Details

Time bar (total: 30.7s)

sample42.0ms

Algorithm
intervals
Results
30.0ms266×body80valid

simplify144.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
144.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.9b

localize24.0ms

Local error

Found 2 expressions with local error:

22.9b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
0.3b
(- (* b c) (* a d))

rewrite46.0ms

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
29.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
16.0ms
(- (* b c) (* a d))

series476.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
353.0ms
(- (* b c) (* a d))
123.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify2.2s

Counts
37 → 52
Calls
37 calls:
Slowest
299.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
290.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
269.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
178.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
143.0ms
(/ (exp (* b c)) (exp (* a d)))

prune538.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.5b

localize24.0ms

Local error

Found 4 expressions with local error:

25.9b
(sqrt (+ (* c c) (* d d)))
25.9b
(sqrt (+ (* c c) (* d d)))
12.5b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.3b
(- (* b c) (* a d))

rewrite53.0ms

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
Counts
4 → 90
Calls
4 calls:
Slowest
23.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
12.0ms
(- (* b c) (* a d))
11.0ms
(sqrt (+ (* c c) (* d d)))
7.0ms
(sqrt (+ (* c c) (* d d)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
51.0ms
(- (* b c) (* a d))
48.0ms
(sqrt (+ (* c c) (* d d)))
44.0ms
(sqrt (+ (* c c) (* d d)))

simplify4.2s

Counts
78 → 102
Calls
78 calls:
Slowest
371.0ms
(/ (* (* (- (* 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)))))
340.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
283.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
281.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
264.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 19.4b

localize27.0ms

Local error

Found 4 expressions with local error:

25.9b
(sqrt (+ (* c c) (* d d)))
25.9b
(sqrt (+ (* c c) (* d d)))
12.5b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.3b
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×associate-/r* associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×cbrt-unprod insert-posit16 add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/l/
1×frac-times clear-num frac-2neg flip3-- div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 165
Calls
4 calls:
Slowest
59.0ms
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))))
25.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
18.0ms
(sqrt (+ (* c c) (* d d)))
10.0ms
(sqrt (+ (* c c) (* d d)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
176.0ms
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))))
154.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
43.0ms
(sqrt (+ (* c c) (* d d)))
41.0ms
(sqrt (+ (* c c) (* d d)))

simplify13.1s

Counts
170 → 177
Calls
170 calls:
Slowest
352.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
352.0ms
(/ (* (* (- (* 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)))))
285.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
284.0ms
(* (/ (* (* 1 1) 1) (* (* (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))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))))
269.0ms
(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))

prune2.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 19.4b

localize32.0ms

Local error

Found 4 expressions with local error:

25.9b
(sqrt (+ (* c c) (* d d)))
25.9b
(sqrt (+ (* c c) (* d d)))
25.9b
(sqrt (+ (* c c) (* d d)))
8.5b
(/ (* b c) (sqrt (+ (* c c) (* d d))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
15×sqrt-prod
14×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
9×add-cbrt-cube add-exp-log
8×sqrt-div
7×pow1
6×associate-/r* times-frac
4×flip3-+ flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-undiv div-exp associate-/r/
1×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 78
Calls
4 calls:
Slowest
25.0ms
(/ (* b c) (sqrt (+ (* c c) (* d d))))
7.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series212.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
72.0ms
(/ (* b c) (sqrt (+ (* c c) (* d d))))
50.0ms
(sqrt (+ (* c c) (* d d)))
49.0ms
(sqrt (+ (* c c) (* d d)))
41.0ms
(sqrt (+ (* c c) (* d d)))

simplify2.5s

Counts
57 → 90
Calls
57 calls:
Slowest
276.0ms
(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
263.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
257.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
257.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
229.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 19.4b

regimes420.0ms

Accuracy

2.5% (2.5b remaining)

Error of 25.5b against oracle of 23.0b and baseline of 25.6b

bsearch78.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
978.0ms8475×body80valid