Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

268×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune2.0ms

Filtered

1 candidates to 0 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: 24.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.0b	(+ (* a c) (* b d))
23.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

208×	`*-un-lft-identity`
85×	`distribute-lft-out`
76×	`associate-l`
56×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`swap-sqr`
8×	`associate-/r*`
7×	`associate-/l*` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 118

Calls

3 calls:

15.0ms	(+ (* c c) (* d d))
15.0ms	(+ (* a c) (* b d))
32.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series155.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* c c) (* d d))
34.0ms	(+ (* a c) (* b d))
88.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify183.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	272	1069
1	1142	1021
2	4389	1019
3	5001	1019

prune154.0ms

Filtered

127 candidates to 51 candidates (40.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	116	11	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	11	128

Merged error: 23.3b

Counts

128 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
14.4b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

3825×	`*-un-lft-identity`
1914×	`times-frac`
1475×	`distribute-lft-out`
1432×	`sqrt-prod`
1296×	`associate-l`
519×	`add-sqr-sqrt`
517×	`add-cube-cbrt`
358×	`swap-sqr`
97×	`associate-/l*`
33×	`associate-/r*`
32×	`sqrt-div`
28×	`associate-/r/`
27×	`associate-/l/`
18×	`flip3-+` `flip-+`
14×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 1197

Calls

4 calls:

83.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
36.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
16.0ms	(sqrt (+ (* c c) (* d d)))
15.0ms	(sqrt (+ (* c c) (* d d)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
114.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
43.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))

simplify282.0ms

Algorithm

egg-herbie

Counts

1209 → 1209

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	824	20608
1	2372	19996
2	5002	19963

prune481.0ms

Filtered

1209 candidates to 157 candidates (13.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	1201	8	1209
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	1209	11	1220

Merged error: 21.7b

Counts

1220 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
14.4b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

1291×	`*-un-lft-identity`
507×	`sqrt-prod`
478×	`distribute-lft-out`
473×	`associate-/r*`
455×	`associate-l`
391×	`frac-times`
252×	`add-sqr-sqrt`
210×	`associate-/l*`
209×	`times-frac`
204×	`add-cube-cbrt`
124×	`swap-sqr`
83×	`associate-r`
44×	`clear-num`
43×	`frac-2neg`
38×	`associate-/l/`
28×	`add-exp-log`
24×	`flip3-+` `flip-+`
23×	`associate-*r/`
18×	`add-cbrt-cube`
17×	`associate-*l/`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r/` `un-div-inv`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 746

Calls

4 calls:

119.0ms	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
33.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
16.0ms	(sqrt (+ (* c c) (* d d)))
21.0ms	(sqrt (+ (* c c) (* d d)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
113.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
37.0ms	(sqrt (+ (* c c) (* d d)))
46.0ms	(sqrt (+ (* c c) (* d d)))

simplify157.0ms

Algorithm

egg-herbie

Counts

758 → 758

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	1433	9817
1	5001	9336

prune738.0ms

Filtered

758 candidates to 175 candidates (23.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	755	3	758
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	757	12	769

Merged error: 21.7b

Counts

769 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
14.4b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

3825×	`*-un-lft-identity`
1914×	`times-frac`
1475×	`distribute-lft-out`
1432×	`sqrt-prod`
1296×	`associate-l`
519×	`add-sqr-sqrt`
517×	`add-cube-cbrt`
358×	`swap-sqr`
97×	`associate-/l*`
33×	`associate-/r*`
32×	`sqrt-div`
28×	`associate-/r/`
27×	`associate-/l/`
18×	`flip3-+` `flip-+`
14×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 1197

Calls

4 calls:

82.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
36.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
16.0ms	(sqrt (+ (* c c) (* d d)))
15.0ms	(sqrt (+ (* c c) (* d d)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
118.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
37.0ms	(sqrt (+ (* c c) (* d d)))
47.0ms	(sqrt (+ (* c c) (* d d)))

simplify285.0ms

Algorithm

egg-herbie

Counts

1209 → 1209

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	824	20608
1	2372	19996
2	5002	19963

prune573.0ms

Filtered

1209 candidates to 163 candidates (13.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	1205	4	1209
Fresh	4	6	10
Picked	0	1	1
Done	0	1	1
Total	1209	12	1221

Merged error: 21.7b

Counts

1221 → 12

regimes176.0ms

Accuracy

0% (2.7b remaining)

Error of 25.5b against oracle of 22.8b and baseline of 25.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	15
1	24	15

end0.0ms

sample524.0ms

Algorithm

intervals

Results

309.0ms

8505×

body

valid