Details

analyze512.0ms (7.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
28.1%	71.8%	0.1%	7
42.1%	57.7%	0.1%	8
43.7%	56.2%	0.1%	9
64.4%	35.5%	0.1%	10
71.6%	28.3%	0.1%	11
72.2%	27.7%	0.1%	12
81.6%	18.2%	0.2%	13
84.9%	14.9%	0.2%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample1.0s (16%)

Results

915.0ms	8256×	body	128	valid
27.0ms	250×	body	128	invalid

Compiler

Compiled 47 to 26 computations (44.7% saved)

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
505×	`times-frac_binary64`
497×	`div-sub_binary64`
469×	`neg-mul-1_binary64`
463×	`neg-sub0_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	30	18
2	83	18
3	193	18
4	334	18
5	435	18
6	600	18
7	871	18
8	1369	16
9	3594	16
10	4298	16
11	4856	16

prune4.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.7b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	17.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

Compiler

Compiled 84 to 47 computations (44% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	2.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series89.0ms (1.4%)

Counts

2 → 60

Calls

2 calls:

70.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
19.0ms	(/.f64 v (+.f64 t1 u))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

223×	`times-frac_binary64`
181×	`add-sqr-sqrt_binary64`
174×	`*-un-lft-identity_binary64`
86×	`add-cube-cbrt_binary64`
38×	`difference-of-squares_binary64`

Counts

2 → 186

Calls

2 calls:

13.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
4.0ms	(/.f64 v (+.f64 t1 u))

simplify180.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

795×	`times-frac_binary64`
383×	`fma-def_binary64`
336×	`fma-neg_binary64`
293×	`associate-/l/_binary64`
286×	`distribute-rgt-in_binary64`

Counts

246 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	7288
1	848	7129
2	2435	7053
3	4601	7053
4	5003	7053

prune169.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	214	5	219
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	214	7	221

Error

0.0b

Counts

221 → 7

Alt Table

Status	Error	Program
	9.4b	(.f64 -1 (/.f64 v (+.f64 t1 (+.f64 (/.f64 (pow.f64 u 2) t1) (.f64 2 u)))))
	17.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
▶	2.8b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 (cbrt.f64 v) (cbrt.f64 (+.f64 t1 u))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
	33.6b	(*.f64 (sqrt.f64 v) (/.f64 (/.f64 (sqrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
	3.9b	(/.f64 v (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u))))
✓	2.7b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	3.3b	(.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

Compiler

Compiled 5615 to 2112 computations (62.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))
✓	0.6b	(cbrt.f64 v)
✓	0.6b	(cbrt.f64 (+.f64 t1 u))
✓	7.4b	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))

series129.0ms (2%)

Counts

4 → 84

Calls

4 calls:

45.0ms	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))
35.0ms	(cbrt.f64 v)
26.0ms	(*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))
23.0ms	(cbrt.f64 (+.f64 t1 u))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`cbrt-prod_binary64`
33×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
16×	`cbrt-div_binary64`
15×	`add-cube-cbrt_binary64`

Counts

4 → 102

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))
4.0ms	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))
2.0ms	(cbrt.f64 (+.f64 t1 u))
1.0ms	(cbrt.f64 v)

simplify151.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

849×	`fma-def_binary64`
306×	`cancel-sign-sub-inv_binary64`
246×	`associate-r_binary64`
240×	`unswap-sqr_binary64`
191×	`fma-neg_binary64`

Counts

186 → 216

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	349	4525
1	891	4261
2	2655	3899
3	4643	3628
4	4952	3628
5	4974	3628

prune562.0ms (8.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	468	0	468
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	468	7	475

Error

0.0b

Counts

475 → 7

Alt Table

Status	Error	Program
	9.4b	(.f64 -1 (/.f64 v (+.f64 t1 (+.f64 (/.f64 (pow.f64 u 2) t1) (.f64 2 u)))))
	17.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
✓	2.8b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 (cbrt.f64 v) (cbrt.f64 (+.f64 t1 u))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
	33.6b	(*.f64 (sqrt.f64 v) (/.f64 (/.f64 (sqrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
	3.9b	(/.f64 v (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u))))
✓	2.7b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
▶	3.3b	(.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

Compiler

Compiled 27228 to 11293 computations (58.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (cbrt.f64 v) (cbrt.f64 v))
	0.6b	(cbrt.f64 v)
✓	0.6b	(/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
✓	2.2b	(.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

series227.0ms (3.5%)

Counts

3 → 84

Calls

3 calls:

99.0ms

(/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

89.0ms

(*.f64 (*.f64 (cbrt.f64 v) (cbrt.f64 v)) (/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

