Details

Time bar (total: 10.5s)

sample60.0ms

Algorithm
intervals
Results
24.0ms304×body80valid
6.0ms91×body80nan

simplify48.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.1b

localize18.0ms

Local error

Found 4 expressions with local error:

2.1b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.4b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.5b
(/ (* M D) (* 2.0 d))
6.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite88.0ms

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))))
13.0ms
(/ (* M D) (* 2.0 d))
47.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.7s

Counts
4 → 12
Calls
4 calls:
475.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
419.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
31.0ms
(/ (* M D) (* 2.0 d))
756.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify67.0ms

Counts
125 → 125

prune402.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.5b

localize32.0ms

Local error

Found 4 expressions with local error:

2.1b
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
3.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
4.4b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
5.5b
(/ (* M D) (* 2.0 d))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
179×add-exp-log
88×prod-exp
52×div-exp
28×add-cbrt-cube
25×pow-exp
23×add-sqr-sqrt
14×cbrt-unprod
12×associate-*l*
11×add-cube-cbrt *-un-lft-identity associate-*r*
8×cbrt-undiv unswap-sqr
7×pow1 unpow-prod-down sqrt-prod
6×times-frac
5×pow-to-exp
4×sqrt-div add-log-exp
3×associate-*r/ div-inv sqr-pow
2×flip3-- *-commutative flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 129
Calls
4 calls:
21.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
56.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
13.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
13.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
480.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
597.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
433.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
32.0ms
(/ (* M D) (* 2.0 d))

simplify86.0ms

Counts
141 → 141

prune483.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.0b

localize43.0ms

Local error

Found 4 expressions with local error:

4.3b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
4.4b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
5.5b
(/ (* M D) (* 2.0 d))
5.5b
(/ (* M D) (* 2.0 d))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
189×add-exp-log
91×prod-exp
56×div-exp
38×add-cbrt-cube
25×pow-exp
17×cbrt-unprod
16×add-sqr-sqrt
12×cbrt-undiv
9×associate-*l*
8×add-cube-cbrt *-un-lft-identity
7×unpow-prod-down times-frac
6×unswap-sqr
5×pow1 pow-to-exp associate-*r*
4×div-inv add-log-exp
3×sqrt-prod sqr-pow
2×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 → 126
Calls
4 calls:
61.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
6.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
13.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(/ (* M D) (* 2.0 d))

series1.1s

Counts
4 → 12
Calls
4 calls:
607.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
439.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
36.0ms
(/ (* M D) (* 2.0 d))
33.0ms
(/ (* M D) (* 2.0 d))

simplify93.0ms

Counts
138 → 138

prune508.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.0b

localize51.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (* M D) (* 2.0 d))
16.4b
(cbrt (/ (* M D) (* 2.0 d)))
16.4b
(cbrt (/ (* M D) (* 2.0 d)))
16.4b
(cbrt (/ (* M D) (* 2.0 d)))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log add-cbrt-cube
15×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 cbrt-undiv times-frac div-exp prod-exp cbrt-unprod div-inv add-log-exp
3×cbrt-div pow1/3
1×frac-2neg clear-num associate-/r* associate-/l*
Counts
4 → 63
Calls
4 calls:
13.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(cbrt (/ (* M D) (* 2.0 d)))
6.0ms
(cbrt (/ (* M D) (* 2.0 d)))
6.0ms
(cbrt (/ (* M D) (* 2.0 d)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ (* M D) (* 2.0 d))
117.0ms
(cbrt (/ (* M D) (* 2.0 d)))
114.0ms
(cbrt (/ (* M D) (* 2.0 d)))
119.0ms
(cbrt (/ (* M D) (* 2.0 d)))

simplify34.0ms

Counts
75 → 75

prune478.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 7.0b

regimes809.0ms

Accuracy

0% (2.0b remaining)

Error of 9.9b against oracle of 7.9b and baseline of 9.9b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
889.0ms9379×body80valid
301.0ms3226×body80nan