Details

Time bar (total: 48.8s)

sample61.0ms

Algorithm
intervals
Results
42.0ms278×body80valid

simplify111.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
111.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize24.0ms

Local error

Found 2 expressions with local error:

25.1b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
0.2b
(- (* 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
38.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
7.0ms
(- (* b c) (* a d))

series201.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
126.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
75.0ms
(- (* b c) (* a d))

simplify2.5s

Counts
37 → 52
Calls
37 calls:
Slowest
377.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
346.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
308.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
201.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
131.0ms
(/ (exp (* b c)) (exp (* a d)))

prune597.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.6b

localize50.0ms

Local error

Found 4 expressions with local error:

30.4b
(sqrt (+ (* c c) (* d d)))
30.4b
(sqrt (+ (* c c) (* d d)))
15.4b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.2b
(- (* b c) (* a d))

rewrite64.0ms

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
32.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
14.0ms
(- (* b c) (* a d))
10.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
69.0ms
(- (* b c) (* a d))
57.0ms
(sqrt (+ (* c c) (* d d)))
48.0ms
(sqrt (+ (* c c) (* d d)))

simplify5.1s

Counts
78 → 102
Calls
78 calls:
Slowest
697.0ms
(/ (* (* (- (* 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)))))
368.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
360.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
285.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
276.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.5b

localize42.0ms

Local error

Found 4 expressions with local error:

30.4b
(sqrt (+ (* c c) (* d d)))
30.4b
(sqrt (+ (* c c) (* d d)))
15.5b
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
0.2b
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
100×add-sqr-sqrt
98×*-un-lft-identity add-cube-cbrt
54×sqrt-prod
27×associate-/r*
17×add-exp-log
11×add-cbrt-cube associate-/r/
9×associate-/l*
8×div-exp
7×pow1
6×sqrt-div div-inv
5×flip3-- flip--
4×cbrt-undiv insert-posit16 add-log-exp
3×flip3-+ flip-+
2×rem-sqrt-square rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp associate-/l/
1×pow-flip inv-pow
Counts
4 → 197
Calls
4 calls:
Slowest
35.0ms
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
31.0ms
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series336.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
99.0ms
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
53.0ms
(sqrt (+ (* c c) (* d d)))
39.0ms
(sqrt (+ (* c c) (* d d)))

simplify21.1s

Counts
254 → 209
Calls
254 calls:
Slowest
378.0ms
(/ (sqrt 1) (/ (* (cbrt (sqrt (+ (* c c) (* d d)))) (cbrt (sqrt (+ (* c c) (* d d))))) (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d))))))
376.0ms
(/ (* (* 1 1) 1) (* (* (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))) (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))) (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))))
372.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt (+ (* c c) (* d d)))) (cbrt (sqrt (+ (* c c) (* d d))))) (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d))))))
351.0ms
(/ (cbrt 1) (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
341.0ms
(/ (* (* (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))))

prune2.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.5b

localize30.0ms

Local error

Found 3 expressions with local error:

24.8b
(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))
0.4b
(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
0.2b
(- (* b c) (* a d))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
55×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×associate-/r*
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
8×div-exp
6×flip3-- div-inv flip-- associate-/l*
5×add-log-exp
4×pow1 cbrt-undiv
3×insert-posit16
2×rec-exp clear-num frac-2neg 1-exp associate-/l/
1×sub-neg flip3-+ diff-log flip-+ pow-flip inv-pow
Counts
3 → 130
Calls
3 calls:
Slowest
38.0ms
(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))
27.0ms
(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
13.0ms
(- (* b c) (* a d))

series306.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
164.0ms
(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
75.0ms
(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))
67.0ms
(- (* b c) (* a d))

simplify11.6s

Counts
154 → 139
Calls
154 calls:
Slowest
475.0ms
(/ (sqrt 1) (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
377.0ms
(/ (* (* 1 1) 1) (* (* (/ (+ (* c c) (* d d)) (- (* b c) (* a d))) (/ (+ (* c c) (* d d)) (- (* b c) (* a d)))) (/ (+ (* c c) (* d d)) (- (* b c) (* a d)))))
290.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d)))) (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d))))))
274.0ms
(/ (cbrt 1) (+ (* (* b c) (* b c)) (+ (* (* a d) (* a d)) (* (* b c) (* a d)))))
258.0ms
(/ (sqrt 1) (/ (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d)))) (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d))))))

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.5b

regimes267.0ms

Accuracy

0% (2.7b remaining)

Error of 25.9b against oracle of 23.2b and baseline of 25.9b

bsearch2.0ms

end0.0ms

sample1.0s

Algorithm
intervals
Results
800.0ms8493×body80valid