Details

Time bar (total: 2.5m)

sample113.0ms

Algorithm
intervals
Results
60.0ms298×body80valid
19.0ms104×body80nan

simplify203.0ms

Calls
1 calls:
Slowest
203.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.8b

localize49.0ms

Local error

Found 4 expressions with local error:

9.3b
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
4.2b
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))
3.5b
(/ (* M D) (* 2 d))
3.5b
(/ (* M D) (* 2 d))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
26×add-cbrt-cube add-exp-log
11×cbrt-undiv div-exp
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×associate-/r* times-frac
5×div-inv
4×expm1-log1p-u pow1 prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg sqrt-prod associate-/l* associate-/l/
2×sqrt-div
1×frac-times rem-sqrt-square flip3-- pow1/2 associate-*l/ associate-*r/ associate-/r/ flip--
Calls
4 calls:
Slowest
24.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
13.0ms
(/ (* M D) (* 2 d))
7.0ms
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))
7.0ms
(/ (* M D) (* 2 d))

series286.0ms

Calls
4 calls:
Slowest
146.0ms
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))
98.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
21.0ms
(/ (* M D) (* 2 d))
21.0ms
(/ (* M D) (* 2 d))

simplify25.5s

Calls
52 calls:
Slowest
4.0s
(/ (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h)))
3.5s
(/ (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h)))
2.7s
(/ (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h)))
1.3s
(/ (/ (* M D) (* 2 d)) (sqrt (/ l h)))
1.1s
(- (+ (log (/ (* M D) (* 2 d))) (log (/ (* M D) (* 2 d)))) (log (/ l h)))

prune3.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize34.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (/ (* M D) (* 2 d)) (/ 1 h))
4.2b
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))
4.2b
(/ (/ (* M D) (* 2 d)) l)
3.5b
(/ (* M D) (* 2 d))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
27×times-frac
18×add-sqr-sqrt
17×*-un-lft-identity add-cube-cbrt
15×div-inv
11×add-cbrt-cube add-exp-log associate-/l*
5×associate-/r*
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg sqrt-prod
2×sqrt-div associate-/l/
1×rem-sqrt-square flip3-- pow1/2 associate-/r/ flip--
Calls
4 calls:
Slowest
15.0ms
(/ (/ (* M D) (* 2 d)) l)
10.0ms
(/ (/ (* M D) (* 2 d)) (/ 1 h))
7.0ms
(/ (* M D) (* 2 d))
4.0ms
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))

series286.0ms

Calls
4 calls:
Slowest
165.0ms
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))
51.0ms
(/ (/ (* M D) (* 2 d)) (/ 1 h))
43.0ms
(/ (/ (* M D) (* 2 d)) l)
27.0ms
(/ (* M D) (* 2 d))

simplify20.4s

Calls
80 calls:
Slowest
1.6s
(/ (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (/ 1 h) (/ 1 h)) (/ 1 h)))
1.5s
(sqrt (- (pow 1 3) (pow (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h))) 3)))
1.3s
(/ (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (/ 1 h) (/ 1 h)) (/ 1 h)))
1.0s
(* 1/2 (/ (* M D) (* l d)))
947.0ms
(* 1/2 (/ (* M (* D h)) d))

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize35.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))
4.2b
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
4.2b
(/ (/ (* M D) (* 2 d)) l)
3.5b
(/ (* M D) (* 2 d))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
22×times-frac
18×add-sqr-sqrt
17×*-un-lft-identity add-cube-cbrt
15×div-inv
13×add-exp-log
11×associate-/l*
8×add-cbrt-cube
6×associate-/r/
5×associate-/r* div-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg sqrt-prod
2×cbrt-undiv rec-exp sqrt-div associate-/l/
1×rem-sqrt-square flip3-- pow1/2 flip--
Calls
4 calls:
Slowest
12.0ms
(/ (/ (* M D) (* 2 d)) l)
10.0ms
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))
7.0ms
(/ (* M D) (* 2 d))
4.0ms
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))

series268.0ms

Calls
4 calls:
Slowest
149.0ms
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
52.0ms
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))
38.0ms
(/ (/ (* M D) (* 2 d)) l)
28.0ms
(/ (* M D) (* 2 d))

simplify31.0s

Calls
78 calls:
Slowest
1.7s
(* (cbrt (/ 1 (/ (* 2 d) (* M D)))) (cbrt (/ 1 (/ (* 2 d) (* M D)))))
1.4s
(/ (cbrt (/ 1 (/ (* 2 d) (* M D)))) (cbrt (/ 1 h)))
1.4s
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
1.2s
(/ (sqrt (/ 1 (/ (* 2 d) (* M D)))) (sqrt (/ 1 h)))
1.0s
(sqrt (- (pow 1 3) (pow (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))) 3)))

prune4.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize38.0ms

Local error

Found 4 expressions with local error:

5.8b
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
5.8b
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
5.8b
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
4.5b
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
20×times-frac
18×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×div-inv
11×add-exp-log
9×cbrt-prod
6×cbrt-div add-cbrt-cube associate-/r/
5×associate-/l*
4×expm1-log1p-u pow1 associate-/r* div-exp insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip--
2×rec-exp
1×cbrt-undiv clear-num frac-2neg associate-/l/
Calls
4 calls:
Slowest
10.0ms
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))
2.0ms
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
2.0ms
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
2.0ms
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))

series919.0ms

Calls
4 calls:
Slowest
338.0ms
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
267.0ms
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
265.0ms
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
50.0ms
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))

simplify42.3s

Calls
78 calls:
Slowest
2.4s
(cbrt (- (pow 1 3) (pow (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))) 3)))
1.9s
(cbrt (- (pow 1 3) (pow (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))) 3)))
1.8s
(/ (cbrt (/ 1 (/ (* 2 d) (* M D)))) (sqrt (/ 1 h)))
1.7s
(/ (sqrt (/ 1 (/ (* 2 d) (* M D)))) (cbrt (/ 1 h)))
1.6s
(cbrt (- (* 1 1) (* (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))) (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))))))

prune5.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

regimes2.3s

Accuracy

0% (1.4b remaining)

Error of 8.7b against oracle of 7.3b and baseline of 8.7b

bsearch23.0ms

end0.0ms

sample7.1s

Algorithm
intervals
Results
5.1s9310×body80valid
1.2s3150×body80nan