Details

analyze464.0ms (5.3%)

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)

sample4.7s (53.6%)

Results

2.2s	2603×	body	1024	valid
1.1s	1288×	body	2048	valid
666.0ms	1310×	body	512	valid
374.0ms	2381×	body	128	valid
196.0ms	632×	body	256	valid
119.0ms	42×	body	4096	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify24.0ms (0.3%)

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

prune9.0ms (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

45.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	45.6b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.8b	(+.f64 x (hypot.f64 1 x))
✓	3.1b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series13.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
3.0ms	(+.f64 x (hypot.f64 1 x))
3.0ms	(hypot.f64 1 x)

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-exp-log_binary64`

Counts

3 → 44

Calls

3 calls:

9.0ms	(+.f64 x (hypot.f64 1 x))
4.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
1.0ms	(hypot.f64 1 x)

simplify136.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
469×	`cancel-sign-sub-inv_binary64`
426×	`associate-/r*_binary64`
376×	`fma-def_binary64`
361×	`sub-neg_binary64`

Counts

80 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	1089
1	394	1025
2	959	1013
3	2675	1013
4	4999	1013
5	5338	1013

prune122.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	3	114

Error

0.0b

Counts

114 → 3

Alt Table

Status	Error	Program
	51.9b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
▶	26.9b	(-.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))))
✓	45.6b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 1585 to 1194 computations (24.7% saved)

localize18.0ms (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	(*.f64 5/112 (pow.f64 x 7))
✓	0.1b	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
✓	19.1b	(-.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))))

series35.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

12.0ms	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
8.0ms	(*.f64 5/112 (pow.f64 x 7))
8.0ms	(-.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))))
7.0ms	(fma.f64 3/40 (pow.f64 x 5) x)

rewrite45.0ms (0.5%)

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:

19.0ms	(*.f64 5/112 (pow.f64 x 7))
7.0ms	(-.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))))
1.0ms	(fma.f64 3/40 (pow.f64 x 5) x)
1.0ms	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))

simplify193.0ms (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

prune265.0ms (3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	121	4	125

Error

Counts

125 → 4

Alt Table

Status	Error	Program
	51.9b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
✓	26.9b	(-.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))))
✓	45.6b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	44.7b	(/.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)))))

Compiler

Compiled 3589 to 2846 computations (20.7% saved)

localize30.0ms (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))))
	0.1b	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
✓	23.0b	(-.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)))))
✓	39.4b	(/.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)))))

series33.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

16.0ms

(-.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)))))

11.0ms

(*.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 (*.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)))))

rewrite54.0ms (0.6%)

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:

19.0ms

(*.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))))

11.0ms

(/.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)))))

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)))))

simplify327.0ms (3.7%)

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

prune915.0ms (10.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	231	4	235

Error

Counts

235 → 4

Alt Table

Status	Error	Program
▶	51.9b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
✓	26.9b	(-.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))))
✓	45.6b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	44.7b	(/.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)))))

Compiler

Compiled 14447 to 11312 computations (21.7% saved)

localize19.0ms (0.2%)

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))
✓	0.1b	(/.f64 1/8 (pow.f64 x 3))
✓	12.8b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

series26.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

11.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
8.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

rewrite140.0ms (1.6%)

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:

71.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
47.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
10.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify117.0ms (1.3%)

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

prune206.0ms (2.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	185	4	189

Error

Counts

189 → 4

Alt Table

Status	Error	Program
✓	51.9b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
✓	26.9b	(-.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))))
✓	45.6b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	44.7b	(/.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)))))

Compiler

Compiled 3385 to 2688 computations (20.6% saved)

regimes489.0ms (5.6%)

Accuracy

Total 0.1b remaining (70.5%)

Threshold costs 0.1b (70.5%)

Counts

48 → 3

Compiler

Compiled 4347 to 3367 computations (22.5% saved)

bsearch80.0ms (0.9%)

Steps

Iters	Range		Point
9	8.107219468450077e-6	90.26735218946727	0.022501888022473358
9	-13678.82421558709	-0.0035650359605743677	-1.1236408870514942

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	110
1	45	110
2	49	110
3	51	110
4	52	110
5	51	110

end276.0ms (3.1%)

Compiler: Compiled 244 to 188 computations (23% saved)

Details

analyze464.0ms (5.3%)

sample4.7s (53.6%)

simplify24.0ms (0.3%)

prune9.0ms (0.1%)

localize7.0ms (0.1%)

series13.0ms (0.2%)

rewrite17.0ms (0.2%)

simplify136.0ms (1.6%)

prune122.0ms (1.4%)

localize18.0ms (0.2%)

series35.0ms (0.4%)

rewrite45.0ms (0.5%)

simplify193.0ms (2.2%)

prune265.0ms (3%)

localize30.0ms (0.3%)

series33.0ms (0.4%)

rewrite54.0ms (0.6%)

simplify327.0ms (3.7%)

prune915.0ms (10.4%)

localize19.0ms (0.2%)

series26.0ms (0.3%)

rewrite140.0ms (1.6%)

simplify117.0ms (1.3%)

prune206.0ms (2.3%)

regimes489.0ms (5.6%)

bsearch80.0ms (0.9%)

simplify9.0ms (0.1%)

end276.0ms (3.1%)

Profiling