Details

Time bar (total: 32.4s)

sample62.0ms

Algorithm
intervals
Results
42.0ms276×body80valid

simplify117.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
117.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize45.0ms

Local error

Found 2 expressions with local error:

26.5b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
0.7b
(- (* b c) (* a d))

rewrite30.0ms

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
23.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
7.0ms
(- (* b c) (* a d))

series189.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
118.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
71.0ms
(- (* b c) (* a d))

simplify2.5s

Counts
37 → 52
Calls
37 calls:
Slowest
363.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
350.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
329.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
188.0ms
(/ (exp (* b c)) (exp (* a d)))
177.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))

prune512.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 26.2b

localize26.0ms

Local error

Found 4 expressions with local error:

28.9b
(sqrt (+ (* c c) (* d d)))
28.9b
(sqrt (+ (* c c) (* d d)))
16.6b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.7b
(- (* b c) (* a d))

rewrite63.0ms

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
24.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
19.0ms
(sqrt (+ (* c c) (* d d)))
12.0ms
(sqrt (+ (* c c) (* d d)))
7.0ms
(- (* b c) (* a d))

series296.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
68.0ms
(- (* b c) (* a d))
66.0ms
(sqrt (+ (* c c) (* d d)))
45.0ms
(sqrt (+ (* c c) (* d d)))

simplify4.6s

Counts
78 → 102
Calls
78 calls:
Slowest
432.0ms
(/ (* (* (- (* 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)))))
358.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
331.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
326.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
319.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.5b

localize27.0ms

Local error

Found 4 expressions with local error:

28.9b
(sqrt (+ (* c c) (* d d)))
28.9b
(sqrt (+ (* c c) (* d d)))
16.6b
(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
0.7b
(- (* b c) (* a d))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
22×*-un-lft-identity times-frac
20×add-cube-cbrt
17×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×sqrt-div add-log-exp
5×unswap-sqr
4×prod-exp insert-posit16
3×flip3-+ flip3-- associate-*l* flip-+ flip--
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ associate-/r/ cbrt-unprod
1×cbrt-undiv rec-exp sub-neg diff-log 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 99
Calls
4 calls:
Slowest
70.0ms
(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
7.0ms
(- (* b c) (* a d))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
55.0ms
(sqrt (+ (* c c) (* d d)))
50.0ms
(- (* b c) (* a d))
45.0ms
(sqrt (+ (* c c) (* d d)))

simplify5.2s

Counts
78 → 111
Calls
78 calls:
Slowest
719.0ms
(* (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ 1 (sqrt (+ (* c c) (* d d))))) (/ 1 (sqrt (+ (* c c) (* d d))))))
311.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
283.0ms
(* (- (* (* b c) (* b c)) (* (* a d) (* a d))) (/ 1 (sqrt (+ (* c c) (* d d)))))
271.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
256.0ms
(* (- (* (* b c) (* b c)) (* (* a d) (* a d))) 1)

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 23.5b

localize44.0ms

Local error

Found 3 expressions with local error:

26.2b
(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))
0.7b
(- (* b c) (* a d))
0.5b
(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))

rewrite100.0ms

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
62.0ms
(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))
21.0ms
(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
14.0ms
(- (* b c) (* a d))

series293.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
178.0ms
(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
68.0ms
(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))
48.0ms
(- (* b c) (* a d))

simplify12.8s

Counts
154 → 139
Calls
154 calls:
Slowest
582.0ms
(/ (sqrt 1) (+ (* (* b c) (* b c)) (+ (* (* a d) (* a d)) (* (* b c) (* a d)))))
338.0ms
(/ (* (* 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)))))
326.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d)))) (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d))))))
314.0ms
(/ (sqrt 1) (/ (+ (* c c) (* d d)) (- (* (* b c) (* b c)) (* (* a d) (* a d)))))
306.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (+ (* c c) (* d d)) (- (* (* b c) (* b c)) (* (* a d) (* a d)))))

prune1.2s

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 23.5b

regimes387.0ms

Accuracy

-13.5% (2.9b remaining)

Error of 26.5b against oracle of 23.5b and baseline of 26.1b

bsearch73.0ms

end0.0ms

sample1.1s

Algorithm
intervals
Results
908.0ms8491×body80valid