Details

analyze382.0ms (6.1%)

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)

sample3.5s (55.7%)

Results

1.6s	2519×	body	1024	valid
801.0ms	1273×	body	2048	valid
524.0ms	1318×	body	512	valid
363.0ms	2447×	body	128	valid
149.0ms	656×	body	256	valid
31.0ms	43×	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%)

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

46.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	46.9b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.0b	(+.f64 x (hypot.f64 1 x))
✓	3.3b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series7.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
3.0ms	(+.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)))

simplify84.0ms (1.3%)

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

prune52.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	3	82

Error

0.0b

Counts

82 → 3

Alt Table

Status	Error	Program
	46.5b	(log.f64 (+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7))))
▶	31.3b	(fma.f64 (pow.f64 x 3) -1/6 x)
	47.0b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))

Compiler

Compiled 1198 to 909 computations (24.1% saved)

localize3.0ms (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%)

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 (0.9%)

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

prune8.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	16	3	19

Error

0.0b

Counts

19 → 3

Alt Table

Status	Error	Program
▶	46.5b	(log.f64 (+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7))))
✓	31.3b	(fma.f64 (pow.f64 x 3) -1/6 x)
	47.0b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))

Compiler

Compiled 233 to 176 computations (24.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1/8 (pow.f64 x 3))
✓	11.9b	(log.f64 (+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7))))
✓	19.0b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
✓	23.7b	(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7)))

series18.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

7.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
4.0ms	(log.f64 (+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7))))
4.0ms	(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7)))
3.0ms	(/.f64 1/8 (pow.f64 x 3))

rewrite253.0ms (4%)

Algorithm

1×	rewrite-expression-head

Rules

903×	`*-un-lft-identity_binary64`
618×	`times-frac_binary64`
400×	`prod-diff_binary64`
381×	`add-sqr-sqrt_binary64`
355×	`add-cube-cbrt_binary64`

Counts

4 → 605

Calls

4 calls:

55.0ms	(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7)))
40.0ms	(log.f64 (+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7))))
33.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
4.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify464.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-neg_binary64`
391×	`log-prod_binary64`
267×	`associate-l_binary64`
244×	`associate-r_binary64`
183×	`fma-def_binary64`

Counts

641 → 689

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	414	19921
1	869	16376
2	3529	12868
3	4622	12868
4	4935	12868

prune868.0ms (13.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	689	0	689
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	689	3	692

Error

0.0b

Counts

692 → 3

Alt Table

Status	Error	Program
✓	46.5b	(log.f64 (+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7))))
✓	31.3b	(fma.f64 (pow.f64 x 3) -1/6 x)
▶	47.0b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))

Compiler

Compiled 36672 to 30069 computations (18% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x (hypot.f64 1 x)))
	1.0b	(+.f64 x (hypot.f64 1 x))
✓	3.3b	(log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))

series16.0ms (0.3%)

Counts

2 → 8

Calls

2 calls:

9.0ms	(log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))
7.0ms	(sqrt.f64 (+.f64 x (hypot.f64 1 x)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
8×	`sqrt-prod_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`log-prod_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 41

Calls

2 calls:

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

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-def_binary64`
491×	`sub-neg_binary64`
390×	`distribute-rgt-neg-in_binary64`
314×	`distribute-lft-neg-in_binary64`
304×	`associate-l_binary64`

Counts

49 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	757
1	173	708
2	375	700
3	935	694
4	2658	694
5	4292	694
6	4822	694
7	4935	694

prune122.0ms (1.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	195	4	199

Error

0.0b

Counts

199 → 4

Alt Table

Status	Error	Program
✓	46.5b	(log.f64 (+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7))))
	47.1b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))
✓	31.3b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	47.0b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))

Compiler

Compiled 4330 to 3277 computations (24.3% saved)

regimes155.0ms (2.5%)

Accuracy

Total 0.1b remaining (76.4%)

Threshold costs 0.1b (76.4%)

Counts

43 → 3

Compiler

Compiled 1731 to 1348 computations (22.1% saved)

bsearch41.0ms (0.6%)

Steps

Iters	Range		Point
8	0.0001530763031767488	0.03967031542385064	0.0011232502346767796
9	-157.69045295168064	-1.750927037754488e-7	-0.9682457514610505

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	77
1	42	77
2	50	77
3	64	77
4	69	77
5	71	77
6	68	77

end104.0ms (1.7%)

Compiler: Compiled 185 to 143 computations (22.7% saved)

Details

analyze382.0ms (6.1%)

sample3.5s (55.7%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize11.0ms (0.2%)

series7.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify84.0ms (1.3%)

prune52.0ms (0.8%)

localize3.0ms (0.1%)

series3.0ms (0%)

rewrite1.0ms (0%)

simplify59.0ms (0.9%)

prune8.0ms (0.1%)

localize13.0ms (0.2%)

series18.0ms (0.3%)

rewrite253.0ms (4%)

simplify464.0ms (7.4%)

prune868.0ms (13.8%)

localize6.0ms (0.1%)

series16.0ms (0.3%)

rewrite7.0ms (0.1%)

simplify91.0ms (1.5%)

prune122.0ms (1.9%)

regimes155.0ms (2.5%)

bsearch41.0ms (0.6%)

simplify4.0ms (0.1%)

end104.0ms (1.7%)

Profiling