Details

Time bar (total: 2.4m)

sample57.0ms

Algorithm
intervals
Results
38.0ms260×body80valid

simplify121.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
121.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize38.0ms

Local error

Found 2 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* associate-/l*
2×pow1 flip3-- associate-/r/ insert-posit16 flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Counts
2 → 46
Calls
2 calls:
Slowest
34.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
8.0ms
(- (* b c) (* a d))

series163.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
107.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
56.0ms
(- (* b c) (* a d))

simplify2.7s

Counts
37 → 52
Calls
37 calls:
Slowest
351.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
350.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
298.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
237.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
186.0ms
(/ (exp (* b c)) (exp (* a d)))

prune697.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.4b

localize39.0ms

Local error

Found 4 expressions with local error:

28.5b
(sqrt (+ (* c c) (* d d)))
28.5b
(sqrt (+ (* c c) (* d d)))
16.4b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.1b
(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×*-un-lft-identity add-cube-cbrt
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r*
11×flip3-+ add-cbrt-cube add-exp-log flip-+
9×div-inv
6×pow1
4×cbrt-undiv div-exp insert-posit16 add-log-exp
3×div-sub associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×flip3-- flip--
Counts
4 → 270
Calls
4 calls:
Slowest
43.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
41.0ms
(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
113.0ms
(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
65.0ms
(sqrt (+ (* c c) (* d d)))
52.0ms
(sqrt (+ (* c c) (* d d)))

simplify29.4s

Counts
402 → 282
Calls
402 calls:
Slowest
703.0ms
(/ (* (* (- (* 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)))))
299.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
288.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
281.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
278.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))

prune2.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.0b

localize32.0ms

Local error

Found 4 expressions with local error:

28.5b
(sqrt (+ (* c c) (* d d)))
28.5b
(sqrt (+ (* c c) (* d d)))
16.4b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.1b
(/ (/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) 1) (sqrt (+ (* c c) (* d d))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
1356×times-frac
625×add-sqr-sqrt
623×*-un-lft-identity add-cube-cbrt
438×sqrt-prod
79×associate-/l*
50×sqrt-div
46×associate-/r/
30×div-inv
25×flip3-+ flip-+
20×add-exp-log
15×add-cbrt-cube
12×associate-/r* div-exp
7×cbrt-undiv
6×pow1
4×div-sub insert-posit16 add-log-exp
3×associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 1-exp
1×flip3-- flip--
Counts
4 → 638
Calls
4 calls:
Slowest
37.0ms
(/ (/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) 1) (sqrt (+ (* c c) (* d d))))
23.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series285.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
114.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
88.0ms
(/ (/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) 1) (sqrt (+ (* c c) (* d d))))
46.0ms
(sqrt (+ (* c c) (* d d)))
37.0ms
(sqrt (+ (* c c) (* d d)))

simplify1.6m

Counts
1082 → 650
Calls
1082 calls:
Slowest
485.0ms
(/ (/ (/ (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (sqrt (sqrt (+ (* c c) (* d d))))) (* (cbrt 1) (cbrt 1))) (* (cbrt (sqrt (+ (* c c) (* d d)))) (cbrt (sqrt (+ (* c c) (* d d))))))
443.0ms
(/ (/ (/ (- (* b c) (* a d)) (sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))) (* (cbrt 1) (cbrt 1))) (sqrt 1))
443.0ms
(/ (/ (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d))))) (cbrt 1)) (sqrt (+ (* c c) (* d d))))
277.0ms
(/ (* (* (- (* 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)))))
277.0ms
(/ (/ (/ (- (* b c) (* a d)) (sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))) 1) 1)

prune6.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.0b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* associate-/l*
2×pow1 flip3-- associate-/r/ insert-posit16 flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Counts
2 → 46
Calls
2 calls:
Slowest
22.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
7.0ms
(- (* b c) (* a d))

series136.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
89.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
46.0ms
(- (* b c) (* a d))

simplify1.7s

Counts
37 → 52
Calls
37 calls:
Slowest
250.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
237.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
206.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
120.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
110.0ms
(/ (exp (* b c)) (exp (* a d)))

prune370.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 23.0b

regimes321.0ms

Accuracy

0% (2.6b remaining)

Error of 25.5b against oracle of 22.9b and baseline of 25.5b

bsearch2.0ms

end0.0ms

sample1.0s

Algorithm
intervals
Results
763.0ms8454×body80valid