Details

Time bar (total: 1.2m)

sample35.0ms

Algorithm
intervals
Results
11.0ms256×pre80true
11.0ms256×body80valid

simplify247.0ms

Calls
1 calls:
Slowest
247.0ms
(* (+ a (+ b (+ c d))) 2)

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize21.0ms

Local error

Found 2 expressions with local error:

2.7b
(+ a (+ b (+ c d)))
0.5b
(+ b (+ c d))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
2×add-sqr-sqrt pow1 +-commutative associate-+r+ *-un-lft-identity flip3-+ add-cbrt-cube add-exp-log add-cube-cbrt flip-+ insert-posit16 add-log-exp
Calls
2 calls:
Slowest
2.0ms
(+ a (+ b (+ c d)))
1.0ms
(+ b (+ c d))

series35.0ms

Calls
2 calls:
Slowest
24.0ms
(+ a (+ b (+ c d)))
11.0ms
(+ b (+ c d))

simplify106.0ms

Calls
7 calls:
Slowest
21.0ms
(+ a (+ b c))
21.0ms
(+ b (+ c d))
19.0ms
(+ b (+ c d))
14.0ms
(+ b (+ c d))
13.0ms
(+ b (+ c d))

prune279.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

localize19.0ms

Local error

Found 1 expressions with local error:

2.7b
(+ a (+ (+ b c) d))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
1×add-sqr-sqrt pow1 +-commutative associate-+r+ *-un-lft-identity flip3-+ add-cbrt-cube add-exp-log add-cube-cbrt flip-+ insert-posit16 add-log-exp
Calls
1 calls:
Slowest
5.0ms
(+ a (+ (+ b c) d))

series30.0ms

Calls
1 calls:
Slowest
30.0ms
(+ a (+ (+ b c) d))

simplify57.0ms

Calls
3 calls:
Slowest
19.0ms
(+ b (+ c d))
19.0ms
(+ b (+ c d))
19.0ms
(+ a (+ b c))

prune160.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 1.9b

localize13.0ms

Local error

Found 4 expressions with local error:

2.7b
(+ a (+ (+ b c) d))
2.7b
(+ a (+ (+ b c) d))
2.7b
(+ a (+ (+ b c) d))
0.6b
(cbrt (* (* (+ a (+ (+ b c) d)) (+ a (+ (+ b c) d))) (+ a (+ (+ b c) d))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
30×flip3-+ flip-+
28×frac-times
26×cbrt-div
14×associate-*l/
8×associate-*r/
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
3×+-commutative associate-+r+
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Calls
4 calls:
Slowest
31.0ms
(cbrt (* (* (+ a (+ (+ b c) d)) (+ a (+ (+ b c) d))) (+ a (+ (+ b c) d))))
3.0ms
(+ a (+ (+ b c) d))
3.0ms
(+ a (+ (+ b c) d))
3.0ms
(+ a (+ (+ b c) d))

series129.0ms

Calls
4 calls:
Slowest
57.0ms
(cbrt (* (* (+ a (+ (+ b c) d)) (+ a (+ (+ b c) d))) (+ a (+ (+ b c) d))))
30.0ms
(+ a (+ (+ b c) d))
21.0ms
(+ a (+ (+ b c) d))
21.0ms
(+ a (+ (+ b c) d))

simplify10.7s

Calls
39 calls:
Slowest
923.0ms
(cbrt (* (* (+ a (+ (+ b c) d)) (+ (pow a 3) (pow (+ (+ b c) d) 3))) (+ (pow a 3) (pow (+ (+ b c) d) 3))))
630.0ms
(cbrt (* (* (- (* a a) (* (+ (+ b c) d) (+ (+ b c) d))) (+ a (+ (+ b c) d))) (+ (pow a 3) (pow (+ (+ b c) d) 3))))
518.0ms
(cbrt (* (* (+ a (+ (+ b c) d)) (+ (pow a 3) (pow (+ (+ b c) d) 3))) (- (* a a) (* (+ (+ b c) d) (+ (+ b c) d)))))
516.0ms
(cbrt (* (* (- (* a a) (* (+ (+ b c) d) (+ (+ b c) d))) (+ (pow a 3) (pow (+ (+ b c) d) 3))) (+ (pow a 3) (pow (+ (+ b c) d) 3))))
489.0ms
(cbrt (* (* (- (* a a) (* (+ (+ b c) d) (+ (+ b c) d))) (+ (pow a 3) (pow (+ (+ b c) d) 3))) (+ a (+ (+ b c) d))))

prune946.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 1.4b

localize92.0ms

Local error

Found 4 expressions with local error:

