Details

Time bar (total: 3.8s)

sample26.0ms

Algorithm
intervals
Results
12.0ms266×body80valid

simplify4.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.4b
(- (* b c) (* a d))
26.4b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite59.0ms

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
3×pow1 associate-/r* associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg diff-log div-sub div-exp clear-num sum-log div-inv
Counts
3 → 55
Calls
3 calls:
9.0ms
(+ (* c c) (* d d))
9.0ms
(- (* b c) (* a d))
40.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series177.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* c c) (* d d))
47.0ms
(- (* b c) (* a d))
100.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify34.0ms

Counts
64 → 64

prune196.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 26.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b c) (* a d))
16.3b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.7b
(sqrt (+ (* c c) (* d d)))
29.7b
(sqrt (+ (* c c) (* d d)))

rewrite65.0ms

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
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
9.0ms
(- (* b c) (* a d))
30.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
9.0ms
(sqrt (+ (* c c) (* d d)))
14.0ms
(sqrt (+ (* c c) (* d d)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b c) (* a d))
131.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
38.0ms
(sqrt (+ (* c c) (* d d)))
42.0ms
(sqrt (+ (* c c) (* d d)))

simplify91.0ms

Counts
98 → 98

prune294.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.6b

localize19.0ms

Local error

Found 4 expressions with local error:

16.3b
(/ (- (* b c) (* a d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))
29.7b
(sqrt (+ (* c c) (* d d)))
29.7b
(sqrt (+ (* c c) (* d d)))
29.7b
(sqrt (+ (* c c) (* d d)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-div
12×add-sqr-sqrt
9×add-exp-log add-cube-cbrt *-un-lft-identity flip3-+ sqrt-prod add-cbrt-cube flip-+
8×associate-/r/
7×pow1
4×frac-times add-log-exp
3×rem-sqrt-square sqrt-pow1 times-frac pow1/2 associate-/l*
2×cbrt-undiv associate-*r/ div-exp associate-*l/ associate-/l/
1×flip3-- frac-2neg div-sub prod-exp clear-num associate-/r* flip-- cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
48.0ms
(/ (- (* b c) (* a d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))
9.0ms
(sqrt (+ (* c c) (* d d)))
15.0ms
(sqrt (+ (* c c) (* d d)))
9.0ms
(sqrt (+ (* c c) (* d d)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(/ (- (* b c) (* a d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))
41.0ms
(sqrt (+ (* c c) (* d d)))
40.0ms
(sqrt (+ (* c c) (* d d)))
42.0ms
(sqrt (+ (* c c) (* d d)))

simplify70.0ms

Counts
89 → 89

prune335.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 23.8b

localize22.0ms

Local error

Found 4 expressions with local error:

3.2b
(/ a (/ (sqrt (+ (* c c) (* d d))) d))
29.7b
(sqrt (+ (* c c) (* d d)))
29.7b
(sqrt (+ (* c c) (* d d)))
29.7b
(sqrt (+ (* c c) (* d d)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
85×add-sqr-sqrt
82×add-cube-cbrt *-un-lft-identity
45×sqrt-prod
22×associate-/r*
9×add-exp-log add-cbrt-cube
7×pow1
6×sqrt-div
5×div-inv
4×add-log-exp
3×cbrt-undiv rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 div-exp flip-+ associate-/l*
1×frac-2neg clear-num associate-/r/
Counts
4 → 151
Calls
4 calls:
18.0ms
(/ a (/ (sqrt (+ (* c c) (* d d))) d))
9.0ms
(sqrt (+ (* c c) (* d d)))
9.0ms
(sqrt (+ (* c c) (* d d)))
9.0ms
(sqrt (+ (* c c) (* d d)))

series183.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ a (/ (sqrt (+ (* c c) (* d d))) d))
42.0ms
(sqrt (+ (* c c) (* d d)))
39.0ms
(sqrt (+ (* c c) (* d d)))
39.0ms
(sqrt (+ (* c c) (* d d)))

simplify55.0ms

Counts
163 → 163

prune485.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 23.8b

regimes140.0ms

Accuracy

0% (0.4b remaining)

Error of 22.5b against oracle of 22.2b and baseline of 22.5b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample878.0ms

Algorithm
intervals
Results
528.0ms8476×body80valid