Details

analyze51.0ms

Algorithm

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

sample18.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
0.0ms	3×	body	80	invalid
0.0ms	1×	body	80	nan

simplify122.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	1582	12
1	1582	12

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.3b

Counts

2 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.3b	(*.f64 3 (sqrt.f64 x))
0.4b	(/.f64 1 (*.f64 x 9))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log_binary64`
21×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
15×	`associate-r_binary64`
14×	`pow1_binary64`
10×	`add-cube-cbrt_binary64`
7×	`prod-exp_binary64`
6×	`add-log-exp_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
4×	`distribute-lft-out_binary64` `associate-l_binary64` `div-exp_binary64` `sqrt-prod_binary64`
3×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `div-inv_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `pow-flip_binary64` `associate--l+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r*_binary64` `flip3--_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 93

Calls

4 calls:

6.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
16.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
5.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(/.f64 1 (*.f64 x 9))

series25.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
13.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
5.0ms	(*.f64 3 (sqrt.f64 x))
2.0ms	(/.f64 1 (*.f64 x 9))

simplify60.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4973	853
1	4973	853

prune95.0ms

Filtered

66 candidates to 105 candidates (-59.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	94	11	105
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	96	11	107

Merged error: 0.0b

Counts

107 → 11

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/9 x) y)
0.2b	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
0.4b	(/.f64 1/9 x)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
9×	`associate-l_binary64` `times-frac_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-*r/_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `flip-+_binary64`
2×	`unswap-sqr_binary64` `*-commutative_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 91

Calls

4 calls:

7.0ms	(+.f64 (/.f64 1/9 x) y)
13.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
14.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
4.0ms	(/.f64 1/9 x)

series32.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 (/.f64 1/9 x) y)
10.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
13.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
2.0ms	(/.f64 1/9 x)

simplify55.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4869	1015
1	4869	1015

prune77.0ms

Filtered

68 candidates to 103 candidates (-51.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	102	12	114

Merged error: 0.0b

Counts

114 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 3 (sqrt.f64 x))
0.3b	(*.f64 3 (sqrt.f64 x))
0.4b	(/.f64 1 (*.f64 x 9))
0.5b	(.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (*.f64 3 (sqrt.f64 x))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

60×	`pow1_binary64`
28×	`sqrt-pow1_binary64`
26×	`add-sqr-sqrt_binary64`
23×	`pow-prod-down_binary64`
21×	`add-exp-log_binary64`
16×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
15×	`add-cbrt-cube_binary64`
12×	`sqrt-prod_binary64`
10×	`pow1/2_binary64` `pow-prod-up_binary64` `associate-l_binary64`
6×	`prod-exp_binary64` `pow-sqr_binary64`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `cbrt-unprod_binary64` `div-exp_binary64`
3×	`associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `pow-flip_binary64`
1×	`associate-/r*_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow2_binary64`

Counts

4 → 121

Calls

4 calls:

5.0ms	(*.f64 3 (sqrt.f64 x))
6.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(/.f64 1 (*.f64 x 9))
11.0ms	(.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (*.f64 3 (sqrt.f64 x))))

series20.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(*.f64 3 (sqrt.f64 x))
2.0ms	(/.f64 1 (*.f64 x 9))
8.0ms	(.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (*.f64 3 (sqrt.f64 x))))

simplify50.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4947	717
1	4947	717

prune78.0ms

Filtered

72 candidates to 133 candidates (-84.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	135	10	145

Merged error: 0b

Counts

145 → 10

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
0.2b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.3b	(sqrt.f64 (*.f64 x 9))
0.4b	(/.f64 1 (*.f64 x 9))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
17×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`
11×	`add-cbrt-cube_binary64`
9×	`associate-r_binary64`
8×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
4×	`distribute-lft-out_binary64` `associate-l_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `div-inv_binary64`
2×	`sub-neg_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `pow-flip_binary64` `sqrt-prod_binary64` `associate--l+_binary64`
1×	`flip3-+_binary64` `associate-/r_binary64` `pow1/2_binary64` `flip3--_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

6.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
15.0ms	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
2.0ms	(sqrt.f64 (*.f64 x 9))
5.0ms	(/.f64 1 (*.f64 x 9))

series24.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
13.0ms	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
4.0ms	(sqrt.f64 (*.f64 x 9))
2.0ms	(/.f64 1 (*.f64 x 9))

simplify53.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4941	793
1	4941	793

prune52.0ms

Filtered

65 candidates to 95 candidates (-46.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	96	9	105

Merged error: 0b

Counts

105 → 9

regimes77.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	12
1	15	12

end0.0ms

sample483.0ms

Algorithm

intervals

Results

339.0ms	8000×	body	80	valid
6.0ms	146×	body	80	nan
3.0ms	68×	body	80	invalid

Details

analyze51.0ms

sample18.0ms

simplify122.0ms

prune10.0ms

localize9.0ms

rewrite35.0ms

series25.0ms

simplify60.0ms

prune95.0ms

localize8.0ms

rewrite40.0ms

series32.0ms

simplify55.0ms

prune77.0ms

localize14.0ms

rewrite31.0ms

series20.0ms

simplify50.0ms

prune78.0ms

localize8.0ms

rewrite32.0ms

series24.0ms

simplify53.0ms

prune52.0ms

regimes77.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample483.0ms

Profiling