Details

analyze347.0ms (7.8%)

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)

sample94.0ms (2.1%)

Algorithm

1×

intervals

Results

38.0ms	88×	body	1024	valid
19.0ms	36×	body	2048	valid
9.0ms	36×	body	512	valid
4.0ms	74×	body	128	valid
3.0ms	20×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 22 to 16 computations (27.3% 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

prune7.0ms (0.2%)

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
✓	0.2b	(+.f64 x (hypot.f64 1 x))
✓	4.8b	(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)))

simplify83.0ms (1.9%)

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

prune49.0ms (1.1%)

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)))
	46.3b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3))
	48.5b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
▶	28.3b	(-.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))))

Compiler

Compiled 1191 to 904 computations (24.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 5/112 (pow.f64 x 7))
✓	0.1b	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
✓	0.2b	(fma.f64 3/40 (pow.f64 x 5) x)
✓	20.4b	(-.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))))

series18.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

6.0ms	(-.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))))
5.0ms	(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 (0.3%)

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)

simplify113.0ms (2.5%)

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

prune112.0ms (2.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	121	5	126

Error

0.0b

Counts

126 → 5

Alt Table

Status	Error	Program
✓	46.2b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	46.3b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3))
	48.5b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
▶	44.5b	(/.f64 (-.f64 (.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 3/40 (pow.f64 x 5) x)) (.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))))) (+.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)))))
✓	28.3b	(-.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))))

Compiler

Compiled 3609 to 2862 computations (20.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
	0.2b	(fma.f64 3/40 (pow.f64 x 5) x)
✓	26.1b	(-.f64 (.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 3/40 (pow.f64 x 5) x)) (.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7)))))
✓	40.0b	(/.f64 (-.f64 (.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 3/40 (pow.f64 x 5) x)) (.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))))) (+.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)))))

series24.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

12.0ms

(*.f64 (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))

6.0ms

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

5.0ms

(/.f64 (-.f64 (*.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 3/40 (pow.f64 x 5) x)) (*.f64 (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))) (+.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)))))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`
16×	`times-frac_binary64`
10×	`pow1_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

(/.f64 (-.f64 (*.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 3/40 (pow.f64 x 5) x)) (*.f64 (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))) (+.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 (*.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 3/40 (pow.f64 x 5) x)) (*.f64 (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))))

3.0ms

(*.f64 (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))

simplify153.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

985×	`fma-neg_binary64`
710×	`fma-def_binary64`
273×	`associate-/l*_binary64`
239×	`cancel-sign-sub-inv_binary64`
162×	`associate-*l/_binary64`

Counts

129 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	7431
1	461	6739
2	1662	5103
3	4327	5103
4	5136	5103

prune377.0ms (8.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	222	5	227

Error

0.0b

Counts

227 → 5

Alt Table

Status	Error	Program
✓	46.2b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	46.3b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3))
	48.5b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
✓	44.5b	(/.f64 (-.f64 (.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 3/40 (pow.f64 x 5) x)) (.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))))) (+.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)))))
✓	28.3b	(-.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))))

Compiler

Compiled 13909 to 10881 computations (21.8% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(+.f64 x (hypot.f64 1 x))
✓	0.2b	(pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3)
✓	0.2b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3))
	4.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series23.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

19.0ms	(pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3)
4.0ms	(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`cbrt-prod_binary64`
8×	`cube-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`unpow-prod-down_binary64`

Counts

2 → 52

Calls

2 calls:

2.0ms	(pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3)
2.0ms	(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3))

simplify81.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

816×	`times-frac_binary64`
313×	`fma-def_binary64`
247×	`sub-neg_binary64`
238×	`associate-+r+_binary64`
217×	`unswap-sqr_binary64`

Counts

76 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	262	2306
1	804	2191
2	2930	2169
3	4925	2169

prune118.0ms (2.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	1	1
Picked	1	0	1
Done	0	3	3
Total	178	5	183

Error

0.0b

Counts

183 → 5

Alt Table

Status	Error	Program
✓	46.2b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	47.8b	(cbrt.f64 (pow.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 3)) (sqrt.f64 3)))
	48.5b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
✓	44.5b	(/.f64 (-.f64 (.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 3/40 (pow.f64 x 5) x)) (.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))))) (+.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)))))
✓	28.3b	(-.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))))

Compiler

Compiled 4305 to 3447 computations (19.9% saved)

regimes273.0ms (6.1%)

Accuracy

Total 0.1b remaining (63.9%)

Threshold costs 0.1b (63.9%)

Counts

62 → 3

Compiler

Compiled 4302 to 3376 computations (21.5% saved)

bsearch31.0ms (0.7%)

Steps

Iters	Range		Point
6	0.004492472159323548	0.025802969660267096	0.024276286807807215
8	-1.1517380062423406	-0.0004777114536734605	-1.1298727095782863

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
8×	`*-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	64
1	45	64
2	53	64
3	75	64
4	84	64
5	90	64
6	92	64
7	89	64

end1.0ms (0%)

Compiler: Compiled 44 to 34 computations (22.7% saved)

sample2.4s (55%)

Algorithm

1×

intervals

Results

1.1s	2566×	body	1024	valid
442.0ms	1174×	body	2048	valid
300.0ms	1253×	body	512	valid
144.0ms	2296×	body	128	valid
113.0ms	665×	body	256	valid
26.0ms	46×	body	4096	valid

Compiler

Compiled 160 to 125 computations (21.9% saved)

Details

analyze347.0ms (7.8%)

sample94.0ms (2.1%)

simplify6.0ms (0.1%)

prune7.0ms (0.2%)

localize4.0ms (0.1%)

series7.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify83.0ms (1.9%)

prune49.0ms (1.1%)

localize10.0ms (0.2%)

series18.0ms (0.4%)

rewrite11.0ms (0.3%)

simplify113.0ms (2.5%)

prune112.0ms (2.5%)

localize14.0ms (0.3%)

series24.0ms (0.5%)

rewrite24.0ms (0.5%)

simplify153.0ms (3.4%)

prune377.0ms (8.5%)

localize6.0ms (0.1%)

series23.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify81.0ms (1.8%)

prune118.0ms (2.7%)

regimes273.0ms (6.1%)

bsearch31.0ms (0.7%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample2.4s (55%)

Profiling