Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

sample61.0ms

Algorithm

intervals

Results

26.0ms	73×	body	640	valid
12.0ms	31×	body	1280	valid
9.0ms	125×	body	80	valid
3.0ms	15×	body	320	valid
2.0ms	12×	body	160	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	265	11
1	265	11

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 21.4b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
0.2b	(/.f64 1.0 (sqrt.f64 x))
2.8b	(-.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64`
70×	`add-sqr-sqrt_binary64`
69×	`times-frac_binary64`
46×	`sqrt-prod_binary64`
40×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`
11×	`distribute-lft-out--_binary64`
9×	`difference-of-squares_binary64`
7×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64`
5×	`add-log-exp_binary64`
4×	`div-inv_binary64`
3×	`pow1_binary64`
2×	`cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64`

Counts

3 → 116

Calls

3 calls:

6.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
4.0ms	(/.f64 1.0 (sqrt.f64 x))
46.0ms	(-.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

series33.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
10.0ms	(/.f64 1.0 (sqrt.f64 x))
15.0ms	(-.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

simplify33.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5020	1656

prune158.0ms

Filtered

87 candidates to 125 candidates (-43.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	113	12	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	12	126

Merged error: 20.8b

Counts

126 → 12

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b

(/.f64 (*.f64 1.0 (-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))

0.3b

(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))

2.7b

(-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`sqrt-prod_binary64`
17×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`*-un-lft-identity_binary64`
7×	`pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64`
6×	`associate-r/_binary64` `associate-l*_binary64`
5×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `div-exp_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `distribute-lft-out--_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `flip--_binary64` `flip-+_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

3 → 76

Calls

3 calls:

19.0ms

(/.f64 (*.f64 1.0 (-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))

9.0ms

(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))

9.0ms

(-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))

series62.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms

(/.f64 (*.f64 1.0 (-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))

8.0ms

(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))

12.0ms

(-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))

simplify37.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4982	1388
1	4982	1388

prune110.0ms

Filtered

61 candidates to 85 candidates (-39.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	89	8	97

Merged error: 0.3b

Counts

97 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))
0.2b	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
0.2b	(/.f64 (.f64 1.0 (/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
35×	`sqrt-prod_binary64`
32×	`distribute-lft-out_binary64`
29×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
28×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
9×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
7×	`associate-/r_binary64` `associate-r*_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
5×	`flip3-+_binary64` `associate-r/_binary64` `associate-/l_binary64` `flip-+_binary64`
4×	`associate-/r/_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `associate-/l/_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`sqrt-unprod_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 125

Calls

4 calls:

8.0ms	(+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))
14.0ms	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
25.0ms	(/.f64 (.f64 1.0 (/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))
13.0ms	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
40.0ms	(/.f64 (.f64 1.0 (/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5519	2095

prune181.0ms

Filtered

91 candidates to 137 candidates (-50.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	130	7	137
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	134	11	145

Merged error: 0.0b

Counts

145 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1.0))))
0.1b	(/.f64 (/.f64 (.f64 1.0 1.0) (+.f64 x (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1.0))))) (sqrt.f64 (+.f64 1.0 x)))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1.0)))
0.3b	(/.f64 (.f64 1.0 1.0) (+.f64 x (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1.0)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

106×	`times-frac_binary64`
72×	`*-un-lft-identity_binary64`
67×	`add-sqr-sqrt_binary64`
55×	`sqrt-prod_binary64`
48×	`add-cube-cbrt_binary64`
23×	`distribute-lft-out_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
12×	`flip3-+_binary64` `flip-+_binary64`
11×	`associate-/r_binary64` `associate-/l_binary64`
10×	`div-inv_binary64`
8×	`pow1_binary64`
7×	`associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`unswap-sqr_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
2×	`pow1/2_binary64` `associate-*r/_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sqrt-unprod_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 176

Calls

4 calls:

3.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1.0))))
13.0ms	(/.f64 (/.f64 (.f64 1.0 1.0) (+.f64 x (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1.0))))) (sqrt.f64 (+.f64 1.0 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1.0)))
7.0ms	(/.f64 (.f64 1.0 1.0) (+.f64 x (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1.0)))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1.0))))
30.0ms	(/.f64 (/.f64 (.f64 1.0 1.0) (+.f64 x (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1.0))))) (sqrt.f64 (+.f64 1.0 x)))
8.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1.0)))
16.0ms	(/.f64 (.f64 1.0 1.0) (+.f64 x (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1.0)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4960	4287
1	4960	4287

prune235.0ms

Filtered

130 candidates to 188 candidates (-44.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	190	9	199

Merged error: 0b

Counts

199 → 9

regimes45.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	18
1	13	18

end0.0ms

sample829.0ms

Algorithm

intervals

Results

274.0ms	1889×	body	640	valid
212.0ms	1140×	body	1280	valid
154.0ms	3991×	body	80	valid
70.0ms	639×	body	320	valid
24.0ms	341×	body	160	valid

Details

analyze2.0ms

sample61.0ms

simplify26.0ms

prune8.0ms

localize13.0ms

rewrite64.0ms

series33.0ms

simplify33.0ms

prune158.0ms

localize10.0ms

rewrite38.0ms

series62.0ms

simplify37.0ms

prune110.0ms

localize11.0ms

rewrite61.0ms

series71.0ms

simplify69.0ms

prune181.0ms

localize11.0ms

rewrite39.0ms

series61.0ms

simplify85.0ms

prune235.0ms

regimes45.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample829.0ms

Profiling