Details

Time bar (total: 30.3s)

sample103.0ms

Algorithm
intervals
Results
48.0ms302×body80valid
13.0ms104×body80nan

simplify2.8s

Counts
1 → 1
Iterations
IterNodes
done5001
52638
4446
3177
281
136
017

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize34.0ms

Local error

Found 4 expressions with local error:

1.5b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.7b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.1b
(/ (* M D) (* 2.0 d))
11.3b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite94.0ms

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×*-un-lft-identity add-cube-cbrt
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 clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-/l*
Counts
4 → 113
Calls
4 calls:
34.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
7.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
15.0ms
(/ (* M D) (* 2.0 d))
29.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.3s

Counts
4 → 12
Calls
4 calls:
676.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
563.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
53.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify2.1s

Counts
125 → 125
Iterations
IterNodes
done5000
23068
1619
0236

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize40.0ms

Local error

Found 4 expressions with local error:

4.2b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
4.7b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
6.1b
(/ (* M D) (* 2.0 d))
6.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite86.0ms

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×*-un-lft-identity add-cube-cbrt
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 clear-num associate-/r* frac-2neg sqrt-pow1 flip3-- pow1/2 pow-prod-down associate-*r/ un-div-inv flip-- associate-/l*
Counts
4 → 128
Calls
4 calls:
40.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
4.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
12.0ms
(/ (* M D) (* 2.0 d))
24.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series2.6s

Counts
4 → 12
Calls
4 calls:
954.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
587.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
49.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify3.3s

Counts
140 → 140
Iterations
IterNodes
done5001
24350
1768
0269

prune956.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize65.0ms

Local error

Found 4 expressions with local error:

4.2b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
4.7b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
6.1b
(/ (* M D) (* 2.0 d))
6.1b
(/ (* M D) (* 2.0 d))

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
1381×add-exp-log
896×prod-exp
362×div-exp
300×pow-exp
60×pow-to-exp
57×rec-exp 1-exp
49×add-cbrt-cube
20×cbrt-unprod
13×add-sqr-sqrt associate-*r*
12×*-un-lft-identity add-cube-cbrt
11×cbrt-undiv times-frac
7×pow1
4×add-log-exp
3×sqrt-prod div-inv
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l*
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* pow-prod-down associate-*r/ un-div-inv *-commutative flip--
Counts
4 → 316
Calls
4 calls:
157.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
4.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
10.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(/ (* M D) (* 2.0 d))

series1.6s

Counts
4 → 12
Calls
4 calls:
995.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
550.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
40.0ms
(/ (* M D) (* 2.0 d))
42.0ms
(/ (* M D) (* 2.0 d))

simplify1.5s

Counts
328 → 328
Iterations
IterNodes
done5000
11586
0418

prune975.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.5b

localize36.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
4.8b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
6.1b
(/ (* M D) (* 2.0 d))
6.1b
(/ (* M D) (* 2.0 d))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
156×add-exp-log
84×prod-exp
40×add-cbrt-cube div-exp
20×pow-exp
14×cbrt-unprod
13×add-sqr-sqrt associate-*r*
12×*-un-lft-identity add-cube-cbrt
11×times-frac
10×cbrt-undiv
8×rec-exp 1-exp
7×pow1
4×pow-to-exp add-log-exp
3×sqrt-prod div-inv
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l*
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* pow-prod-down associate-*r/ un-div-inv *-commutative flip--
Counts
4 → 118
Calls
4 calls:
4.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
38.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
10.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(/ (* M D) (* 2.0 d))

series1.7s

Counts
4 → 12
Calls
4 calls:
601.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
1.0s
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
36.0ms
(/ (* M D) (* 2.0 d))
52.0ms
(/ (* M D) (* 2.0 d))

simplify3.2s

Counts
130 → 130
Iterations
IterNodes
done5000
23648
1678
0225

prune944.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.5b

regimes2.2s

Accuracy

0% (1.5b remaining)

Error of 8.7b against oracle of 7.2b and baseline of 8.7b

bsearch0.0ms

simplify10.0ms

Iterations
IterNodes
done30
130
022

end0.0ms

sample2.2s

Algorithm
intervals
Results
996.0ms9265×body80valid
555.0ms3173×body80nan