2.4b
(+ (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* a (* a a)))
2.4b
(+ (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* a (* a a)))
0.5b
(* (+ (* a a) (- (* (+ (+ b c) d) (+ (+ b c) d)) (* a (+ (+ b c) d)))) (+ (* a a) (- (* (+ (+ b c) d) (+ (+ b c) d)) (* a (+ (+ b c) d)))))
0.5b
(cbrt (* (* (+ (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* a (* a a))) (+ (+ a d) (+ b c))) (+ (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* a (* a a)))))

rewrite375.0ms

Algorithm
rewrite-expression-head
Rules
95×flip3-+ flip-+
80×frac-times
62×cbrt-div
36×frac-add
28×associate-*l/
22×associate-*r/
9×distribute-rgt-in pow1 distribute-lft-in
8×associate-+l+ add-log-exp
6×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×cube-unmult insert-posit16
3×associate-*r* associate-*l*
2×+-commutative sum-log sum-cubes
1×cbrt-prod pow2 pow-plus pow1/3 pow-prod-down prod-exp *-commutative pow-prod-up cbrt-unprod
Calls
4 calls:
Slowest
180.0ms
(cbrt (* (* (+ (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* a (* a a))) (+ (+ a d) (+ b c))) (+ (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* a (* a a)))))
100.0ms
(* (+ (* a a) (- (* (+ (+ b c) d) (+ (+ b c) d)) (* a (+ (+ b c) d)))) (+ (* a a) (- (* (+ (+ b c) d) (+ (+ b c) d)) (* a (+ (+ b c) d)))))
45.0ms
(+ (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* a (* a a)))
44.0ms
(+ (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* a (* a a)))

series3.4s

Calls
4 calls:
Slowest
1.5s
(* (+ (* a a) (- (* (+ (+ b c) d) (+ (+ b c) d)) (* a (+ (+ b c) d)))) (+ (* a a) (- (* (+ (+ b c) d) (+ (+ b c) d)) (* a (+ (+ b c) d)))))
693.0ms
(cbrt (* (* (+ (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* a (* a a))) (+ (+ a d) (+ b c))) (+ (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* a (* a a)))))
570.0ms
(+ (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* a (* a a)))
544.0ms
(+ (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* a (* a a)))

simplify48.6s

Calls
114 calls:
Slowest
1.6s
(cbrt (* (* (+ (pow (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) 3) (pow (* a (* a a)) 3)) (+ (* (- (* a a) (* d d)) (- b c)) (* (- a d) (- (* b b) (* c c))))) (+ (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* a (* a a)))))
1.5s
(cbrt (* (* (+ (pow (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) 3) (pow (* a (* a a)) 3)) (+ (* (- (* a a) (* d d)) (- b c)) (* (- a d) (- (* b b) (* c c))))) (- (* (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d)))) (* (* a (* a a)) (* a (* a a))))))
1.4s
(cbrt (* (* (+ (pow (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) 3) (pow (* a (* a a)) 3)) (+ (* (- (* a a) (* d d)) (- b c)) (* (- a d) (- (* b b) (* c c))))) (+ (pow (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) 3) (pow (* a (* a a)) 3))))
1.4s
(cbrt (* (* (+ (pow (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) 3) (pow (* a (* a a)) 3)) (+ (* (+ (pow a 3) (pow d 3)) (- b c)) (* (+ (* a a) (- (* d d) (* a d))) (- (* b b) (* c c))))) (+ (pow (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) 3) (pow (* a (* a a)) 3))))
1.3s
(cbrt (* (* (+ (pow (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) 3) (pow (* a (* a a)) 3)) (+ (* (+ (pow a 3) (pow d 3)) (- b c)) (* (+ (* a a) (- (* d d) (* a d))) (- (* b b) (* c c))))) (- (* (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d))) (* (+ (+ b c) d) (* (+ (+ b c) d) (+ (+ b c) d)))) (* (* a (* a a)) (* a (* a a))))))

prune2.7s

Pruning

36 alts after pruning (35 fresh and 1 done)

Merged error: 0.8b

regimes2.4s

Accuracy

0% (1.6b remaining)

Error of 2.7b against oracle of 1.1b and baseline of 2.7b

bsearch9.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
624.0ms8000×body80valid
402.0ms8000×pre80true