Details

analyze397.0ms (6.2%)

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)

sample3.2s (50%)

Results

1.5s	2626×	body	1024	valid
699.0ms	1214×	body	2048	valid
480.0ms	1300×	body	512	valid
273.0ms	2430×	body	128	valid
152.0ms	643×	body	256	valid
32.0ms	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

41.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	41.4b	(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
✓	1.2b	(+.f64 x (hypot.f64 1 x))
✓	1.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series10.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(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)))

simplify188.0ms (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

prune51.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	5	82

Error

0.0b

Counts

82 → 5

Alt Table

Status	Error	Program
	49.8b	(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))))
▶	33.5b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	41.4b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	60.1b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
	41.6b	(cbrt.f64 (.f64 (.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (+.f64 x (hypot.f64 1 x)))))

Compiler

Compiled 1255 to 948 computations (24.5% 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)

series5.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(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)

simplify57.0ms (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

prune11.0ms (0.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	16	5	21

Error

0.0b

Counts

21 → 5

Alt Table

Status	Error	Program
	49.8b	(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))))
✓	33.5b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	41.4b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	60.1b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
▶	41.6b	(cbrt.f64 (.f64 (.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (+.f64 x (hypot.f64 1 x)))))

Compiler

Compiled 290 to 215 computations (25.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x))))
✓	0.2b	(cbrt.f64 (.f64 (.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (+.f64 x (hypot.f64 1 x)))))
	1.2b	(+.f64 x (hypot.f64 1 x))
	1.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series12.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

8.0ms

(*.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x))))

4.0ms

(cbrt.f64 (*.f64 (*.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (+.f64 x (hypot.f64 1 x)))))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`pow1_binary64`
14×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`log-prod_binary64`
8×	`add-cube-cbrt_binary64`

Counts

2 → 52

Calls

2 calls:

6.0ms

(*.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x))))

3.0ms

(cbrt.f64 (*.f64 (*.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (+.f64 x (hypot.f64 1 x)))))

simplify100.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

728×	`fma-def_binary64`
378×	`cancel-sign-sub-inv_binary64`
355×	`fma-neg_binary64`
289×	`associate-l_binary64`
269×	`times-frac_binary64`

Counts

76 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	203	2358
1	558	1905
2	1831	1654
3	4647	1640
4	4982	1640
5	4935	1640

prune323.0ms (5.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	350	1	351
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	351	5	356

Error

0.0b

Counts

356 → 5

Alt Table

Status	Error	Program
▶	49.8b	(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))))
✓	33.5b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	41.4b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	60.1b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
	60.4b	(cbrt.f64 (.f64 (.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x)))))))

Compiler

Compiled 10260 to 7687 computations (25.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1/8 (pow.f64 x 3))
✓	15.5b	(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))))
✓	19.4b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
✓	22.0b	(+.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)))

series17.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

6.0ms	(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)))
4.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
3.0ms	(/.f64 1/8 (pow.f64 x 3))

rewrite274.0ms (4.3%)

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)))
49.0ms	(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))

simplify461.0ms (7.2%)

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

prune912.0ms (14.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	689	0	689
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	689	5	694

Error

0.0b

Counts

694 → 5

Alt Table

Status	Error	Program
✓	49.8b	(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))))
✓	33.5b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	41.4b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	60.1b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
	60.4b	(cbrt.f64 (.f64 (.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x)))))))

Compiler

Compiled 36690 to 30081 computations (18% saved)

regimes148.0ms (2.3%)

Accuracy

Total 0.1b remaining (68.8%)

Threshold costs 0.1b (68.8%)

Counts

34 → 3

Compiler

Compiled 1635 to 1306 computations (20.1% saved)

bsearch39.0ms (0.6%)

Steps

Iters	Range		Point
10	1.9245033666535066e-12	15.368854129090709	0.0010205228116615234
8	-50.56721751997784	-0.10126646975189933	-0.9813746759942605

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (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	33	62
1	40	62
2	48	62
3	62	62
4	67	62
5	69	62
6	66	62

end116.0ms (1.8%)

Compiler: Compiled 166 to 126 computations (24.1% saved)

Details

analyze397.0ms (6.2%)

sample3.2s (50%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize4.0ms (0.1%)

series10.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify188.0ms (3%)

prune51.0ms (0.8%)

localize3.0ms (0.1%)

series5.0ms (0.1%)

rewrite1.0ms (0%)

simplify57.0ms (0.9%)

prune11.0ms (0.2%)

localize8.0ms (0.1%)

series12.0ms (0.2%)

rewrite12.0ms (0.2%)

simplify100.0ms (1.6%)

prune323.0ms (5.1%)

localize15.0ms (0.2%)

series17.0ms (0.3%)

rewrite274.0ms (4.3%)

simplify461.0ms (7.2%)

prune912.0ms (14.3%)

regimes148.0ms (2.3%)

bsearch39.0ms (0.6%)

simplify5.0ms (0.1%)

end116.0ms (1.8%)

Profiling