Details

Time bar (total: 15.3s)

sample105.0ms

Algorithm
intervals
Results
37.0ms299×body80valid
14.0ms111×body80nan

simplify70.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize32.0ms

Local error

Found 4 expressions with local error:

1.9b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.0b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.7b
(/ (* M D) (* 2.0 d))
9.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite114.0ms

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:
25.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
6.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
15.0ms
(/ (* M D) (* 2.0 d))
65.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.4s

Counts
4 → 12
Calls
4 calls:
715.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
637.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
35.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify74.0ms

Counts
125 → 125

prune555.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.1b

localize38.0ms

Local error

Found 4 expressions with local error:

4.5b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.0b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
5.7b
(/ (* M D) (* 2.0 d))
6.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
165×add-exp-log
91×prod-exp
40×div-exp
30×add-cbrt-cube
25×pow-exp
21×add-sqr-sqrt
16×associate-*r*
15×add-cube-cbrt *-un-lft-identity
11×times-frac cbrt-unprod
10×associate-*l*
8×rec-exp 1-exp
7×pow1
6×cbrt-undiv unpow-prod-down
5×pow-to-exp
4×add-log-exp
3×sqrt-prod div-inv unswap-sqr
2×sqrt-div *-commutative sqr-pow
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num associate-/r* un-div-inv flip-- associate-/l*
Counts
4 → 128
Calls
4 calls:
76.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
9.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
22.0ms
(/ (* M D) (* 2.0 d))
37.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series2.5s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
526.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
46.0ms
(/ (* M D) (* 2.0 d))
928.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify77.0ms

Counts
140 → 140

prune562.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

localize27.0ms

Local error

Found 4 expressions with local error:

5.0b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
5.2b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.7b
(/ (* M D) (* 2.0 d))
5.7b
(/ (* M D) (* 2.0 d))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
14×add-sqr-sqrt
12×div-exp
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt *-un-lft-identity
6×unpow-prod-down
5×pow1 pow-exp
4×add-log-exp
3×times-frac associate-*r* sqrt-prod div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l* sqr-pow
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip--
Counts
4 → 88
Calls
4 calls:
6.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
31.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
14.0ms
(/ (* M D) (* 2.0 d))
30.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
552.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
913.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
34.0ms
(/ (* M D) (* 2.0 d))
37.0ms
(/ (* M D) (* 2.0 d))

simplify68.0ms

Counts
100 → 100

prune484.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

localize27.0ms

Local error

Found 4 expressions with local error:

5.0b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))))
5.2b
(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
5.6b
(/ (* 2.0 d) (* M D))
5.7b
(/ (* M D) (* 2.0 d))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
92×add-exp-log
38×prod-exp
30×div-exp add-cbrt-cube
27×add-sqr-sqrt
24×associate-*l*
23×unpow-prod-down
22×times-frac
17×*-un-lft-identity
16×add-cube-cbrt pow-exp
9×cbrt-unprod
8×cbrt-undiv
6×div-inv
5×pow1 rec-exp 1-exp unswap-sqr
4×add-log-exp
3×associate-*r* sqrt-prod
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l* sqr-pow
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ *-commutative flip--
Counts
4 → 116
Calls
4 calls:
5.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))))
44.0ms
(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
21.0ms
(/ (* 2.0 d) (* M D))
14.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
497.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))))
912.0ms
(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
31.0ms
(/ (* 2.0 d) (* M D))
31.0ms
(/ (* M D) (* 2.0 d))

simplify77.0ms

Counts
128 → 128

prune525.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.5b

regimes1.4s

Accuracy

-74% (3.5b remaining)

Error of 10.9b against oracle of 7.4b and baseline of 9.4b

bsearch2.0ms

simplify88.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.4s9307×body80valid
327.0ms3114×body80nan