Details

Time bar (total: 21.1s)

sample45.0ms

Algorithm
intervals
Results
32.0ms272×body80valid

simplify101.0ms

Calls
1 calls:
Slowest
100.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize40.0ms

Local error

Found 3 expressions with local error:

24.9b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
0.7b
(- (* b c) (* a d))
0.0b
(+ (* c c) (* d d))

rewrite22.0ms

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
Calls
3 calls:
Slowest
16.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
3.0ms
(+ (* c c) (* d d))
3.0ms
(- (* b c) (* a d))

series151.0ms

Calls
3 calls:
Slowest
85.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
47.0ms
(- (* b c) (* a d))
19.0ms
(+ (* c c) (* d d))

simplify2.5s

Calls
41 calls:
Slowest
430.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
383.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
275.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
163.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
123.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))

prune853.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.5b

localize17.0ms

Local error

Found 4 expressions with local error:

28.1b
(sqrt (+ (* c c) (* d d)))
28.1b
(sqrt (+ (* c c) (* d d)))
15.7b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.7b
(- (* b c) (* a d))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
4×pow1 insert-posit16
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square 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
Calls
4 calls:
Slowest
18.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
5.0ms
(- (* b c) (* a d))
4.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))

series183.0ms

Calls
4 calls:
Slowest
86.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
46.0ms
(- (* b c) (* a d))
33.0ms
(sqrt (+ (* c c) (* d d)))
19.0ms
(sqrt (+ (* c c) (* d d)))

simplify4.1s

Calls
76 calls:
Slowest
361.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
361.0ms
(/ (* (* (- (* 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)))))
337.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
228.0ms
(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
209.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.4b

localize15.0ms

Local error

Found 4 expressions with local error:

28.1b
(sqrt (+ (* c c) (* d d)))
28.1b
(sqrt (+ (* c c) (* d d)))
15.9b
(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
0.7b
(- (* b c) (* a d))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-exp-log add-cube-cbrt
6×pow1 add-cbrt-cube sqrt-div associate-*r* sqrt-prod add-log-exp
4×insert-posit16
3×flip3-+ flip3-- associate-*l* flip-+ flip--
2×frac-times rem-sqrt-square pow1/2 associate-*l/ prod-exp associate-/r/
1×rec-exp sub-neg diff-log pow-prod-down associate-*r/ un-div-inv *-commutative cbrt-unprod div-inv
Calls
4 calls:
Slowest
9.0ms
(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
2.0ms
(sqrt (+ (* c c) (* d d)))
2.0ms
(- (* b c) (* a d))
2.0ms
(sqrt (+ (* c c) (* d d)))

series202.0ms

Calls
4 calls:
Slowest
105.0ms
(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
44.0ms
(- (* b c) (* a d))
30.0ms
(sqrt (+ (* c c) (* d d)))
23.0ms
(sqrt (+ (* c c) (* d d)))

simplify3.9s

Calls
45 calls:
Slowest
718.0ms
(* (* (* (- (* 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))))))
355.0ms
(* (- (pow (* b c) 3) (pow (* a d) 3)) (/ 1 (sqrt (+ (* c c) (* d d)))))
309.0ms
(* (- (* (* b c) (* b c)) (* (* a d) (* a d))) (/ 1 (sqrt (+ (* c c) (* d d)))))
287.0ms
(* (- (pow (* b c) 3) (pow (* a d) 3)) 1)
258.0ms
(* (- (* (* b c) (* b c)) (* (* a d) (* a d))) 1)

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.4b

localize4.0ms

Local error

Found 4 expressions with local error:

28.1b
(sqrt (+ (* c c) (* d d)))
28.1b
(sqrt (+ (* c c) (* d d)))
15.7b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.7b
(- (* b c) (* a d))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
4×pow1 insert-posit16
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square 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
Calls
4 calls:
Slowest
9.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
5.0ms
(- (* b c) (* a d))
2.0ms
(sqrt (+ (* c c) (* d d)))
2.0ms
(sqrt (+ (* c c) (* d d)))

series154.0ms

Calls
4 calls:
Slowest
79.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
35.0ms
(- (* b c) (* a d))
21.0ms
(sqrt (+ (* c c) (* d d)))
19.0ms
(sqrt (+ (* c c) (* d d)))

simplify3.5s

Calls
76 calls:
Slowest
361.0ms
(/ (* (* (- (* 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)))))
286.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
261.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
204.0ms
(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
174.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.4b

regimes352.0ms

Accuracy

0% (2.5b remaining)

Error of 25.7b against oracle of 23.1b and baseline of 25.7b

bsearch3.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.3s8498×body80valid