Details

analyze402.0ms (8.5%)

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)

sample3.4s (72.3%)

Results

1.6s	2616×	body	1024	valid
755.0ms	1210×	body	2048	valid
555.0ms	1271×	body	512	valid
342.0ms	2447×	body	128	valid
151.0ms	674×	body	256	valid
31.0ms	38×	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

44.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	44.5b	(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
✓	0.6b	(+.f64 x (hypot.f64 1 x))
✓	3.0b	(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))

rewrite7.0ms (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:

4.0ms	(+.f64 x (hypot.f64 1 x))
2.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))

simplify75.0ms (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

prune44.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	6	82

Error

0.0b

Counts

82 → 6

Alt Table

Status	Error	Program
	48.7b	(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x))))
✓	44.5b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	47.2b	(+.f64 (log.f64 2) (log.f64 x))
▶	32.1b	(fma.f64 (pow.f64 x 3) -1/6 x)
	44.5b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
	48.7b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 1221 to 926 computations (24.2% 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)

series4.0ms (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)

simplify58.0ms (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

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	16	6	22

Error

0.0b

Counts

22 → 6

Alt Table

Status	Error	Program
	48.7b	(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x))))
✓	44.5b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	47.2b	(+.f64 (log.f64 2) (log.f64 x))
✓	32.1b	(fma.f64 (pow.f64 x 3) -1/6 x)
▶	44.5b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
	48.7b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 256 to 193 computations (24.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (+.f64 x (hypot.f64 1 x)))
	0.6b	(+.f64 x (hypot.f64 1 x))
✓	2.8b	(log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))

series11.0ms (0.2%)

Counts

2 → 8

Calls

2 calls:

7.0ms	(log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))
4.0ms	(sqrt.f64 (+.f64 x (hypot.f64 1 x)))

rewrite7.0ms (0.2%)

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

simplify105.0ms (2.2%)

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

prune120.0ms (2.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	0	3	3
Picked	0	1	1
Done	1	1	2
Total	196	6	202

Error

0.0b

Counts

202 → 6

Alt Table

Status	Error	Program
	48.7b	(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x))))
▶	47.2b	(+.f64 (log.f64 2) (log.f64 x))
✓	32.1b	(fma.f64 (pow.f64 x 3) -1/6 x)
	53.9b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (-.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3)))) (log.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 (hypot.f64 1 x) (hypot.f64 1 x)) (*.f64 x (hypot.f64 1 x))))))))
✓	44.5b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
	48.7b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 4414 to 3341 computations (24.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (log.f64 2) (log.f64 x))

series41.0ms (0.9%)

Counts

1 → 12

Calls

1 calls:

41.0ms

(+.f64 (log.f64 2) (log.f64 x))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
6×	`log-prod_binary64`
6×	`pow1_binary64`
5×	`log-pow_binary64`
4×	`distribute-lft-out_binary64`

Counts

1 → 27

Calls

1 calls:

4.0ms

(+.f64 (log.f64 2) (log.f64 x))

simplify81.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

539×	`sub-neg_binary64`
476×	`fma-def_binary64`
458×	`distribute-neg-in_binary64`
398×	`fma-neg_binary64`
397×	`unsub-neg_binary64`

Counts

39 → 38

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	363
1	120	344
2	274	342
3	660	342
4	2248	342
5	3872	342
6	4273	342
7	4971	342

prune20.0ms (0.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	38	6	44

Error

0.0b

Counts

44 → 6

Alt Table

Status	Error	Program
	48.7b	(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x))))
✓	47.2b	(+.f64 (log.f64 2) (log.f64 x))
✓	32.1b	(fma.f64 (pow.f64 x 3) -1/6 x)
	53.9b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (-.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3)))) (log.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 (hypot.f64 1 x) (hypot.f64 1 x)) (*.f64 x (hypot.f64 1 x))))))))
✓	44.5b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
	48.7b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 491 to 356 computations (27.5% saved)

regimes131.0ms (2.8%)

Accuracy

Total 0.2b remaining (88.3%)

Threshold costs 0.2b (88.3%)

Counts

34 → 3

Compiler

Compiled 1332 to 1039 computations (22% saved)

bsearch36.0ms (0.8%)

Steps

Iters	Range		Point
9	1.9940700643074258e-9	0.8958851127807921	0.0009794900121172633
8	-239.09968009848868	-0.3289946045222207	-0.9508788240618709

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	58
1	39	58
2	45	58
3	47	58
4	48	58
5	46	58

end121.0ms (2.5%)

Compiler: Compiled 174 to 132 computations (24.1% saved)

Details

analyze402.0ms (8.5%)

sample3.4s (72.3%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series6.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify75.0ms (1.6%)

prune44.0ms (0.9%)

localize3.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify58.0ms (1.2%)

prune10.0ms (0.2%)

localize8.0ms (0.2%)

series11.0ms (0.2%)

rewrite7.0ms (0.2%)

simplify105.0ms (2.2%)

prune120.0ms (2.5%)

localize4.0ms (0.1%)

series41.0ms (0.9%)

rewrite5.0ms (0.1%)

simplify81.0ms (1.7%)

prune20.0ms (0.4%)

regimes131.0ms (2.8%)

bsearch36.0ms (0.8%)

simplify3.0ms (0.1%)

end121.0ms (2.5%)

Profiling