39.0ms

(*.f64 (cbrt.f64 v) (cbrt.f64 v))

rewrite174.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

738×	`times-frac_binary64`
590×	`add-sqr-sqrt_binary64`
546×	`*-un-lft-identity_binary64`
268×	`add-cube-cbrt_binary64`
192×	`associate-r_binary64`

Counts

3 → 493

Calls

3 calls:

45.0ms

(*.f64 (*.f64 (cbrt.f64 v) (cbrt.f64 v)) (/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

15.0ms

(/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

6.0ms

(*.f64 (cbrt.f64 v) (cbrt.f64 v))

simplify607.0ms (9.3%)

Algorithm

1×	egg-herbie

Rules

585×	`associate-/l*_binary64`
404×	`associate-*l/_binary64`
399×	`associate-/l/_binary64`
314×	`times-frac_binary64`
265×	`associate-/r*_binary64`

Counts

577 → 599

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	575	19008
1	1728	16895
2	5056	16895

prune557.0ms (8.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	653	0	653
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	653	7	660

Error

0.0b

Counts

660 → 7

Alt Table

Status	Error	Program
	9.4b	(.f64 -1 (/.f64 v (+.f64 t1 (+.f64 (/.f64 (pow.f64 u 2) t1) (.f64 2 u)))))
	17.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
✓	2.8b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 (cbrt.f64 v) (cbrt.f64 (+.f64 t1 u))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
	33.6b	(*.f64 (sqrt.f64 v) (/.f64 (/.f64 (sqrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
▶	3.9b	(/.f64 v (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u))))
✓	2.7b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
✓	3.3b	(.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

Compiler

Compiled 21358 to 6987 computations (67.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 t1 u))
✓	0.2b	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u)))
✓	3.8b	(/.f64 v (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u))))

series90.0ms (1.4%)

Counts

3 → 84

Calls

3 calls:

73.0ms	(/.f64 v (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u))))
9.0ms	(/.f64 1 (+.f64 t1 u))
8.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u)))

rewrite191.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

1354×	`times-frac_binary64`
924×	`add-sqr-sqrt_binary64`
845×	`*-un-lft-identity_binary64`
469×	`add-cube-cbrt_binary64`
182×	`difference-of-squares_binary64`

Counts

3 → 669

Calls

3 calls:

26.0ms	(/.f64 v (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u))))
16.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u)))
4.0ms	(/.f64 1 (+.f64 t1 u))

simplify523.0ms (8%)

Algorithm

1×	egg-herbie

Rules

498×	`associate-/r/_binary64`
468×	`fma-def_binary64`
387×	`associate-*l/_binary64`
376×	`associate-/l/_binary64`
342×	`*-commutative_binary64`

Counts

753 → 739

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	541	23987
1	1314	23137
2	4556	23097
3	5004	23097

prune556.0ms (8.5%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	738	1	739
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	739	7	746

Error

0.0b

Counts

746 → 7

Alt Table

Status	Error	Program
✓	3.9b	(/.f64 v (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u))))
	9.4b	(/.f64 v (neg.f64 (+.f64 t1 (+.f64 (/.f64 (pow.f64 u 2) t1) (*.f64 2 u)))))
✓	2.8b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 (cbrt.f64 v) (cbrt.f64 (+.f64 t1 u))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
	33.6b	(*.f64 (sqrt.f64 v) (/.f64 (/.f64 (sqrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
✓	2.7b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	17.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
✓	3.3b	(.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

Compiler

Compiled 22261 to 10457 computations (53% saved)

regimes478.0ms (7.3%)

Accuracy

Total 1.0b remaining (86.2%)

Threshold costs 0b (0%)

Counts

121 → 1

Compiler

Compiled 11670 to 7286 computations (37.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	13	16
2	19	16
3	23	16
4	26	16
5	27	16
6	27	16

end91.0ms (1.4%)

Compiler: Compiled 176 to 105 computations (40.3% saved)

Details

analyze512.0ms (7.9%)

sample1.0s (16%)

simplify71.0ms (1.1%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series89.0ms (1.4%)

rewrite44.0ms (0.7%)

simplify180.0ms (2.8%)

prune169.0ms (2.6%)

localize17.0ms (0.3%)

series129.0ms (2%)

rewrite23.0ms (0.4%)

simplify151.0ms (2.3%)

prune562.0ms (8.6%)

localize10.0ms (0.2%)

series227.0ms (3.5%)

rewrite174.0ms (2.7%)

simplify607.0ms (9.3%)

prune557.0ms (8.5%)

localize9.0ms (0.1%)

series90.0ms (1.4%)

rewrite191.0ms (2.9%)

simplify523.0ms (8%)

prune556.0ms (8.5%)

regimes478.0ms (7.3%)

simplify2.0ms (0%)

end91.0ms (1.4%)

Profiling