Details

Time bar (total: 1.1m)

sample670.0ms

Algorithm
intervals
Results
424.0ms1128×body80nan
182.0ms393×body80valid

simplify271.0ms

Calls
1 calls:
Slowest
271.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.6b

localize81.0ms

Local error

Found 4 expressions with local error:

13.5b
(pow (/ d l) (/ 1 2))
13.2b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.2b
(pow (/ d h) (/ 1 2))
6.5b
(/ (* M D) (* 2 d))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
11×add-cbrt-cube
9×add-sqr-sqrt *-un-lft-identity prod-exp add-cube-cbrt
8×pow1 pow-unpow unpow-prod-down
6×div-inv
4×expm1-log1p-u associate-*r* pow-exp insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp associate-*l/ cbrt-unprod
2×pow-pow div-exp
1×frac-times cbrt-undiv clear-num associate-/r* frac-2neg times-frac associate-*l* pow-prod-down associate-*r/ *-commutative associate-/l*
Calls
4 calls:
Slowest
17.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
4.0ms
(pow (/ d l) (/ 1 2))
3.0ms
(/ (* M D) (* 2 d))
2.0ms
(pow (/ d h) (/ 1 2))

series232.0ms

Calls
4 calls:
Slowest
86.0ms
(pow (/ d h) (/ 1 2))
71.0ms
(pow (/ d l) (/ 1 2))
58.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
17.0ms
(/ (* M D) (* 2 d))

simplify5.5s

Calls
52 calls:
Slowest
616.0ms
(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ h l) (/ h l)) (/ h l)))
428.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
416.0ms
(* (* (* (* (/ 1 2) (/ 1 2)) (/ 1 2)) (* (* (pow (/ (* M D) (* 2 d)) 2) (pow (/ (* M D) (* 2 d)) 2)) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ h l) (/ h l)) (/ h l)))
283.0ms
(+ (+ (log (/ 1 2)) (* (log (/ (* M D) (* 2 d))) 2)) (log (/ h l)))
274.0ms
(+ (+ (log (/ 1 2)) (* (log (/ (* M D) (* 2 d))) 2)) (log (/ h l)))

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 18.4b

localize13.0ms

Local error

Found 4 expressions with local error:

13.5b
(pow (/ d l) (/ 1 2))
11.2b
(pow (/ d h) (/ 1 2))
6.5b
(/ (* M D) (* 2 d))
6.1b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt pow-unpow unpow-prod-down *-un-lft-identity add-exp-log add-cube-cbrt
6×pow1 add-cbrt-cube
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp pow-pow associate-*l/ pow-exp
1×cbrt-undiv clear-num associate-/r* frac-2neg times-frac div-exp associate-*l* *-commutative associate-/l*
Calls
4 calls:
Slowest
20.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
5.0ms
(/ (* M D) (* 2 d))
2.0ms
(pow (/ d l) (/ 1 2))
2.0ms
(pow (/ d h) (/ 1 2))

series254.0ms

Calls
4 calls:
Slowest
98.0ms
(pow (/ d l) (/ 1 2))
73.0ms
(pow (/ d h) (/ 1 2))
61.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
22.0ms
(/ (* M D) (* 2 d))

simplify4.2s

Calls
38 calls:
Slowest
861.0ms
(* 1/8 (/ (* (pow M 2) (* (pow D 2) h)) (pow d 2)))
490.0ms
(* 1/8 (/ (* (pow M 2) (* (pow D 2) h)) (pow d 2)))
488.0ms
(* 1/8 (/ (* (pow M 2) (* (pow D 2) h)) (pow d 2)))
446.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
268.0ms
(exp (* 1/2 (- (log (/ 1 l)) (log (/ 1 d)))))

prune1.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 17.2b

localize21.0ms

Local error

Found 4 expressions with local error:

