Details

Time bar (total: 22.2s)

sample97.0ms

Algorithm
intervals
Results
34.0ms308×body80valid
11.0ms98×body80nan

simplify925.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize29.0ms

Local error

Found 4 expressions with local error:

2.0b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.6b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0b
(/ (* M D) (* 2.0 d))
9.0b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite116.0ms

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:
19.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms
(/ (* M D) (* 2.0 d))
60.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.3s

Counts
4 → 12
Calls
4 calls:
698.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
549.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
55.0ms
(/ (* M D) (* 2.0 d))
985.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.2s

Counts
125 → 125

prune655.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.2b

localize19.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
3.6b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
4.0b
(/ (* M D) (* 2.0 d))
5.3b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite102.0ms

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:
42.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
13.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
13.0ms
(/ (* M D) (* 2.0 d))
25.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series2.9s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
609.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
50.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify1.5s

Counts
140 → 140

prune552.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize38.0ms

Local error

Found 4 expressions with local error:

3.6b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
4.0b
(/ (* M D) (* 2.0 d))
4.0b
(/ (* M D) (* 2.0 d))
5.4b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite88.0ms

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:
9.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
24.0ms
(/ (* M D) (* 2.0 d))
19.0ms
(/ (* M D) (* 2.0 d))
30.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series2.0s

Counts
4 → 12
Calls
4 calls:
870.0ms
(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
(/ (* M D) (* 2.0 d))
47.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify819.0ms

Counts
100 → 100

prune463.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize30.0ms

Local error

Found 4 expressions with local error:

2.0b
(* w0 (sqrt (- 1.0 (* (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (* (cbrt l) (cbrt l))) (/ (cbrt 1) (cbrt l))))))
3.6b
(sqrt (- 1.0 (* (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (* (cbrt l) (cbrt l))) (/ (cbrt 1) (cbrt l)))))
4.0b
(/ (* M D) (* 2.0 d))
5.3b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
21×add-sqr-sqrt
20×add-cbrt-cube
16×prod-exp
12×associate-*l*
11×add-cube-cbrt *-un-lft-identity
9×associate-*r*
8×div-exp
7×pow1 sqrt-prod
6×unpow-prod-down cbrt-unprod
5×pow-exp unswap-sqr
4×cbrt-undiv sqrt-div add-log-exp
2×flip3-- times-frac associate-*r/ *-commutative flip-- div-inv sqr-pow
1×pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 91
Calls
4 calls:
28.0ms
(* w0 (sqrt (- 1.0 (* (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (* (cbrt l) (cbrt l))) (/ (cbrt 1) (cbrt l))))))
5.0ms
(sqrt (- 1.0 (* (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (* (cbrt l) (cbrt l))) (/ (cbrt 1) (cbrt l)))))
13.0ms
(/ (* M D) (* 2.0 d))
31.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series2.3s

Counts
4 → 12
Calls
4 calls:
614.0ms
(* w0 (sqrt (- 1.0 (* (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (* (cbrt l) (cbrt l))) (/ (cbrt 1) (cbrt l))))))
559.0ms
(sqrt (- 1.0 (* (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (* (cbrt l) (cbrt l))) (/ (cbrt 1) (cbrt l)))))
50.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify950.0ms

Counts
103 → 103

prune604.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

regimes840.0ms

Accuracy

-30.2% (2.0b remaining)

Error of 9.7b against oracle of 7.6b and baseline of 9.2b

bsearch103.0ms

Steps
ItersRangePoint
10
1.678402821110943e+289
+inf.0
1.769921175136562e+308

simplify860.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.3s9344×body80valid
415.0ms3165×body80nan