Details

Time bar (total: 20.9s)

sample42.0ms

Algorithm
intervals
Results
30.0ms273×body80valid

simplify148.0ms

Calls
1 calls:
Slowest
148.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.2b

localize43.0ms

Local error

Found 3 expressions with local error:

23.2b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
1.0b
(- (* b c) (* a d))
0.0b
(+ (* c c) (* d d))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
7×add-log-exp
5×add-cbrt-cube add-exp-log
3×pow1 associate-/r* insert-posit16 associate-/l*
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-sub div-exp div-inv
Calls
3 calls:
Slowest
33.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
12.0ms
(+ (* c c) (* d d))
7.0ms
(- (* b c) (* a d))

series243.0ms

Calls
3 calls:
Slowest
138.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
60.0ms
(- (* b c) (* a d))
45.0ms
(+ (* c c) (* d d))

simplify2.6s

Calls
41 calls:
Slowest
385.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
323.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
322.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
162.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
162.0ms
(/ (exp (* b c)) (exp (* a d)))

prune735.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.8b

localize30.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (+ (* c c) (* d d)))
27.4b
(sqrt (+ (* c c) (* d d)))
13.4b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
1.0b
(- (* b c) (* a d))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
4×insert-posit16
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Calls
4 calls:
Slowest
28.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
8.0ms
(- (* b c) (* a d))
7.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series301.0ms

Calls
4 calls:
Slowest
139.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
63.0ms
(sqrt (+ (* c c) (* d d)))
59.0ms
(- (* b c) (* a d))
40.0ms
(sqrt (+ (* c c) (* d d)))

simplify4.5s

Calls
78 calls:
Slowest
333.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
318.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
300.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
287.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
268.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 20.8b

localize44.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (+ (* c c) (* d d)))
27.4b
(sqrt (+ (* c c) (* d d)))
13.4b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
1.0b
(- (* b c) (* a d))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
4×insert-posit16
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Calls
4 calls:
Slowest
51.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
15.0ms
(- (* b c) (* a d))
13.0ms
(sqrt (+ (* c c) (* d d)))
12.0ms
(sqrt (+ (* c c) (* d d)))

series293.0ms

Calls
4 calls:
Slowest
152.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
57.0ms
(- (* b c) (* a d))
45.0ms
(sqrt (+ (* c c) (* d d)))
38.0ms
(sqrt (+ (* c c) (* d d)))

simplify3.8s

Calls
78 calls:
Slowest
304.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
297.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
272.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
264.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
254.0ms
(- (pow (* b c) 3) (pow (* a d) 3))

prune948.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.8b

localize27.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (+ (* c c) (* d d)))
27.4b
(sqrt (+ (* c c) (* d d)))
13.5b
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
1.0b
(- (* b c) (* a d))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 add-cbrt-cube sqrt-div add-exp-log associate-/l* add-log-exp
4×insert-posit16
3×associate-/r* flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp div-inv
Calls
4 calls:
Slowest
25.0ms
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
8.0ms
(- (* b c) (* a d))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series210.0ms

Calls
4 calls:
Slowest
85.0ms
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
45.0ms
(- (* b c) (* a d))
41.0ms
(sqrt (+ (* c c) (* d d)))
38.0ms
(sqrt (+ (* c c) (* d d)))

simplify2.9s

Calls
77 calls:
Slowest
227.0ms
(/ (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))) (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))))
221.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
221.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
220.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
178.0ms
(+ (* (* b c) (* b c)) (+ (* (* a d) (* a d)) (* (* b c) (* a d))))

prune930.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 20.8b

regimes342.0ms

Accuracy

0% (2.0b remaining)

Error of 25.2b against oracle of 23.3b and baseline of 25.2b

bsearch2.0ms

end0.0ms

sample997.0ms

Algorithm
intervals
Results
835.0ms8465×body80valid