Details

Time bar (total: 18.8s)

sample31.0ms

Algorithm
intervals
Results
22.0ms269×body80valid

simplify9.0ms

Calls
1 calls:
Slowest
8.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.2b

localize21.0ms

Local error

Found 3 expressions with local error:

25.2b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
0.2b
(+ (* a c) (* b d))
0.0b
(+ (* c c) (* d d))

rewrite34.0ms

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
4×flip3-+ flip-+
3×pow1 associate-/r* insert-posit16 associate-/l*
2×+-commutative sum-log associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Calls
3 calls:
Slowest
28.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
3.0ms
(+ (* c c) (* d d))
2.0ms
(+ (* a c) (* b d))

series115.0ms

Calls
3 calls:
Slowest
66.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
29.0ms
(+ (* a c) (* b d))
21.0ms
(+ (* c c) (* d d))

simplify1.6s

Calls
40 calls:
Slowest
370.0ms
(- (* (* a c) (* a c)) (* (* b d) (* b d)))
239.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
221.0ms
(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
161.0ms
(+ (pow (* a c) 3) (pow (* b d) 3))
56.0ms
(/ (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d)))) (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d)))))

prune688.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.7b

localize8.0ms

Local error

Found 4 expressions with local error:

29.5b
(sqrt (+ (* c c) (* d d)))
29.5b
(sqrt (+ (* c c) (* d d)))
15.9b
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.2b
(+ (* a c) (* b d))

rewrite23.0ms

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
5×flip3-+ flip-+
4×pow1 insert-posit16
3×associate-/l*
2×rem-sqrt-square pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg div-exp div-inv
Calls
4 calls:
Slowest
13.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
4.0ms
(+ (* a c) (* b d))
2.0ms
(sqrt (+ (* c c) (* d d)))
2.0ms
(sqrt (+ (* c c) (* d d)))

series155.0ms

Calls
4 calls:
Slowest
76.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
31.0ms
(sqrt (+ (* c c) (* d d)))
24.0ms
(+ (* a c) (* b d))
24.0ms
(sqrt (+ (* c c) (* d d)))

simplify2.4s

Calls
75 calls:
Slowest
281.0ms
(- (* (* a c) (* a c)) (* (* b d) (* b d)))
238.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
213.0ms
(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
191.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
180.0ms
(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))

prune1.3s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 22.0b

localize14.0ms

Local error

Found 4 expressions with local error:

16.6b
(cbrt (+ (* a c) (* b d)))
16.6b
(cbrt (+ (* a c) (* b d)))
16.6b
(cbrt (+ (* a c) (* b d)))
15.2b
(* (/ (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d)))) 1) (/ (cbrt (+ (* a c) (* b d))) (+ (* c c) (* d d))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
24×associate-*r*
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×cbrt-prod times-frac
9×add-exp-log
8×add-cbrt-cube
6×pow1 cbrt-div
4×flip3-+ associate-*l* flip-+ insert-posit16 add-log-exp
3×pow1/3
2×prod-exp associate-/r/ cbrt-unprod div-inv
1×frac-times cbrt-undiv div-exp pow-prod-down associate-*l/ associate-*r/ *-commutative
Calls
4 calls:
Slowest
33.0ms
(* (/ (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d)))) 1) (/ (cbrt (+ (* a c) (* b d))) (+ (* c c) (* d d))))
3.0ms
(cbrt (+ (* a c) (* b d)))
2.0ms
(cbrt (+ (* a c) (* b d)))
1.0ms
(cbrt (+ (* a c) (* b d)))

series412.0ms

Calls
4 calls:
Slowest
127.0ms
(cbrt (+ (* a c) (* b d)))
117.0ms
(cbrt (+ (* a c) (* b d)))
94.0ms
(cbrt (+ (* a c) (* b d)))
74.0ms
(* (/ (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d)))) 1) (/ (cbrt (+ (* a c) (* b d))) (+ (* c c) (* d d))))

simplify5.6s

Calls
63 calls:
Slowest
659.0ms
(* (* (* (/ (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d)))) 1) (/ (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d)))) 1)) (/ (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d)))) 1)) (* (* (/ (cbrt (+ (* a c) (* b d))) (+ (* c c) (* d d))) (/ (cbrt (+ (* a c) (* b d))) (+ (* c c) (* d d)))) (/ (cbrt (+ (* a c) (* b d))) (+ (* c c) (* d d)))))
589.0ms
(cbrt (- (* (* a c) (* a c)) (* (* b d) (* b d))))
305.0ms
(cbrt (- (* (* a c) (* a c)) (* (* b d) (* b d))))
278.0ms
(cbrt (- (* (* a c) (* a c)) (* (* b d) (* b d))))
249.0ms
(exp (* -1/3 (+ (log (/ 1 a)) (log (/ 1 c)))))

prune1.2s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 22.0b

localize13.0ms

Local error

Found 4 expressions with local error:

25.5b
(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
0.2b
(/ 1 (+ (* c c) (* d d)))
0.2b
(+ (* a c) (* b d))
0.0b
(+ (* c c) (* d d))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
9×add-exp-log
8×add-log-exp
7×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
6×flip3-+ add-cbrt-cube associate-*r* flip-+
4×associate-/r/ insert-posit16
3×associate-/r* associate-*l*
2×frac-times +-commutative rec-exp sum-log associate-*l/ prod-exp div-inv
1×clear-num frac-2neg pow-prod-down associate-*r/ un-div-inv *-commutative cbrt-unprod pow-flip inv-pow
Calls
4 calls:
Slowest
7.0ms
(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
2.0ms
(+ (* a c) (* b d))
2.0ms
(+ (* c c) (* d d))
2.0ms
(/ 1 (+ (* c c) (* d d)))

series124.0ms

Calls
4 calls:
Slowest
63.0ms
(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
24.0ms
(+ (* a c) (* b d))
19.0ms
(/ 1 (+ (* c c) (* d d)))
18.0ms
(+ (* c c) (* d d))

simplify2.4s

Calls
40 calls:
Slowest
348.0ms
(* (+ (pow (* a c) 3) (pow (* b d) 3)) 1)
288.0ms
(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) 1)
221.0ms
(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (+ (* c c) (* d d))))
220.0ms
(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) (/ 1 (+ (* c c) (* d d))))
218.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))

prune911.0ms

Pruning

13 alts after pruning (9 fresh and 4 done)

Merged error: 22.0b

regimes537.0ms

Accuracy

0% (2.6b remaining)

Error of 25.6b against oracle of 23.0b and baseline of 25.6b

bsearch4.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
1.0s8484×body80valid