Details

Time bar (total: 3.3s)

sample23.0ms

Algorithm
intervals
Results
12.0ms275×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1157

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 26.9b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.2b
(+ (* a c) (* b d))
26.5b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite16.0ms

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))
3.0ms
(+ (* a c) (* b d))
8.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series143.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(+ (* c c) (* d d))
32.0ms
(+ (* a c) (* b d))
81.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify132.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune160.0ms

Filtered
62 candidates to 49 candidates (79.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New55762
Fresh000
Picked011
Done000
Total55863

Merged error: 26.1b

Counts
63 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* a c) (* b d))
17.5b
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.7b
(sqrt (+ (* c c) (* d d)))
28.7b
(sqrt (+ (* c c) (* d d)))

rewrite22.0ms

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:
4.0ms
(+ (* a c) (* b d))
9.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms
(sqrt (+ (* c c) (* d d)))
3.0ms
(sqrt (+ (* c c) (* d d)))

series208.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* a c) (* b d))
103.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
37.0ms
(sqrt (+ (* c c) (* d d)))
35.0ms
(sqrt (+ (* c c) (* d d)))

simplify82.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0273893
1868840
22693828
35001828

prune242.0ms

Filtered
96 candidates to 74 candidates (77.1%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New91596
Fresh246
Picked011
Done011
Total9311104

Merged error: 23.8b

Counts
104 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.2b
(+ (* a c) (* b d))
0.7b
(/ 1 (+ (* c c) (* d d)))
26.0b
(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
20×add-cube-cbrt times-frac
17×add-exp-log
15×associate-*r*
11×add-cbrt-cube
8×add-log-exp
7×pow1
6×flip3-+ flip-+
4×div-exp prod-exp associate-/r/
3×associate-*l* associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv +-commutative frac-times rec-exp 1-exp associate-*l/ sum-log cbrt-unprod div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
4 → 97
Calls
4 calls:
4.0ms
(+ (* c c) (* d d))
3.0ms
(+ (* a c) (* b d))
5.0ms
(/ 1 (+ (* c c) (* d d)))
14.0ms
(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

series178.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* c c) (* d d))
32.0ms
(+ (* a c) (* b d))
36.0ms
(/ 1 (+ (* c c) (* d d)))
80.0ms
(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

simplify55.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0393853
12037749
25003720

prune192.0ms

Filtered
109 candidates to 69 candidates (63.3%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1081109
Fresh178
Picked011
Done022
Total10911120

Merged error: 23.8b

Counts
120 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* a c) (* b d))
26.0b
(* (+ (* a c) (* b d)) (/ (/ 1 (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
28.7b
(sqrt (+ (* c c) (* d d)))
28.7b
(sqrt (+ (* c c) (* d d)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
270×times-frac
173×add-sqr-sqrt
150×associate-*r*
141×sqrt-prod
138×*-un-lft-identity
134×add-cube-cbrt
19×add-exp-log
18×sqrt-div
14×associate-/r/
13×add-cbrt-cube
12×flip3-+ flip-+ unswap-sqr
8×pow1 div-inv
6×div-exp add-log-exp
5×prod-exp
3×cbrt-undiv associate-*l* cbrt-unprod
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/
1×+-commutative rec-exp 1-exp associate-*r/ pow-prod-down sum-log *-commutative
Counts
4 → 228
Calls
4 calls:
3.0ms
(+ (* a c) (* b d))
47.0ms
(* (+ (* a c) (* b d)) (/ (/ 1 (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
3.0ms
(sqrt (+ (* c c) (* d d)))
3.0ms
(sqrt (+ (* c c) (* d d)))

series186.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* a c) (* b d))
79.0ms
(* (+ (* a c) (* b d)) (/ (/ 1 (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
34.0ms
(sqrt (+ (* c c) (* d d)))
40.0ms
(sqrt (+ (* c c) (* d d)))

simplify58.0ms

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09753429
150012870

prune655.0ms

Filtered
240 candidates to 128 candidates (53.3%)
Pruning

11 alts after pruning (7 fresh and 4 done)

PrunedKeptTotal
New2400240
Fresh077
Picked011
Done033
Total24011251

Merged error: 23.8b

Counts
251 → 11

regimes220.0ms

Accuracy

33.3% (2.0b remaining)

Error of 25.0b against oracle of 23.1b and baseline of 26.0b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02626
12826
22826

end0.0ms

sample547.0ms

Algorithm
intervals
Results
318.0ms8450×body80valid