Details

Time bar (total: 10.9s)

sample47.0ms

Algorithm
intervals
Results
15.0ms307×body80valid
6.0ms115×body80nan

simplify55.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019
done50019

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize14.0ms

Local error

Found 4 expressions with local error:

2.9b
(* 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))))
3.9b
(/ (* M D) (* 2.0 d))
11.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite78.0ms

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:
19.0ms
(* 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))))
13.0ms
(/ (* M D) (* 2.0 d))
34.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
446.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
401.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
29.0ms
(/ (* M D) (* 2.0 d))
707.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify71.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06301135
127791057
250021054
done50021054

prune415.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.7b

localize13.0ms

Local error

Found 4 expressions with local error:

3.6b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
3.9b
(/ (* M D) (* 2.0 d))
4.5b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.8b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
26×prod-exp
23×add-cbrt-cube
20×div-exp
18×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt pow-exp
9×associate-*l*
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1 times-frac sqrt-prod
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×associate-*r* 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-- distribute-lft-out-- difference-of-squares
Counts
4 → 104
Calls
4 calls:
17.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
13.0ms
(/ (* M D) (* 2.0 d))
26.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
16.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

series1.9s

Counts
4 → 12
Calls
4 calls:
407.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
29.0ms
(/ (* M D) (* 2.0 d))
755.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
721.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify64.0ms

Counts
116 → 116
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0576880
12585798
25001796
done5001796

prune381.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.5b

localize16.0ms

Local error

Found 4 expressions with local error:

3.9b
(/ (* M D) (* 2.0 d))
3.9b
(/ (* M D) (* 2.0 d))
5.7b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.8b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
373×add-exp-log
184×prod-exp
129×div-exp
80×pow-exp
39×add-cbrt-cube
16×pow-to-exp
14×add-sqr-sqrt
12×cbrt-unprod
11×cbrt-undiv
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×sqr-pow
1×*-commutative
Counts
4 → 158
Calls
4 calls:
15.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* M D) (* 2.0 d))
24.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
45.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

series1.6s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
29.0ms
(/ (* M D) (* 2.0 d))
763.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
733.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

simplify82.0ms

Counts
170 → 170
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
08821759
131701336
250021332
done50021332

prune437.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.3b

localize20.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
3.9b
(/ (* M D) (* 2.0 d))
3.9b
(/ (* M D) (* 2.0 d))
5.7b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
98×add-exp-log
34×div-exp prod-exp
33×add-cbrt-cube
16×add-sqr-sqrt unpow-prod-down
15×pow-exp
14×times-frac
11×add-cube-cbrt *-un-lft-identity associate-/l*
10×cbrt-undiv cbrt-unprod
9×associate-*l*
6×div-inv
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×pow-to-exp frac-2neg associate-*r* clear-num associate-/r* unswap-sqr
1×*-commutative
Counts
4 → 126
Calls
4 calls:
23.0ms
(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
13.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.3s

Counts
4 → 12
Calls
4 calls:
506.0ms
(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
35.0ms
(/ (* M D) (* 2.0 d))
29.0ms
(/ (* M D) (* 2.0 d))
754.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify67.0ms

Counts
138 → 138
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05621148
123581017
250011011
done50011011

prune519.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.3b

regimes807.0ms

Accuracy

23.7% (1.0b remaining)

Error of 7.7b against oracle of 6.7b and baseline of 8.1b

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04734
14734
done4734

end0.0ms

sample1.2s

Algorithm
intervals
Results
448.0ms9307×body80valid
157.0ms3148×body80nan