Details

Time bar (total: 11.2s)

sample65.0ms

Algorithm
intervals
Results
29.0ms304×body80valid
7.0ms103×body80nan

simplify49.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize19.0ms

Local error

Found 4 expressions with local error:

1.9b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.2b
(/ (* M D) (* 2.0 d))
5.4b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
7.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
35×add-sqr-sqrt
27×prod-exp
23×add-cbrt-cube
19×div-exp associate-*r*
17×add-cube-cbrt *-un-lft-identity
14×times-frac
12×associate-*l*
10×pow-exp
8×unswap-sqr
7×pow1 unpow-prod-down sqrt-prod cbrt-unprod
5×cbrt-undiv
4×sqrt-div add-log-exp
3×associate-*r/ div-inv sqr-pow
2×pow-to-exp flip3-- *-commutative flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 113
Calls
4 calls:
20.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
14.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
41.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.7s

Counts
4 → 12
Calls
4 calls:
489.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
30.0ms
(/ (* M D) (* 2.0 d))
432.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
768.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify73.0ms

Counts
125 → 125

prune424.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.1b

localize20.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ (* M D) (* 2.0 d))
5.2b
(/ (* M D) (* 2.0 d))
5.4b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
7.5b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
33×add-cbrt-cube
30×prod-exp
28×add-sqr-sqrt
23×div-exp
15×times-frac
14×add-cube-cbrt *-un-lft-identity
13×associate-*r*
10×pow-exp cbrt-unprod
9×cbrt-undiv associate-*l*
7×unpow-prod-down
6×unswap-sqr
5×pow1
4×div-inv add-log-exp
3×sqrt-prod sqr-pow
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ *-commutative flip--
Counts
4 → 110
Calls
4 calls:
13.0ms
(/ (* M D) (* 2.0 d))
14.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
35.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.3s

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ (* M D) (* 2.0 d))
31.0ms
(/ (* M D) (* 2.0 d))
427.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
763.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify65.0ms

Counts
122 → 122

prune440.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.9b

localize20.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ (* M D) (* 2.0 d))
5.3b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.4b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
5.9b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
26×prod-exp
23×add-cbrt-cube
20×div-exp
16×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity pow-exp
9×associate-*l*
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1 times-frac
4×associate-/r* add-log-exp
3×associate-*r* sqrt-prod div-inv unswap-sqr
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/l* sqr-pow
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip--
Counts
4 → 94
Calls
4 calls:
14.0ms
(/ (* M D) (* 2.0 d))
32.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
17.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)

series2.2s

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ (* M D) (* 2.0 d))
763.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
419.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
1.0s
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)

simplify65.0ms

Counts
106 → 106

prune393.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.9b

localize29.0ms

Local error

Found 4 expressions with local error:

5.9b
(/ (* (pow (* (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) (cbrt (/ (* M D) (* 2.0 d)))) (/ 2.0 2)) h) l)
16.8b
(cbrt (/ (* M D) (* 2.0 d)))
16.8b
(cbrt (/ (* M D) (* 2.0 d)))
16.8b
(cbrt (/ (* M D) (* 2.0 d)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
15×cbrt-prod
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
8×prod-exp
6×times-frac div-exp
4×pow1 div-inv add-log-exp
3×cbrt-div pow1/3 pow-exp associate-/r*
2×cbrt-undiv
1×pow-to-exp frac-2neg clear-num cbrt-unprod associate-/l*
Counts
4 → 67
Calls
4 calls:
31.0ms
(/ (* (pow (* (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) (cbrt (/ (* M D) (* 2.0 d)))) (/ 2.0 2)) h) l)
6.0ms
(cbrt (/ (* M D) (* 2.0 d)))
6.0ms
(cbrt (/ (* M D) (* 2.0 d)))
6.0ms
(cbrt (/ (* M D) (* 2.0 d)))

series1.3s

Counts
4 → 12
Calls
4 calls:
918.0ms
(/ (* (pow (* (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) (cbrt (/ (* M D) (* 2.0 d)))) (/ 2.0 2)) h) l)
112.0ms
(cbrt (/ (* M D) (* 2.0 d)))
110.0ms
(cbrt (/ (* M D) (* 2.0 d)))
111.0ms
(cbrt (/ (* M D) (* 2.0 d)))

simplify34.0ms

Counts
79 → 79

prune428.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.9b

regimes494.0ms

Accuracy

0% (1.2b remaining)

Error of 8.4b against oracle of 7.2b and baseline of 8.4b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
750.0ms9375×body80valid
267.0ms3087×body80nan