Details

Time bar (total: 30.4s)

sample55.0ms

Algorithm
intervals
Results
21.0ms256×pre80true
17.0ms256×body80valid

simplify116.0ms

Calls
1 calls:
Slowest
116.0ms
(* a (+ (+ b c) d))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×fma-def associate-*r*
2×expm1-log1p-u pow1 flip3-+ add-cbrt-cube associate-*r/ add-exp-log flip-+ insert-posit16 log1p-expm1-u add-log-exp
1×distribute-rgt-in +-commutative associate-+l+ distribute-lft-in *-commutative
Calls
2 calls:
Slowest
6.0ms
(+ (+ b c) d)
5.0ms
(* a (+ (+ b c) d))

series71.0ms

Calls
2 calls:
Slowest
46.0ms
(* a (+ (+ b c) d))
24.0ms
(+ (+ b c) d)

simplify635.0ms

Calls
15 calls:
Slowest
269.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
92.0ms
(+ (* a d) (+ (* a b) (* a c)))
91.0ms
(+ (* a d) (+ (* a b) (* a c)))
31.0ms
(- (+ b c) d)
26.0ms
(cbrt (+ (+ b c) d))

prune366.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
4×add-log-exp
3×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
2×expm1-log1p-u pow1 flip3-+ add-cbrt-cube associate-*l/ add-exp-log flip-+ insert-posit16 log1p-expm1-u
1×+-commutative sum-log fma-def distribute-rgt-out *-commutative
Calls
2 calls:
Slowest
10.0ms
(+ (* (+ b c) a) (* d a))
6.0ms
(* (+ b c) a)

series84.0ms

Calls
2 calls:
Slowest
48.0ms
(+ (* (+ b c) a) (* d a))
35.0ms
(* (+ b c) a)

simplify803.0ms

Calls
13 calls:
Slowest
208.0ms
(* (- (* b b) (* c c)) a)
192.0ms
(* (exp (* (+ b c) a)) (exp (* d a)))
121.0ms
(+ (* a d) (+ (* a b) (* a c)))
121.0ms
(+ (* a d) (+ (* a b) (* a c)))
77.0ms
(* (+ (pow b 3) (pow c 3)) a)

prune416.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))
0.3b
(* a (sqrt (+ (+ b c) d)))
0.0b
(sqrt (+ (+ b c) d))
0.0b
(sqrt (+ (+ b c) d))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-div
12×add-sqr-sqrt associate-*r* sqrt-prod
10×*-un-lft-identity associate-*r/ add-cube-cbrt
9×flip3-+ flip-+
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square pow1/2 associate-*l/ *-commutative
1×associate-*l* pow-prod-down prod-exp cbrt-unprod
Calls
4 calls:
Slowest
23.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))
6.0ms
(* a (sqrt (+ (+ b c) d)))
4.0ms
(sqrt (+ (+ b c) d))
4.0ms
(sqrt (+ (+ b c) d))

series382.0ms

Calls
4 calls:
Slowest
130.0ms
(* a (sqrt (+ (+ b c) d)))
121.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))
69.0ms
(sqrt (+ (+ b c) d))
62.0ms
(sqrt (+ (+ b c) d))

simplify5.7s

Calls
53 calls:
Slowest
611.0ms
(* (sqrt (+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))) (sqrt (+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))))
596.0ms
(sqrt (+ (pow (+ b c) 3) (pow d 3)))
527.0ms
(sqrt (+ (pow (+ b c) 3) (pow d 3)))
417.0ms
(* (* a (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (- (* (+ b c) (+ b c)) (* d d))))
348.0ms
(* (* a (sqrt (- (* (+ b c) (+ b c)) (* d d)))) (sqrt (+ (pow (+ b c) 3) (pow d 3))))

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (* a (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))) (sqrt (sqrt (+ (+ b c) d))))
0.3b
(* (* a (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))
0.3b
(* a (sqrt (+ (+ b c) d)))
0.1b
(sqrt (sqrt (+ (+ b c) d)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
114×sqrt-div
36×associate-*r/
35×flip3-+ flip-+
32×frac-times
31×sqrt-prod
24×associate-*r*
16×add-sqr-sqrt associate-*l/
14×*-un-lft-identity add-cube-cbrt
11×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×rem-sqrt-square associate-*l*
1×pow1/2
Calls
4 calls:
Slowest
87.0ms
(* (* (* a (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))) (sqrt (sqrt (+ (+ b c) d))))
19.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))
7.0ms
(* a (sqrt (+ (+ b c) d)))
5.0ms
(sqrt (sqrt (+ (+ b c) d)))

series1.5s

Calls
4 calls:
Slowest
831.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))
450.0ms
(sqrt (sqrt (+ (+ b c) d)))
121.0ms
(* a (sqrt (+ (+ b c) d)))
99.0ms
(* (* (* a (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))) (sqrt (sqrt (+ (+ b c) d))))

simplify16.1s

Calls
112 calls:
Slowest
551.0ms
(* (* a (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (sqrt (+ (pow (+ b c) 3) (pow d 3)))))
513.0ms
(* (* (* a (sqrt (- (* (+ b c) (+ b c)) (* d d)))) (sqrt (sqrt (+ (pow (+ b c) 3) (pow d 3))))) (sqrt (sqrt (+ (pow (+ b c) 3) (pow d 3)))))
511.0ms
(* (* (* a (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (sqrt (+ (pow (+ b c) 3) (pow d 3))))) (sqrt (sqrt (- (* (+ b c) (+ b c)) (* d d)))))
507.0ms
(sqrt (sqrt (+ (pow (+ b c) 3) (pow d 3))))
496.0ms
(* (* (* a (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (sqrt (- (* (+ b c) (+ b c)) (* d d))))) (sqrt (sqrt (+ (pow (+ b c) 3) (pow d 3)))))

prune1.5s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes292.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.0s

Algorithm
intervals
Results
511.0ms8000×pre80true
394.0ms8000×body80valid