Details

analyze416.0ms (8.7%)

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)

sample3.3s (69.1%)

Results

1.5s	2561×	body	1024	valid
790.0ms	1329×	body	2048	valid
469.0ms	1273×	body	512	valid
272.0ms	2398×	body	128	valid
151.0ms	647×	body	256	valid
37.0ms	48×	body	4096	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify92.0ms (1.9%)

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

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

45.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	52.3b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
▶	45.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 50 to 35 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))
✓	2.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series8.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(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)))

simplify80.0ms (1.7%)

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

prune48.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	77	6	83

Error

0.0b

Counts

83 → 6

Alt Table

Status	Error	Program
	60.5b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
	55.1b	(log.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3)) (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))
	47.1b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
	45.8b	(log.f64 (/.f64 -1/2 x))
✓	45.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	32.9b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))

Compiler

Compiled 1251 to 942 computations (24.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 3/40 (pow.f64 x 5) x)
✓	20.4b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))

series10.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
3.0ms	(fma.f64 3/40 (pow.f64 x 5) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 3/40 (pow.f64 x 5) x)
0.0ms	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

612×	`associate-l_binary64`
578×	`associate-r_binary64`
480×	`distribute-lft-in_binary64`
480×	`distribute-rgt-in_binary64`
291×	`fma-def_binary64`

Counts

44 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	584
1	65	520
2	153	518
3	599	518
4	3541	518
5	4941	518

prune22.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	31	6	37

Error

0.0b

Counts

37 → 6

Alt Table

Status	Error	Program
	60.5b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
	55.1b	(log.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3)) (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))
	47.1b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
▶	45.8b	(log.f64 (/.f64 -1/2 x))
✓	45.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	32.9b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))

Compiler

Compiled 590 to 443 computations (24.9% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 -1/2 x))

series28.0ms (0.6%)

Counts

1 → 12

Calls

1 calls:

28.0ms

(log.f64 (/.f64 -1/2 x))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`log-prod_binary64`
9×	`times-frac_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

1 → 26

Calls

1 calls:

2.0ms

(log.f64 (/.f64 -1/2 x))

simplify113.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

935×	`unsub-neg_binary64`
616×	`fma-def_binary64`
451×	`fma-neg_binary64`
429×	`sub-neg_binary64`
423×	`distribute-neg-out_binary64`

Counts

38 → 36

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	424
1	114	406
2	227	395
3	415	393
4	975	391
5	2148	391
6	3642	391
7	4491	391
8	4900	391
9	4996	391
10	4892	391

prune18.0ms (0.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	36	6	42

Error

0.0b

Counts

42 → 6

Alt Table

Status	Error	Program
	60.5b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
	55.1b	(log.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3)) (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))
▶	47.1b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
✓	45.8b	(log.f64 (/.f64 -1/2 x))
✓	45.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	32.9b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))

Compiler

Compiled 498 to 379 computations (23.9% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))
✓	0.4b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
	1.4b	(+.f64 x (hypot.f64 1 x))
	2.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series19.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

15.0ms	(log.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))
4.0ms	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`log-prod_binary64`
6×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 33

Calls

2 calls:

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

simplify135.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

526×	`associate-/r*_binary64`
422×	`fma-neg_binary64`
340×	`fma-def_binary64`
322×	`associate-l_binary64`
319×	`associate-r_binary64`

Counts

57 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	1368
1	426	1264
2	1317	1256
3	4484	1256
4	4966	1256
5	4992	1256

prune129.0ms (2.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	165	6	171

Error

0.0b

Counts

171 → 6

Alt Table

Status	Error	Program
	47.1b	(exp.f64 (log1p.f64 (expm1.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))
	60.5b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
	55.1b	(log.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3)) (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))
✓	45.8b	(log.f64 (/.f64 -1/2 x))
✓	45.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	32.9b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))

Compiler

Compiled 3084 to 2442 computations (20.8% saved)

regimes132.0ms (2.8%)

Accuracy

Total 0.2b remaining (74%)

Threshold costs 0.2b (74%)

Counts

22 → 3

Compiler

Compiled 843 to 631 computations (25.1% saved)

bsearch27.0ms (0.6%)

Steps

Iters	Range		Point
7	0.00046721786720771115	0.08599722859018712	0.007449937847527183
6	-4.61550595984419	-0.4014785429718377	-1.296739964094347

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	42
1	27	42
2	26	42

end106.0ms (2.2%)

Compiler: Compiled 138 to 101 computations (26.8% saved)

Details

analyze416.0ms (8.7%)

sample3.3s (69.1%)

simplify92.0ms (1.9%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series8.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify80.0ms (1.7%)

prune48.0ms (1%)

localize6.0ms (0.1%)

series10.0ms (0.2%)

rewrite1.0ms (0%)

simplify56.0ms (1.2%)

prune22.0ms (0.5%)

localize3.0ms (0.1%)

series28.0ms (0.6%)

rewrite3.0ms (0.1%)

simplify113.0ms (2.4%)

prune18.0ms (0.4%)

localize6.0ms (0.1%)

series19.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify135.0ms (2.8%)

prune129.0ms (2.7%)

regimes132.0ms (2.8%)

bsearch27.0ms (0.6%)

simplify3.0ms (0.1%)

end106.0ms (2.2%)

Profiling