Details

Time bar (total: 39.9s)

sample55.0ms

Algorithm
intervals
Results
39.0ms269×body80valid

simplify127.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
127.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize23.0ms

Local error

Found 3 expressions with local error:

25.7b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
0.5b
(- (* b c) (* a d))
0.0b
(+ (* c c) (* d d))

rewrite57.0ms

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
Counts
3 → 58
Calls
3 calls:
Slowest
41.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
8.0ms
(- (* b c) (* a d))
8.0ms
(+ (* c c) (* d d))

series214.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
123.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
53.0ms
(- (* b c) (* a d))
38.0ms
(+ (* c c) (* d d))

simplify2.7s

Counts
41 → 67
Calls
41 calls:
Slowest
412.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
331.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
258.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
188.0ms
(/ (* (* (- (* 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)))

prune747.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 25.3b

localize45.0ms

Local error

Found 4 expressions with local error:

29.1b
(sqrt (+ (* c c) (* d d)))
29.1b
(sqrt (+ (* c c) (* d d)))
13.6b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.5b
(- (* b c) (* a d))

rewrite65.0ms

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
31.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
13.0ms
(sqrt (+ (* c c) (* d d)))
12.0ms
(sqrt (+ (* c c) (* d d)))
7.0ms
(- (* b c) (* a d))

series363.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
173.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
68.0ms
(sqrt (+ (* c c) (* d d)))
64.0ms
(sqrt (+ (* c c) (* d d)))
58.0ms
(- (* b c) (* a d))

simplify5.4s

Counts
78 → 102
Calls
78 calls:
Slowest
476.0ms
(/ (* (* (- (* 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)))))
441.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
396.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
369.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
350.0ms
(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))

prune1.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 24.4b

localize55.0ms

Local error

Found 4 expressions with local error:

29.1b
(sqrt (+ (* c c) (* d d)))
29.1b
(sqrt (+ (* c c) (* d d)))
29.1b
(sqrt (+ (* c c) (* d d)))
7.1b
(* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d))))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
137×add-sqr-sqrt
108×sqrt-prod
99×times-frac
57×*-un-lft-identity
45×add-cube-cbrt
33×associate-*r* associate-*l*
28×unswap-sqr
26×add-exp-log
16×add-cbrt-cube
14×sqrt-div
9×pow1
8×div-exp prod-exp
5×flip3-+ flip-+
4×cbrt-undiv associate-/r/ cbrt-unprod insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×rec-exp 1-exp div-inv
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 167
Calls
4 calls:
Slowest
90.0ms
(* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d))))))
14.0ms
(sqrt (+ (* c c) (* d d)))
10.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d))))))
63.0ms
(sqrt (+ (* c c) (* d d)))
50.0ms
(sqrt (+ (* c c) (* d d)))
45.0ms
(sqrt (+ (* c c) (* d d)))

simplify17.1s

Counts
170 → 179
Calls
170 calls:
Slowest
494.0ms
(* (sqrt (/ 1 (sqrt (sqrt (+ (* c c) (* d d)))))) (/ (sqrt (- (* b c) (* a d))) (sqrt (sqrt (sqrt (+ (* c c) (* d d)))))))
455.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))) (sqrt (sqrt (+ (* c c) (* d d)))))) (/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))) (sqrt (sqrt (+ (* c c) (* d d)))))))
350.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))) (sqrt (sqrt (+ (* c c) (* d d)))))) (* (* (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d))))) (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d)))))) (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d)))))))
326.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
314.0ms
(/ 1 (sqrt (sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))))

prune2.4s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 24.4b

localize48.0ms

Local error

Found 4 expressions with local error:

29.1b
(sqrt (+ (* c c) (* d d)))
29.1b
(sqrt (+ (* c c) (* d d)))
29.1b
(sqrt (+ (* c c) (* d d)))
7.1b
(/ (* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (- (* b c) (* a d))) (sqrt (sqrt (+ (* c c) (* d d)))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
27×sqrt-prod
19×add-exp-log
16×add-sqr-sqrt
13×*-un-lft-identity add-cbrt-cube add-cube-cbrt
10×sqrt-div
9×associate-/r* times-frac
7×pow1 div-exp
5×associate-/l/
4×cbrt-undiv flip3-+ prod-exp flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×frac-times flip3-- associate-*r/ associate-/r/ cbrt-unprod flip--
1×rec-exp clear-num frac-2neg 1-exp associate-*l/ div-inv associate-/l*
Counts
4 → 93
Calls
4 calls:
Slowest
65.0ms
(/ (* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (- (* b c) (* a d))) (sqrt (sqrt (+ (* c c) (* d d)))))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(/ (* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (- (* b c) (* a d))) (sqrt (sqrt (+ (* c c) (* d d)))))
58.0ms
(sqrt (+ (* c c) (* d d)))
53.0ms
(sqrt (+ (* c c) (* d d)))
50.0ms
(sqrt (+ (* c c) (* d d)))

simplify5.6s

Counts
76 → 105
Calls
76 calls:
Slowest
326.0ms
(/ (* (/ (* (* 1 1) 1) (* (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))) (sqrt (sqrt (+ (* c c) (* d d)))))) (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d)))) (* (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))) (sqrt (sqrt (+ (* c c) (* d d))))))
311.0ms
(/ (* (* (* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (- (* b c) (* a d))) (* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (- (* b c) (* a d)))) (* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (- (* b c) (* a d)))) (* (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))) (sqrt (sqrt (+ (* c c) (* d d))))))
307.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
293.0ms
(- (log (* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (- (* b c) (* a d)))) (log (sqrt (sqrt (+ (* c c) (* d d))))))
287.0ms
(* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (- (* (* b c) (* b c)) (* (* a d) (* a d))))

prune1.1s

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 24.4b

regimes389.0ms

Accuracy

0% (2.4b remaining)

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

bsearch2.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
1.1s8461×body80valid