Details

Time bar (total: 1.2m)

sample60.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
21.0ms256×pre80true

simplify56.0ms

Calls
1 calls:
Slowest
56.0ms
(* a (+ (+ b c) d))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 1 expressions with local error:

0.0b
(* a (+ (+ b c) d))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
5×add-sqr-sqrt associate-*r*
3×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt distribute-lft-out
2×associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ insert-posit16 add-log-exp unswap-sqr
Calls
1 calls:
Slowest
92.0ms
(* a (+ (+ b c) d))

series37.0ms

Calls
1 calls:
Slowest
37.0ms
(* a (+ (+ b c) d))

simplify1.1s

Calls
19 calls:
Slowest
384.0ms
(* (* (* a a) a) (* (* (+ (+ b c) d) (+ (+ b c) d)) (+ (+ b c) d)))
259.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
76.0ms
(+ (* a d) (+ (* a b) (* a c)))
76.0ms
(* a (+ (+ b c) d))
53.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune272.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d))))
0.4b
(* (sqrt a) (sqrt (+ (+ b c) d)))
0.4b
(* (sqrt a) (sqrt (+ (+ b c) d)))
0.0b
(sqrt (+ (+ b c) d))

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
68×pow1
41×pow-prod-down
30×add-sqr-sqrt
29×sqrt-prod
28×*-un-lft-identity
21×sqrt-pow1 pow1/2
20×add-cbrt-cube add-exp-log
18×sqrt-div associate-*r/
17×associate-*r*
13×associate-*l* add-cube-cbrt
10×prod-exp cbrt-unprod
9×flip3-+ flip-+ distribute-lft-out
8×pow-prod-up unswap-sqr
7×sqrt-unprod
6×pow-sqr
4×frac-times insert-posit16 add-log-exp
3×*-commutative
2×pow-plus associate-*l/
1×pow2 rem-sqrt-square rem-square-sqrt swap-sqr
Calls
4 calls:
Slowest
142.0ms
(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d))))
49.0ms
(* (sqrt a) (sqrt (+ (+ b c) d)))
45.0ms
(* (sqrt a) (sqrt (+ (+ b c) d)))
34.0ms
(sqrt (+ (+ b c) d))

series605.0ms

Calls
4 calls:
Slowest
227.0ms
(* (sqrt a) (sqrt (+ (+ b c) d)))
214.0ms
(* (sqrt a) (sqrt (+ (+ b c) d)))
87.0ms
(sqrt (+ (+ b c) d))
78.0ms
(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d))))

simplify9.7s

Calls
144 calls:
Slowest
506.0ms
(* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d))))
494.0ms
(* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d))))
486.0ms
(* (* (* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d)))) (* (sqrt a) (sqrt (+ (+ b c) d)))) (* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))))
400.0ms
(* (* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))) (* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))))
344.0ms
(* (* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))) (* (* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d)))) (* (sqrt a) (sqrt (+ (+ b c) d)))))

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))
0.5b
(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))))
0.4b
(* (sqrt a) (sqrt (+ (+ b c) d)))
0.4b
(* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))))

rewrite835.0ms

Algorithm
rewrite-expression-head
Rules
140×sqrt-div
122×sqrt-prod
71×*-un-lft-identity
70×associate-*r/
65×pow1
62×add-sqr-sqrt
42×sqrt-pow1
40×flip3-+ flip-+
38×pow-prod-down
36×frac-times
34×add-cbrt-cube add-exp-log
27×distribute-lft-out
26×pow1/2
24×associate-*l*
23×swap-sqr
22×add-cube-cbrt
21×associate-*r*
20×prod-exp cbrt-unprod
15×unswap-sqr
12×associate-*l/
9×pow-prod-up
8×sqrt-unprod
5×pow-sqr
4×*-commutative insert-posit16 add-log-exp
1×pow2 rem-square-sqrt pow-plus
Calls
4 calls:
Slowest
501.0ms
(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))))
139.0ms
(* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))))
113.0ms
(* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))
76.0ms
(* (sqrt a) (sqrt (+ (+ b c) d)))

