.0ms (2.4%)

prune186.0ms (2.5%)

regimes189.0ms (2.6%)

bsearch61.0ms (0.8%)

simplify11.0ms (0.2%)

end4.0ms (0.1%)

sample4.6s (62.8%)

Profiling