Details

Time bar (total: 3.4m)

sample74.0ms

Algorithm
intervals
Results
41.0ms296×body80valid
12.0ms102×body80nan

simplify165.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
165.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize52.0ms

Local error

Found 4 expressions with local error:

10.4b
(* (/ h l) (/ (* M D) (* 2 d)))
4.5b
(/ (* M D) (* 2 d))
4.5b
(/ (* M D) (* 2 d))
4.3b
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

rewrite96.0ms

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
56.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
22.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
5.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
219.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
100.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
44.0ms
(/ (* M D) (* 2 d))
31.0ms
(/ (* M D) (* 2 d))

simplify40.4s

Counts
142 → 133
Calls
142 calls:
Slowest
1.4s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.4s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))))
1.4s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.3s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
1.3s
(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize31.0ms

Local error

Found 4 expressions with local error:

5.8b
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
5.0b
(* (/ 1 l) (/ (* M D) (* 2 d)))
4.5b
(/ (* M D) (* 2 d))
4.5b
(/ (* M D) (* 2 d))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
204×add-exp-log
122×add-cbrt-cube
101×prod-exp
60×div-exp
55×cbrt-unprod
34×cbrt-undiv
20×add-sqr-sqrt
16×associate-*l*
14×*-un-lft-identity times-frac
13×add-cube-cbrt
11×pow1
10×rec-exp 1-exp
6×associate-*r*
5×associate-*r/
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u div-inv add-log-exp
3×unswap-sqr
2×frac-times clear-num associate-/r* frac-2neg associate-*l/ *-commutative associate-/l*
Counts
4 → 166
Calls
4 calls:
Slowest
75.0ms
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
25.0ms
(* (/ 1 l) (/ (* M D) (* 2 d)))
13.0ms
(/ (* M D) (* 2 d))
12.0ms
(/ (* M D) (* 2 d))

series252.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
93.0ms
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
72.0ms
(* (/ 1 l) (/ (* M D) (* 2 d)))
49.0ms
(/ (* M D) (* 2 d))
37.0ms
(/ (* M D) (* 2 d))

simplify1.0m

Counts
184 → 178
Calls
184 calls:
Slowest
2.2s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.7s
(* (* (* h h) h) (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.7s
(* (* (* h h) h) (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.7s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))))
1.7s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))

prune3.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize54.0ms

Local error

Found 4 expressions with local error:

5.8b
(* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d)))))
4.5b
(/ (* M D) (* 2 d))
4.5b
(/ (* M D) (* 2 d))
4.3b
(sqrt (- 1 (* (* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d)))))

rewrite365.0ms

Algorithm
rewrite-expression-head
Rules
98×add-exp-log
76×add-cbrt-cube
57×prod-exp cbrt-unprod
26×associate-*r/
24×cbrt-div
23×pow1
17×frac-times
16×cbrt-undiv div-exp
13×pow-prod-down
11×associate-*l/
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* sqrt-prod
2×clear-num associate-/r* frac-2neg times-frac sqrt-div div-inv associate-/l*
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*r* *-commutative flip--
Counts
4 → 127
Calls
4 calls:
Slowest
304.0ms
(* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d)))))
23.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* M D) (* 2 d))
11.0ms
(sqrt (- 1 (* (* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d)))))

series428.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
215.0ms
(sqrt (- 1 (* (* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d)))))
139.0ms
(* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d)))))
44.0ms
(/ (* M D) (* 2 d))
30.0ms
(/ (* M D) (* 2 d))

simplify46.9s

Counts
145 → 139
Calls
145 calls:
Slowest
2.3s
(* (* (* h h) h) (* (* (/ 1 l) (/ 1 l)) (* (/ 1 l) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))))
1.9s
(sqrt (+ (* 1 1) (+ (* (* (* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d))) (* (* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d)))) (* 1 (* (* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d)))))))
1.8s
(* (* (* h h) h) (* (* (/ 1 l) (/ 1 l)) (* (/ 1 l) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))))
1.5s
(* (* (* h h) h) (* (* (/ 1 l) (/ 1 l)) (* (/ 1 l) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))))
1.5s
(* (* (* h h) h) (* (* (/ 1 l) (/ 1 l)) (* (/ 1 l) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))))))

prune2.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize65.0ms

Local error

Found 4 expressions with local error:

23.1b
(cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))
23.1b
(cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))
23.1b
(cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))
5.8b
(* h (* (* (cbrt (* (/ 1 l) (/ (* M D) (* 2 d)))) (cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))) (cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
153×cbrt-div
132×frac-times
129×associate-*r/
78×associate-*l/
13×pow1 add-exp-log
9×add-cbrt-cube
6×pow-prod-down prod-exp cbrt-unprod
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3 associate-*l*
1×associate-*r* *-commutative
Counts
4 → 132
Calls
4 calls:
Slowest
83.0ms
(* h (* (* (cbrt (* (/ 1 l) (/ (* M D) (* 2 d)))) (cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))) (cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))))
37.0ms
(cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))
21.0ms
(cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))
17.0ms
(cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))

series766.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
240.0ms
(* h (* (* (cbrt (* (/ 1 l) (/ (* M D) (* 2 d)))) (cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))) (cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))))
191.0ms
(cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))
181.0ms
(cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))
154.0ms
(cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))

simplify36.1s

Counts
152 → 144
Calls
152 calls:
Slowest
880.0ms
(* (* (* h h) h) (* (* (* (/ 1 l) (/ (* M D) (* 2 d))) (* (/ 1 l) (/ (* M D) (* 2 d)))) (* (/ 1 l) (/ (* M D) (* 2 d)))))
812.0ms
(* h (* (* (cbrt (* (/ 1 l) (/ (* M D) (* 2 d)))) (cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))) (cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))))
520.0ms
(* h (* (* (cbrt (* 1 (/ (* M D) (* 2 d)))) (cbrt (* 1 (* M D)))) (cbrt (* 1 (* M D)))))
474.0ms
(cbrt (cbrt (* (/ 1 l) (/ (* M D) (* 2 d)))))
470.0ms
(* h (* (* (cbrt (* (/ 1 l) (/ (* M D) (* 2 d)))) (cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))) (cbrt (* (/ 1 l) (/ (* M D) (* 2 d))))))

prune3.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

regimes1.5s

Accuracy

0% (1.1b remaining)

Error of 8.0b against oracle of 6.9b and baseline of 8.0b

bsearch5.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.8s9262×body80valid
668.0ms3132×body80nan