Details

Time bar (total: 14.0s)

sample37.0ms

Algorithm
intervals
Results
28.0ms275×body80valid

simplify73.0ms

Calls
1 calls:
Slowest
72.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.4b

localize30.0ms

Local error

Found 2 expressions with local error:

23.4b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
0.5b
(- (* b c) (* a d))

rewrite16.0ms

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
Calls
2 calls:
Slowest
12.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
4.0ms
(- (* b c) (* a d))

series176.0ms

Calls
2 calls:
Slowest
127.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
49.0ms
(- (* b c) (* a d))

simplify2.0s

Calls
37 calls:
Slowest
336.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
257.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
210.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
196.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
111.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune496.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.1b

localize8.0ms

Local error

Found 4 expressions with local error:

27.8b
(sqrt (+ (* c c) (* d d)))
27.8b
(sqrt (+ (* c c) (* d d)))
13.8b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.5b
(- (* b c) (* a d))

rewrite16.0ms

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))))
2.0ms
(- (* b c) (* a d))
2.0ms
(sqrt (+ (* c c) (* d d)))
2.0ms
(sqrt (+ (* c c) (* d d)))

series250.0ms

Calls
4 calls:
Slowest
121.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
53.0ms
(- (* b c) (* a d))
40.0ms
(sqrt (+ (* c c) (* d d)))
36.0ms
(sqrt (+ (* c c) (* d d)))

simplify3.0s

Calls
76 calls:
Slowest
265.0ms
(/ (* (* (- (* 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)))))
225.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
219.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
192.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
158.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune832.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.1b

localize7.0ms

Local error

Found 3 expressions with local error:

16.8b
(/ (* b c) (+ (* c c) (* d d)))
14.4b
(/ (* a d) (+ (* c c) (* d d)))
0.0b
(- (/ (* b c) (+ (* c c) (* d d))) (/ (* a d) (+ (* c c) (* d d))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity
8×associate-/r/
7×add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-/r* times-frac
5×add-log-exp
4×flip3-+ flip-+ div-inv
3×pow1 distribute-rgt-out-- insert-posit16
2×cbrt-undiv clear-num frac-2neg div-exp associate-/l*
1×sub-neg flip3-- diff-log frac-sub flip-- distribute-lft-out-- sub-div difference-of-squares
Calls
3 calls:
Slowest
21.0ms
(- (/ (* b c) (+ (* c c) (* d d))) (/ (* a d) (+ (* c c) (* d d))))
5.0ms
(/ (* a d) (+ (* c c) (* d d)))
5.0ms
(/ (* b c) (+ (* c c) (* d d)))

series206.0ms

Calls
3 calls:
Slowest
116.0ms
(- (/ (* b c) (+ (* c c) (* d d))) (/ (* a d) (+ (* c c) (* d d))))
46.0ms
(/ (* a d) (+ (* c c) (* d d)))
44.0ms
(/ (* b c) (+ (* c c) (* d d)))

simplify1.9s

Calls
49 calls:
Slowest
165.0ms
(/ (* (* (* b c) (* b c)) (* b c)) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
161.0ms
(/ (* (* (* a d) (* a d)) (* a d)) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
158.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
157.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
156.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))

prune542.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.3b

localize13.0ms

Local error

Found 4 expressions with local error:

27.8b
(sqrt (+ (* c c) (* d d)))
27.8b
(sqrt (+ (* c c) (* d d)))
16.8b
(/ (* b c) (+ (* c c) (* d d)))
2.2b
(* (/ a (sqrt (+ (* c c) (* d d)))) (/ d (sqrt (+ (* c c) (* d d)))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×add-cbrt-cube sqrt-div add-exp-log
6×pow1 associate-*r* associate-*l* associate-/r/ sqrt-prod
5×flip3-+ flip-+
4×insert-posit16 add-log-exp
3×associate-/r* times-frac div-inv
2×rem-sqrt-square pow1/2
1×frac-times cbrt-undiv clear-num frac-2neg div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod associate-/l*
Calls
4 calls:
Slowest
5.0ms
(* (/ a (sqrt (+ (* c c) (* d d)))) (/ d (sqrt (+ (* c c) (* d d)))))
5.0ms
(/ (* b c) (+ (* c c) (* d d)))
2.0ms
(sqrt (+ (* c c) (* d d)))
2.0ms
(sqrt (+ (* c c) (* d d)))

series168.0ms

Calls
4 calls:
Slowest
48.0ms
(* (/ a (sqrt (+ (* c c) (* d d)))) (/ d (sqrt (+ (* c c) (* d d)))))
43.0ms
(/ (* b c) (+ (* c c) (* d d)))
40.0ms
(sqrt (+ (* c c) (* d d)))
37.0ms
(sqrt (+ (* c c) (* d d)))

simplify1.9s

Calls
54 calls:
Slowest
433.0ms
(* (* (* (/ a (sqrt (+ (* c c) (* d d)))) (/ a (sqrt (+ (* c c) (* d d))))) (/ a (sqrt (+ (* c c) (* d d))))) (* (* (/ d (sqrt (+ (* c c) (* d d)))) (/ d (sqrt (+ (* c c) (* d d))))) (/ d (sqrt (+ (* c c) (* d d))))))
163.0ms
(/ (* (* (* b c) (* b c)) (* b c)) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
158.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
154.0ms
(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
142.0ms
(/ a (sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d)))))

prune745.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.3b

regimes345.0ms

Accuracy

31.3% (0.7b remaining)

Error of 22.7b against oracle of 22.0b and baseline of 23.0b

bsearch9.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
797.0ms8454×body80valid