13.5b
(pow (/ d l) (/ 1 2))
11.2b
(sqrt (/ (/ -1 h) (/ -1 d)))
6.5b
(/ (* M D) (* 2 d))
6.1b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
21×sqrt-prod
18×add-sqr-sqrt times-frac
15×*-un-lft-identity add-cube-cbrt
12×div-inv
7×add-exp-log
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u pow-unpow unpow-prod-down insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square associate-*l/
1×pow-to-exp cbrt-undiv clear-num associate-/r* pow-pow frac-2neg pow1/2 sqrt-div div-exp associate-*l* pow-exp associate-/r/ *-commutative associate-/l*
Calls
4 calls:
Slowest
21.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
7.0ms
(pow (/ d l) (/ 1 2))
7.0ms
(/ (* M D) (* 2 d))
3.0ms
(sqrt (/ (/ -1 h) (/ -1 d)))

series184.0ms

Calls
4 calls:
Slowest
72.0ms
(pow (/ d l) (/ 1 2))
66.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
28.0ms
(sqrt (/ (/ -1 h) (/ -1 d)))
17.0ms
(/ (* M D) (* 2 d))

simplify3.8s

Calls
52 calls:
Slowest
535.0ms
(* 1/8 (/ (* (pow M 2) (* (pow D 2) h)) (pow d 2)))
495.0ms
(* 1/8 (/ (* (pow M 2) (* (pow D 2) h)) (pow d 2)))
488.0ms
(* 1/8 (/ (* (pow M 2) (* (pow D 2) h)) (pow d 2)))
417.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
232.0ms
(exp (* 1/2 (- (log (/ -1 l)) (log (/ -1 d)))))

prune1.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 14.2b

localize34.0ms

Local error

Found 4 expressions with local error:

13.5b
(pow (/ d l) (/ 1 2))
6.5b
(/ (* M D) (* 2 d))
6.1b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
5.8b
(* (* (* (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d))))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
16×prod-exp
15×add-cbrt-cube
7×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
6×associate-*l/ cbrt-unprod
5×associate-*r/
4×expm1-log1p-u pow-unpow unpow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp sqrt-div associate-*r* pow-exp div-inv
2×distribute-rgt-in frac-times sub-neg distribute-lft-in flip3-- associate-*l* *-commutative flip--
1×cbrt-undiv clear-num associate-/r* pow-pow frac-2neg times-frac div-exp pow-prod-down associate-/l*
Calls
4 calls:
Slowest
93.0ms
(* (* (* (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d))))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))))
25.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
6.0ms
(/ (* M D) (* 2 d))
3.0ms
(pow (/ d l) (/ 1 2))

series1.1s

Calls
4 calls:
Slowest
920.0ms
(* (* (* (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d))))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))))
80.0ms
(pow (/ d l) (/ 1 2))
53.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
23.0ms
(/ (* M D) (* 2 d))

simplify15.5s

Calls
54 calls:
Slowest
1.1s
(* (* (* (* (* (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d))))) (* (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))))) (* (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))))) (* (* (pow (/ d l) (/ 1 2)) (pow (/ d l) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l)))))
1.0s
(* (* (* (* (* (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d))))) (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d))))) (* (* (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d))))) (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))))) (* (* (pow (/ d l) (/ 1 2)) (pow (/ d l) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l)))))
813.0ms
(* (* (* (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (sqrt (cbrt (/ -1 h)))) (pow (/ d l) (/ 1 2))) (- (pow 1 3) (pow (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l)) 3)))
796.0ms
(* (* (* (* (* (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d))))) (pow (/ d l) (/ 1 2))) (* (* (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d))))) (pow (/ d l) (/ 1 2)))) (* (* (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d))))) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l)))))
627.0ms
(* (- (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))) (* (* (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d))))) (pow (/ d l) (/ 1 2))))

prune2.3s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 13.0b

regimes2.5s

Accuracy

40.8% (4.2b remaining)

Error of 16.6b against oracle of 12.4b and baseline of 19.5b

bsearch992.0ms

end0.0ms

sample23.9s

Algorithm
intervals
Results
15.1s38613×body80nan
6.9s12916×body80valid