Details

Time bar (total: 26.7s)

sample77.0ms

Algorithm
intervals
Results
24.0ms288×body80valid
9.0ms105×body80nan

simplify2.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01718
13618
28118
318118
445718
5267818
done500118

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize31.0ms

Local error

Found 4 expressions with local error:

2.4b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.3b
(/ (* M D) (* 2.0 d))
11.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite107.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u 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 → 121
Calls
4 calls:
35.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
8.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
14.0ms
(/ (* M D) (* 2.0 d))
42.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.3s

Counts
4 → 12
Calls
4 calls:
652.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
535.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
36.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.9s

Counts
133 → 133
Iterations

Useful iterations: 2 (575.0ms)

IterNodesCost
02442427
16442218
231322042
done50002042

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.2b

localize63.0ms

Local error

Found 4 expressions with local error:

4.0b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
6.3b
(/ (* M D) (* 2.0 d))
6.3b
(/ (* M D) (* 2.0 d))
9.8b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite126.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 118
Calls
4 calls:
15.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
32.0ms
(/ (* M D) (* 2.0 d))
21.0ms
(/ (* M D) (* 2.0 d))
48.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.7s

Counts
4 → 12
Calls
4 calls:
589.0ms
(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
(/ (* M D) (* 2.0 d))
53.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify2.1s

Counts
130 → 130
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02172546
16082358
230251907
done50011903

prune985.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

localize32.0ms

Local error

Found 4 expressions with local error:

4.8b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
6.3b
(/ (* M D) (* 2.0 d))
6.3b
(/ (* M D) (* 2.0 d))
6.5b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
79×add-exp-log
35×add-cbrt-cube
30×prod-exp
24×div-exp
14×add-sqr-sqrt
10×cbrt-undiv pow-exp cbrt-unprod
9×add-cube-cbrt *-un-lft-identity associate-*l*
6×unpow-prod-down times-frac
5×associate-/r*
4×pow1 expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×frac-2neg associate-*r* clear-num associate-/l* unswap-sqr
2×pow-to-exp sqr-pow
1×*-commutative
Counts
4 → 108
Calls
4 calls:
37.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
25.0ms
(/ (* M D) (* 2.0 d))
14.0ms
(/ (* M D) (* 2.0 d))
63.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series2.2s

Counts
4 → 12
Calls
4 calls:
1.0s
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
35.0ms
(/ (* M D) (* 2.0 d))
55.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify1.7s

Counts
120 → 120
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01941838
15131758
225951498
done50001494

prune934.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.8b

localize70.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
6.3b
(/ (* M D) (* 2.0 d))
6.3b
(/ (* M D) (* 2.0 d))
6.5b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
79×add-exp-log
35×add-cbrt-cube
30×prod-exp
24×div-exp
14×add-sqr-sqrt
10×cbrt-undiv pow-exp cbrt-unprod
9×add-cube-cbrt *-un-lft-identity associate-*l*
6×unpow-prod-down times-frac
5×associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×frac-2neg associate-*r* clear-num associate-/r* unswap-sqr
2×pow-to-exp sqr-pow
1×*-commutative
Counts
4 → 108
Calls
4 calls:
29.0ms
(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
32.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
53.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series2.0s

Counts
4 → 12
Calls
4 calls:
857.0ms
(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
40.0ms
(/ (* M D) (* 2.0 d))
41.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify1.2s

Counts
120 → 120
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01941859
15071783
223431521
done50011515

prune774.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.8b

regimes1.7s

Accuracy

-37% (1.7b remaining)

Error of 9.2b against oracle of 7.6b and baseline of 8.8b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04088
15288
done5288

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.4s9325×body80valid
335.0ms3148×body80nan