Details

analyze419.0ms (8.4%)

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)

sample3.6s (73.3%)

Results

1.7s	2607×	body	1024	valid
855.0ms	1272×	body	2048	valid
642.0ms	1266×	body	512	valid
284.0ms	2445×	body	128	valid
147.0ms	621×	body	256	valid
35.0ms	45×	body	4096	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify6.0ms (0.1%)

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

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

47.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	47.5b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.4b	(+.f64 x (hypot.f64 1 x))
✓	4.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
2.0ms	(+.f64 x (hypot.f64 1 x))

rewrite6.0ms (0.1%)

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:

2.0ms	(+.f64 x (hypot.f64 1 x))
2.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))

simplify78.0ms (1.6%)

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 → 81

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

prune58.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	5	82

Error

0.0b

Counts

82 → 5

Alt Table

Status	Error	Program
	60.1b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
	46.6b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	48.6b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
▶	30.0b	(fma.f64 (pow.f64 x 3) -1/6 x)
	47.5b	(log.f64 (+.f64 (hypot.f64 1 x) x))

Compiler

Compiled 1212 to 915 computations (24.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 3) -1/6 x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 (pow.f64 x 3) -1/6 x)

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 → 10

Calls

1 calls:

0.0ms

(fma.f64 (pow.f64 x 3) -1/6 x)

simplify59.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

435×	`neg-mul-1_binary64`
394×	`associate-l_binary64`
372×	`associate-r_binary64`
317×	`distribute-rgt-out_binary64`
261×	`exp-prod_binary64`

Counts

22 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	232
1	35	197
2	87	197
3	323	197
4	1659	197
5	4536	197
6	5201	197

prune10.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	16	5	21

Error

0.0b

Counts

21 → 5

Alt Table

Status	Error	Program
	60.1b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
▶	46.6b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	48.6b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
✓	30.0b	(fma.f64 (pow.f64 x 3) -1/6 x)
	47.5b	(log.f64 (+.f64 (hypot.f64 1 x) x))

Compiler

Compiled 247 to 182 computations (26.3% saved)

localize42.0ms (0.8%)

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))
✓	0.3b	(/.f64 1/8 (pow.f64 x 3))
✓	11.9b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

series12.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

5.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
4.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
3.0ms	(/.f64 1/8 (pow.f64 x 3))

rewrite63.0ms (1.3%)

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:

25.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
23.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
4.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify82.0ms (1.7%)

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 → 185

Iterations

Useful iterations: 3 (0.0ms)

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

prune96.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	185	5	190

Error

0.0b

Counts

190 → 5

Alt Table

Status	Error	Program
	60.1b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
✓	46.6b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	48.6b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
✓	30.0b	(fma.f64 (pow.f64 x 3) -1/6 x)
▶	47.5b	(log.f64 (+.f64 (hypot.f64 1 x) x))

Compiler

Compiled 3383 to 2682 computations (20.7% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.4b	(+.f64 (hypot.f64 1 x) x)
✓	4.0b	(log.f64 (+.f64 (hypot.f64 1 x) x))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(log.f64 (+.f64 (hypot.f64 1 x) x))
2.0ms	(+.f64 (hypot.f64 1 x) x)

rewrite11.0ms (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:

7.0ms	(+.f64 (hypot.f64 1 x) x)
2.0ms	(log.f64 (+.f64 (hypot.f64 1 x) x))

simplify61.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

690×	`times-frac_binary64`
666×	`fma-neg_binary64`
426×	`associate-/r*_binary64`
388×	`cancel-sign-sub-inv_binary64`
299×	`sub-neg_binary64`

Counts

58 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	867
1	334	811
2	827	799
3	2293	799
4	4455	799
5	5507	799

prune40.0ms (0.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	96	5	101

Error

0.0b

Counts

101 → 5

Alt Table

Status	Error	Program
	60.1b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
✓	46.6b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	48.6b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
✓	30.0b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	47.5b	(log.f64 (+.f64 (hypot.f64 1 x) x))

Compiler

Compiled 1331 to 1007 computations (24.3% saved)

regimes113.0ms (2.3%)

Accuracy

Total 0.1b remaining (78.2%)

Threshold costs 0.1b (78.2%)

Counts

30 → 3

Compiler

Compiled 1032 to 769 computations (25.5% saved)

bsearch45.0ms (0.9%)

Steps

Iters	Range		Point
8	2.861332380623058e-6	0.021286450759173393	0.0010906364138287723
9	-4.83044265941669	-9.161204285302546e-6	-1.0730541910957112

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	44
1	27	44
2	26	44

end99.0ms (2%)

Compiler: Compiled 115 to 85 computations (26.1% saved)

Details

analyze419.0ms (8.4%)

sample3.6s (73.3%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series6.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify78.0ms (1.6%)

prune58.0ms (1.2%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite1.0ms (0%)

simplify59.0ms (1.2%)

prune10.0ms (0.2%)

localize42.0ms (0.8%)

series12.0ms (0.2%)

rewrite63.0ms (1.3%)

simplify82.0ms (1.7%)

prune96.0ms (1.9%)

localize4.0ms (0.1%)

series6.0ms (0.1%)

rewrite11.0ms (0.2%)

simplify61.0ms (1.2%)

prune40.0ms (0.8%)

regimes113.0ms (2.3%)

bsearch45.0ms (0.9%)

simplify3.0ms (0.1%)

end99.0ms (2%)

Profiling