Details

Time bar (total: 9.0s)

sample83.0ms

Algorithm
intervals
Results
29.0ms82×body1280valid
17.0ms76×body640valid
12.0ms235×body80valid
5.0ms34×body320valid
2.0ms23×body160valid

simplify17.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.4b

Counts
2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b
(/ (cos th) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
160×add-sqr-sqrt
92×times-frac
76×add-cube-cbrt *-un-lft-identity
58×sqrt-prod
50×associate-*l*
38×unswap-sqr
36×associate-*r*
32×add-exp-log add-cbrt-cube
24×associate-*l/ associate-/r*
14×pow1
12×swap-sqr prod-exp cbrt-unprod associate-/l*
10×*-commutative
6×cbrt-undiv div-exp pow-prod-down
4×frac-2neg clear-num div-inv add-log-exp
Counts
4 → 242
Calls
4 calls:
24.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
19.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms
(/ (cos th) (sqrt 2.0))
5.0ms
(/ (cos th) (sqrt 2.0))

series367.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
121.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
61.0ms
(/ (cos th) (sqrt 2.0))
68.0ms
(/ (cos th) (sqrt 2.0))

simplify106.0ms

Algorithm
egg-herbie
Counts
254 → 254
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
07481822
141551670
250011662

prune798.0ms

Filtered
254 candidates to 150 candidates (59.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2459254
Fresh101
Picked101
Done000
Total2479256

Merged error: 0b

Counts
256 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
632×sqrt-prod
622×times-frac
394×add-sqr-sqrt
352×add-cube-cbrt *-un-lft-identity
43×associate-/l*
39×associate-/r*
25×add-exp-log associate-*l* add-cbrt-cube
19×unswap-sqr
18×associate-*r*
15×associate-/l/
14×div-inv
12×associate-*l/
9×pow1
7×cbrt-undiv div-exp
6×swap-sqr prod-exp cbrt-unprod
5×frac-2neg clear-num *-commutative
4×add-log-exp
3×pow-prod-down
Counts
4 → 520
Calls
4 calls:
18.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
19.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt 2.0))

series350.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
60.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
106.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
66.0ms
(/ (cos th) (sqrt 2.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
532 → 532
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012476946
150016171

prune968.0ms

Filtered
532 candidates to 216 candidates (40.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New5293532
Fresh448
Picked101
Done000
Total5347541

Merged error: 0b

Counts
541 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* (cos th) (fabs a1)) (sqrt 2.0))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
20.0b
(sqrt (* a1 a1))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
657×sqrt-prod
648×times-frac
389×add-sqr-sqrt
368×add-cube-cbrt *-un-lft-identity
49×associate-/l*
33×associate-/r*
24×associate-*r* associate-*l*
16×add-exp-log add-cbrt-cube
15×associate-/l/
13×div-inv
12×pow1
9×*-commutative unswap-sqr
6×cbrt-undiv sqrt-pow1 div-exp
5×rem-sqrt-square
4×frac-2neg swap-sqr clear-num add-log-exp
1×pow2 pow-plus pow1/2 pow-prod-down prod-exp pow-sqr pow-prod-up cbrt-unprod
Counts
4 → 537
Calls
4 calls:
9.0ms
(/ (* (cos th) (fabs a1)) (sqrt 2.0))
23.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms
(sqrt (* a1 a1))

series247.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ (* (cos th) (fabs a1)) (sqrt 2.0))
59.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
106.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
8.0ms
(sqrt (* a1 a1))

simplify141.0ms

Algorithm
egg-herbie
Counts
549 → 549
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
012446893
144516432
250026418

prune1.2s

Filtered
549 candidates to 228 candidates (41.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New5481549
Fresh156
Picked011
Done000
Total5497556

Merged error: 0b

Counts
556 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (cos th) (fabs a1)) (sqrt (sqrt 2.0)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
20.0b
(sqrt (* a1 a1))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
735×sqrt-prod
684×times-frac
417×add-sqr-sqrt
390×add-cube-cbrt *-un-lft-identity
49×associate-/l*
36×associate-/r*
33×associate-*r* associate-*l*
16×add-exp-log add-cbrt-cube
15×associate-/l/
13×div-inv
12×pow1 *-commutative unswap-sqr
6×cbrt-undiv sqrt-pow1 div-exp
5×rem-sqrt-square
4×frac-2neg swap-sqr clear-num add-log-exp
1×pow2 pow-plus pow1/2 pow-prod-down prod-exp pow-sqr pow-prod-up cbrt-unprod
Counts
4 → 576
Calls
4 calls:
11.0ms
(/ (* (cos th) (fabs a1)) (sqrt (sqrt 2.0)))
23.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
4.0ms
(sqrt (* a1 a1))

series306.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ (* (cos th) (fabs a1)) (sqrt (sqrt 2.0)))
60.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
107.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
8.0ms
(sqrt (* a1 a1))

simplify145.0ms

Algorithm
egg-herbie
Counts
588 → 588
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
012707554
143957098
250017084

prune1.3s

Filtered
588 candidates to 238 candidates (40.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New5871588
Fresh145
Picked101
Done011
Total5896595

Merged error: 0b

Counts
595 → 6

regimes225.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02527
12527

end0.0ms

sample2.3s

Algorithm
intervals
Results
807.0ms2428×body1280valid
480.0ms2116×body640valid
419.0ms8197×body80valid
167.0ms1021×body320valid
57.0ms528×body160valid