Details

analyze411.0ms (8.3%)

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 (69.9%)

Results

1.6s	2554×	body	1024	valid
852.0ms	1338×	body	2048	valid
475.0ms	1260×	body	512	valid
298.0ms	2422×	body	128	valid
156.0ms	629×	body	256	valid
50.0ms	53×	body	4096	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify8.0ms (0.2%)

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

46.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	46.2b	(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
✓	0.8b	(+.f64 x (hypot.f64 1 x))
✓	3.0b	(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))

rewrite5.0ms (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)))

simplify77.0ms (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

prune43.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	4	82

Error

0.0b

Counts

82 → 4

Alt Table

Status	Error	Program
✓	46.2b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	32.7b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
	47.5b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
	45.9b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 1189 to 902 computations (24.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 3/40 (pow.f64 x 5) x)
✓	0.0b	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
✓	0.2b	(*.f64 5/112 (pow.f64 x 7))
✓	24.7b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))

series15.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

5.0ms	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
4.0ms	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
3.0ms	(*.f64 5/112 (pow.f64 x 7))
3.0ms	(fma.f64 3/40 (pow.f64 x 5) x)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`
9×	`prod-diff_binary64`

Counts

4 → 79

Calls

4 calls:

4.0ms	(*.f64 5/112 (pow.f64 x 7))
3.0ms	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
0.0ms	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
0.0ms	(fma.f64 3/40 (pow.f64 x 5) x)

simplify111.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-neg_binary64`
633×	`times-frac_binary64`
600×	`associate-r_binary64`
389×	`fma-def_binary64`
339×	`distribute-lft-in_binary64`

Counts

115 → 122

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	142	2229
1	264	2018
2	793	1831
3	3426	1774
4	4426	1759
5	5632	1759

prune110.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	122	4	126

Error

0.0b

Counts

126 → 4

Alt Table

Status	Error	Program
✓	46.2b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	32.7b	(fma.f64 (pow.f64 x 7) -5/112 (fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x)))
	47.5b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
	45.9b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 3515 to 2788 computations (20.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 3/40 (pow.f64 x 5) x)
✓	20.9b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
✓	24.9b	(fma.f64 (pow.f64 x 7) -5/112 (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))
4.0ms	(fma.f64 (pow.f64 x 7) -5/112 (fma.f64 (pow.f64 x 3) -1/6 (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 (pow.f64 x 7) -5/112 (fma.f64 (pow.f64 x 3) -1/6 (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))

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

645×	`fma-def_binary64`
377×	`unsub-neg_binary64`
319×	`exp-prod_binary64`
319×	`fma-neg_binary64`
267×	`cancel-sign-sub-inv_binary64`

Counts

44 → 44

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	48	857
1	99	753
2	230	745
3	1015	745
4	2663	745
5	4901	745
6	4873	745

prune39.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	57	4	61

Error

0.0b

Counts

61 → 4

Alt Table

Status	Error	Program
✓	46.2b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	32.7b	(fma.f64 (pow.f64 x 7) -5/112 (fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x)))
	47.5b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
▶	45.9b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 1207 to 934 computations (22.6% saved)

localize6.0ms (0.1%)

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))
✓	0.2b	(/.f64 1/8 (pow.f64 x 3))
✓	9.7b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

series10.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

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

rewrite54.0ms (1.1%)

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:

23.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
20.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
4.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify85.0ms (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

prune106.0ms (2.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	185	4	189

Error

0.0b

Counts

189 → 4

Alt Table

Status	Error	Program
✓	46.2b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	32.7b	(fma.f64 (pow.f64 x 7) -5/112 (fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x)))
	47.5b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
✓	45.9b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 3339 to 2652 computations (20.6% saved)

regimes117.0ms (2.4%)

Accuracy

Total 0.0b remaining (71.3%)

Threshold costs 0.0b (71.3%)

Counts

21 → 3

Compiler

Compiled 702 to 544 computations (22.5% saved)

bsearch48.0ms (1%)

Steps

Iters	Range		Point
10	2.882604217358748e-12	0.07644472838022903	0.02314138012114505
8	-6893.847911831632	-0.2958869014464166	-1.1375845794427093

Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	58
1	35	58
2	34	58

end114.0ms (2.3%)

Compiler: Compiled 126 to 96 computations (23.8% saved)

Details

analyze411.0ms (8.3%)

sample3.5s (69.9%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series7.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify77.0ms (1.6%)

prune43.0ms (0.9%)

localize11.0ms (0.2%)

series15.0ms (0.3%)

rewrite11.0ms (0.2%)

simplify111.0ms (2.2%)

prune110.0ms (2.2%)

localize9.0ms (0.2%)

series10.0ms (0.2%)

rewrite1.0ms (0%)

simplify70.0ms (1.4%)

prune39.0ms (0.8%)

localize6.0ms (0.1%)

series10.0ms (0.2%)

rewrite54.0ms (1.1%)

simplify85.0ms (1.7%)

prune106.0ms (2.1%)

regimes117.0ms (2.4%)

bsearch48.0ms (1%)

simplify2.0ms (0%)

end114.0ms (2.3%)

Profiling