Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

266×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.9b	(+ (* a c) (* b d))
26.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

3.0ms	(+ (* c c) (* d d))
2.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series146.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* c c) (* d d))
36.0ms	(+ (* a c) (* b d))
82.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify130.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	272	527
1	1164	479
2	4451	477
3	5003	477

prune173.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 26.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* a c) (* b d))
16.2b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
31.4b	(sqrt (+ (* c c) (* d d)))
31.4b	(sqrt (+ (* c c) (* d d)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

3.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series217.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* a c) (* b d))
108.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
40.0ms	(sqrt (+ (* c c) (* d d)))
35.0ms	(sqrt (+ (* c c) (* d d)))

simplify81.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	273	895
1	868	840
2	2693	828
3	5001	828

prune285.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
0.9b	(+ (* a c) (* b d))
26.3b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`+-commutative` `rec-exp` `frac-2neg` `1-exp` `clear-num` `sum-log` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

3.0ms	(+ (* c c) (* d d))
11.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
2.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* c c) (* d d))
133.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
37.0ms	(+ (* a c) (* b d))
50.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify68.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	518	1821
1	2632	1656
2	5001	1569

prune286.0ms

Filtered

149 candidates to 85 candidates (57.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 24.6b

localize16.0ms

Local error

Found 4 expressions with local error:

16.8b	(cbrt (+ (* a c) (* b d)))
16.8b	(cbrt (+ (* a c) (* b d)))
31.4b	(sqrt (+ (* c c) (* d d)))
31.4b	(sqrt (+ (* c c) (* d d)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

2.0ms	(cbrt (+ (* a c) (* b d)))
2.0ms	(cbrt (+ (* a c) (* b d)))
6.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (+ (* a c) (* b d)))
104.0ms	(cbrt (+ (* a c) (* b d)))
34.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))

simplify118.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 4 (112.0ms)

Iter	Nodes	Cost
0	255	480
1	654	456
2	1696	444
3	4112	440
4	5001	438

prune251.0ms

Filtered

68 candidates to 60 candidates (88.2%)

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 24.6b

regimes227.0ms

Accuracy

4.5% (3.0b remaining)

Error of 26.3b against oracle of 23.4b and baseline of 26.5b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	21
1	33	21
2	36	21
3	38	21
4	38	21

end0.0ms

sample489.0ms

Algorithm

intervals

Results

283.0ms

8455×

body

valid