Details

Time bar (total: 2.5m)

sample107.0ms

Algorithm
intervals
Results
52.0ms293×body80valid
19.0ms105×body80nan

simplify174.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
173.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.3b

localize60.0ms

Local error

Found 4 expressions with local error:

9.0b
(* (/ h l) (/ (* M D) (* 2 d)))
3.5b
(/ (* M D) (* 2 d))
3.5b
(/ (* M D) (* 2 d))
3.3b
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
69×add-cbrt-cube add-exp-log
26×prod-exp cbrt-unprod
21×cbrt-undiv div-exp
19×add-sqr-sqrt
13×*-un-lft-identity times-frac associate-*l* add-cube-cbrt
7×pow1
5×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×sqrt-prod
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l* unswap-sqr
1×frac-times rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 121
Calls
4 calls:
Slowest
36.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
18.0ms
(/ (* M D) (* 2 d))
11.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
11.0ms
(/ (* M D) (* 2 d))

series390.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
185.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
105.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
51.0ms
(/ (* M D) (* 2 d))
48.0ms
(/ (* M D) (* 2 d))

simplify37.9s

Counts
142 → 133
Calls
142 calls:
Slowest
1.4s
(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.2s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.2s
(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.1s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
1.1s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize59.0ms

Local error

Found 4 expressions with local error:

5.4b
(/ (* h (/ (* M D) (* 2 d))) l)
4.5b
(* h (/ (* M D) (* 2 d)))
3.5b
(/ (* M D) (* 2 d))
3.5b
(/ (* M D) (* 2 d))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
71×add-cbrt-cube add-exp-log
26×prod-exp cbrt-unprod
22×cbrt-undiv div-exp
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×pow1 times-frac
5×associate-/r* associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×clear-num frac-2neg associate-*l* associate-/l*
2×associate-*r/
1×pow-prod-down *-commutative unswap-sqr associate-/l/
Counts
4 → 113
Calls
4 calls:
Slowest
27.0ms
(/ (* M D) (* 2 d))
26.0ms
(* h (/ (* M D) (* 2 d)))
23.0ms
(/ (* M D) (* 2 d))
21.0ms
(/ (* h (/ (* M D) (* 2 d))) l)

series232.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
81.0ms
(/ (* h (/ (* M D) (* 2 d))) l)
69.0ms
(* h (/ (* M D) (* 2 d)))
50.0ms
(/ (* M D) (* 2 d))
32.0ms
(/ (* M D) (* 2 d))

simplify34.4s

Counts
133 → 125
Calls
133 calls:
Slowest
1.5s
(/ (* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* l l) l))
1.3s
(/ (* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* l l) l))
1.2s
(/ (* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* l l) l))
1.2s
(/ (* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* l l) l))
1.1s
(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize45.0ms

Local error

Found 4 expressions with local error:

5.4b
(/ (* h (/ (* M D) (* 2 d))) l)
4.5b
(* h (/ (* M D) (* 2 d)))
3.6b
(/ M (/ (* 2 d) D))
3.5b
(/ (* M D) (* 2 d))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
68×add-cbrt-cube add-exp-log
38×times-frac
26×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
23×cbrt-undiv div-exp prod-exp cbrt-unprod
11×associate-/r*
8×div-inv
6×pow1
5×associate-*r* associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*l*
2×associate-*r/
1×pow-prod-down associate-/r/ *-commutative unswap-sqr associate-/l/
Counts
4 → 140
Calls
4 calls:
Slowest
42.0ms
(/ (* h (/ (* M D) (* 2 d))) l)
40.0ms
(* h (/ (* M D) (* 2 d)))
14.0ms
(/ (* M D) (* 2 d))
7.0ms
(/ M (/ (* 2 d) D))

series271.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(/ (* h (/ (* M D) (* 2 d))) l)
72.0ms
(* h (/ (* M D) (* 2 d)))
48.0ms
(/ (* M D) (* 2 d))
45.0ms
(/ M (/ (* 2 d) D))

simplify36.4s

Counts
180 → 152
Calls
180 calls:
Slowest
1.6s
(/ (* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* l l) l))
1.5s
(/ (* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* l l) l))
1.3s
(/ (* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* l l) l))
1.1s
(/ (* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* l l) l))
1.0s
(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize85.0ms

Local error

Found 4 expressions with local error:

23.3b
(cbrt (* h (/ (* M D) (* 2 d))))
23.3b
(cbrt (* h (/ (* M D) (* 2 d))))
23.3b
(cbrt (* h (/ (* M D) (* 2 d))))
5.4b
(/ (* (* (cbrt (* h (/ (* M D) (* 2 d)))) (cbrt (* h (/ (* M D) (* 2 d))))) (cbrt (* h (/ (* M D) (* 2 d))))) l)

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
15×cbrt-div
13×add-exp-log
9×add-cbrt-cube
7×associate-/l/
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×frac-times associate-*l/
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod cbrt-undiv associate-/r* times-frac pow1/3 div-exp prod-exp cbrt-unprod
1×clear-num frac-2neg div-inv associate-/l*
Counts
4 → 72
Calls
4 calls:
Slowest
58.0ms
(/ (* (* (cbrt (* h (/ (* M D) (* 2 d)))) (cbrt (* h (/ (* M D) (* 2 d))))) (cbrt (* h (/ (* M D) (* 2 d))))) l)
27.0ms
(cbrt (* h (/ (* M D) (* 2 d))))
19.0ms
(cbrt (* h (/ (* M D) (* 2 d))))
12.0ms
(cbrt (* h (/ (* M D) (* 2 d))))

series787.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
236.0ms
(/ (* (* (cbrt (* h (/ (* M D) (* 2 d)))) (cbrt (* h (/ (* M D) (* 2 d))))) (cbrt (* h (/ (* M D) (* 2 d))))) l)
200.0ms
(cbrt (* h (/ (* M D) (* 2 d))))
190.0ms
(cbrt (* h (/ (* M D) (* 2 d))))
161.0ms
(cbrt (* h (/ (* M D) (* 2 d))))

simplify22.4s

Counts
91 → 84
Calls
91 calls:
Slowest
1.3s
(/ (* (* (* h (/ (* M D) (* 2 d))) (* h (/ (* M D) (* 2 d)))) (* h (/ (* M D) (* 2 d)))) (* (* l l) l))
455.0ms
(/ (* (* (* (* (cbrt (* h (/ (* M D) (* 2 d)))) (cbrt (* h (/ (* M D) (* 2 d))))) (* (cbrt (* h (/ (* M D) (* 2 d)))) (cbrt (* h (/ (* M D) (* 2 d)))))) (* (cbrt (* h (/ (* M D) (* 2 d)))) (cbrt (* h (/ (* M D) (* 2 d)))))) (* h (/ (* M D) (* 2 d)))) (* (* l l) l))
433.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 d)) (+ (log (/ 1 h)) (+ (log (/ 1 M)) (log (/ 1 D))))))))
431.0ms
(* (cbrt (cbrt (* h (/ (* M D) (* 2 d))))) (cbrt (cbrt (* h (/ (* M D) (* 2 d))))))
398.0ms
(log (cbrt (* h (/ (* M D) (* 2 d)))))

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.5b

regimes1.6s

Accuracy

0% (2.0b remaining)

Error of 9.1b against oracle of 7.0b and baseline of 9.1b

bsearch6.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.8s9325×body80valid
554.0ms3061×body80nan