series690.0ms

Calls
4 calls:
Slowest
267.0ms
(* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))))
254.0ms
(* (sqrt a) (sqrt (+ (+ b c) d)))
97.0ms
(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))))
72.0ms
(* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))

simplify25.3s

Calls
274 calls:
Slowest
992.0ms
(* (* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))) (* (* (* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))) (* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))))) (* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))))))
748.0ms
(* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))))
529.0ms
(* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d))))
487.0ms
(* (* (* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d)))) (* (sqrt a) (sqrt (+ (+ b c) d)))) (* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))))))
449.0ms
(* (sqrt (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (sqrt (- (* (+ b c) (+ b c)) (* d d)))))

prune3.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

20.0b
(/ (* (+ (* d (* d d)) (* (* (+ c b) (+ c b)) (+ c b))) a) (+ (* d d) (* (+ c b) (- (+ c b) d))))
0.5b
(* (+ (* d (* d d)) (* (* (+ c b) (+ c b)) (+ c b))) a)
0.1b
(* (* (+ c b) (+ c b)) (+ c b))
0.1b
(* d (* d d))

rewrite364.0ms

Algorithm
rewrite-expression-head
Rules
39×pow1
30×flip3-+ flip-+
28×frac-times
21×add-cbrt-cube add-exp-log
18×associate-*l/
14×add-sqr-sqrt
12×*-un-lft-identity
11×pow-prod-up
10×add-cube-cbrt
8×associate-*r* associate-*l* prod-exp associate-*r/ cbrt-unprod
7×pow-plus pow-prod-down
4×insert-posit16 add-log-exp
3×pow2 associate-/r* times-frac pow-sqr *-commutative unswap-sqr
2×cbrt-undiv cube-unmult div-exp pow3 associate-/r/ associate-/l/
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in sum-cubes div-inv distribute-lft-out associate-/l*
Calls
4 calls:
Slowest
186.0ms
(* (+ (* d (* d d)) (* (* (+ c b) (+ c b)) (+ c b))) a)
83.0ms
(/ (* (+ (* d (* d d)) (* (* (+ c b) (+ c b)) (+ c b))) a) (+ (* d d) (* (+ c b) (- (+ c b) d))))
80.0ms
(* (* (+ c b) (+ c b)) (+ c b))
13.0ms
(* d (* d d))

series450.0ms

Calls
4 calls:
Slowest
179.0ms
(* (+ (* d (* d d)) (* (* (+ c b) (+ c b)) (+ c b))) a)
177.0ms
(/ (* (+ (* d (* d d)) (* (* (+ c b) (+ c b)) (+ c b))) a) (+ (* d d) (* (+ c b) (- (+ c b) d))))
49.0ms
(* d (* d d))
46.0ms
(* (* (+ c b) (+ c b)) (+ c b))

simplify22.7s

Calls
126 calls:
Slowest
918.0ms
(* (* (* (* (+ c b) (+ c b)) (* (+ c b) (+ c b))) (* (+ c b) (+ c b))) (* (* (+ c b) (+ c b)) (+ c b)))
779.0ms
(/ (* (* (* (+ (* d (* d d)) (* (* (+ c b) (+ c b)) (+ c b))) a) (* (+ (* d (* d d)) (* (* (+ c b) (+ c b)) (+ c b))) a)) (* (+ (* d (* d d)) (* (* (+ c b) (+ c b)) (+ c b))) a)) (* (* (+ (* d d) (* (+ c b) (- (+ c b) d))) (+ (* d d) (* (+ c b) (- (+ c b) d)))) (+ (* d d) (* (+ c b) (- (+ c b) d)))))
708.0ms
(* (* (+ c b) (- (* c c) (* b b))) (- (* c c) (* b b)))
661.0ms
(* (* (- (* c c) (* b b)) (- (* c c) (* b b))) (+ c b))
590.0ms
(* (* (- (* c c) (* b b)) (- (* c c) (* b b))) (- (* c c) (* b b)))

prune1.8s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes327.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
571.0ms8000×pre80true
535.0ms8000×body80valid