Details

Time bar (total: 24.9s)

sample48.0ms

Algorithm
intervals
Results
23.0ms262×body80valid

simplify147.0ms

Counts
1 → 1
Iterations
IterNodes
done70
570
466
348
236
119
011

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

localize38.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* b c) (* a d))
25.9b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite69.0ms

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×associate-/r* associate-/l*
2×pow1 flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-sub div-exp clear-num flip-+ div-inv
Counts
2 → 44
Calls
2 calls:
16.0ms
(- (* b c) (* a d))
51.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series265.0ms

Counts
2 → 6
Calls
2 calls:
85.0ms
(- (* b c) (* a d))
180.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify4.2s

Counts
50 → 50
Iterations
IterNodes
done5002
32959
2909
1258
088

prune570.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 25.7b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
16.4b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.8b
(sqrt (+ (* c c) (* d d)))
28.8b
(sqrt (+ (* c c) (* d d)))

rewrite235.0ms

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×associate-/r*
11×add-exp-log flip3-+ add-cbrt-cube flip-+
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×div-sub associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×flip3-- flip--
Counts
4 → 266
Calls
4 calls:
104.0ms
(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
60.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
16.0ms
(sqrt (+ (* c c) (* d d)))
22.0ms
(sqrt (+ (* c c) (* d d)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
231.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
68.0ms
(sqrt (+ (* c c) (* d d)))
69.0ms
(sqrt (+ (* c c) (* d d)))

simplify3.5s

Counts
278 → 278
Iterations
IterNodes
done5003
22090
1741
0307

prune2.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.4b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
16.5b
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
28.8b
(sqrt (+ (* c c) (* d d)))
28.8b
(sqrt (+ (* c c) (* d d)))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
100×add-sqr-sqrt
98×add-cube-cbrt *-un-lft-identity
54×sqrt-prod
27×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube
9×associate-/l*
8×div-exp
7×pow1
6×sqrt-div div-inv
5×flip3-- flip--
4×cbrt-undiv add-log-exp
3×flip3-+ flip-+
2×rem-sqrt-square rec-exp frac-2neg sqrt-pow1 pow1/2 1-exp clear-num associate-/l/
1×pow-flip inv-pow
Counts
4 → 193
Calls
4 calls:
48.0ms
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
57.0ms
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
13.0ms
(sqrt (+ (* c c) (* d d)))
15.0ms
(sqrt (+ (* c c) (* d d)))

series524.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
175.0ms
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
74.0ms
(sqrt (+ (* c c) (* d d)))
79.0ms
(sqrt (+ (* c c) (* d d)))

simplify3.1s

Counts
205 → 205
Iterations
IterNodes
done5001
21779
1633
0243

prune2.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.4b

localize45.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ (* b c) (+ (* c c) (* d d))) (/ (* a d) (+ (* c c) (* d d))))
15.6b
(/ (* a d) (+ (* c c) (* d d)))
16.6b
(/ (* b c) (+ (* c c) (* d d)))

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log add-cbrt-cube
9×add-sqr-sqrt *-un-lft-identity
8×associate-/r/
7×add-cube-cbrt
6×times-frac associate-/r*
5×add-log-exp
4×cbrt-undiv flip3-+ div-exp flip-+ div-inv
3×pow1 distribute-rgt-out--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l*
1×sub-neg flip3-- diff-log frac-sub flip-- distribute-lft-out-- sub-div difference-of-squares
Counts
3 → 65
Calls
3 calls:
154.0ms
(- (/ (* b c) (+ (* c c) (* d d))) (/ (* a d) (+ (* c c) (* d d))))
32.0ms
(/ (* a d) (+ (* c c) (* d d)))
34.0ms
(/ (* b c) (+ (* c c) (* d d)))

series451.0ms

Counts
3 → 9
Calls
3 calls:
251.0ms
(- (/ (* b c) (+ (* c c) (* d d))) (/ (* a d) (+ (* c c) (* d d))))
109.0ms
(/ (* a d) (+ (* c c) (* d d)))
92.0ms
(/ (* b c) (+ (* c c) (* d d)))

simplify2.5s

Counts
74 → 74
Iterations
IterNodes
done5005
21395
1359
0124

prune648.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.2b

regimes586.0ms

Accuracy

15.5% (2.1b remaining)

Error of 24.1b against oracle of 21.9b and baseline of 24.4b

bsearch139.0ms

Steps
ItersRangePoint
9
-5.107348835255916e-212
-2.866310574210086e-221
-1.7344889748836297e-216
4
-1.2313057480596081e+117
-7.273392168666018e+116
-1.0895651611615752e+117

simplify14.0ms

Iterations
IterNodes
done33
133
028

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.0s8466×body80valid