Details

sample22.0ms

Algorithm

intervals

Results

9.0ms

270×

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* a c) (* b d))
25.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

7.0ms	(+ (* a c) (* b d))
30.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series106.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ (* a c) (* b d))
75.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify85.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	231	450
1	847	413
2	2851	412
3	5003	412

prune142.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 25.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
15.9b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.5b	(sqrt (+ (* c c) (* d d)))
29.5b	(sqrt (+ (* c c) (* d d)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`flip3-+` `associate-/r*` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 264

Calls

4 calls:

55.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
34.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
8.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
103.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
31.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify86.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	714	5680
1	2516	5201
2	5001	5144

prune582.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.3b

localize17.0ms

Local error

Found 4 expressions with local error:

8.2b	(/ (+ (* a c) (* b d)) (sqrt (sqrt (+ (* c c) (* d d)))))
29.5b	(sqrt (+ (* c c) (* d d)))
29.5b	(sqrt (+ (* c c) (* d d)))
29.5b	(sqrt (+ (* c c) (* d d)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`sqrt-div`
9×	`associate-/r*`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

34.0ms	(/ (+ (* a c) (* b d)) (sqrt (sqrt (+ (* c c) (* d d)))))
8.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(sqrt (+ (* c c) (* d d)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (+ (* a c) (* b d)) (sqrt (sqrt (+ (* c c) (* d d)))))
35.0ms	(sqrt (+ (* c c) (* d d)))
32.0ms	(sqrt (+ (* c c) (* d d)))
35.0ms	(sqrt (+ (* c c) (* d d)))

simplify84.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	296	1227
1	871	1172
2	2543	1144
3	5001	1144

prune393.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 23.3b

localize17.0ms

Local error

Found 4 expressions with local error:

16.5b	(cbrt (+ (* a c) (* b d)))
16.5b	(cbrt (+ (* a c) (* b d)))
29.5b	(sqrt (+ (* c c) (* d d)))
29.5b	(sqrt (+ (* c c) (* d d)))

rewrite29.0ms

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:

4.0ms	(cbrt (+ (* a c) (* b d)))
5.0ms	(cbrt (+ (* a c) (* b d)))
11.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (+ (* a c) (* b d)))
99.0ms	(cbrt (+ (* a c) (* b d)))
32.0ms	(sqrt (+ (* c c) (* d d)))
34.0ms	(sqrt (+ (* c c) (* d d)))

simplify125.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 4 (114.0ms)

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

prune267.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 23.3b

regimes227.0ms

Accuracy

25.6% (2.2b remaining)

Error of 25.4b against oracle of 23.2b and baseline of 26.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	26
1	28	26
2	28	26

end0.0ms

sample605.0ms

Algorithm

intervals

Results

297.0ms

8488×

body

valid