Details

Time bar (total: 11.3s)

sample42.0ms

Algorithm
intervals
Results
15.0ms290×body80valid
5.0ms87×body80nan

simplify60.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize14.0ms

Local error

Found 4 expressions with local error:

2.6b
(* 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))))
5.9b
(/ (* M D) (* 2.0 d))
13.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite36.0ms

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:
11.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0ms
(/ (* M D) (* 2.0 d))
14.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
410.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
372.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
28.0ms
(/ (* M D) (* 2.0 d))
689.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify85.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
06091075
12742997
25003994

prune386.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.2b

localize15.0ms

Local error

Found 4 expressions with local error:

4.0b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
5.9b
(/ (* M D) (* 2.0 d))
6.0b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.9b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))

rewrite39.0ms

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:
2.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
4.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
17.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))

series1.8s

Counts
4 → 12
Calls
4 calls:
373.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
28.0ms
(/ (* M D) (* 2.0 d))
734.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
707.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))

simplify95.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
07521137
134671014
250021001

prune364.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.9b

localize15.0ms

Local error

Found 4 expressions with local error:

4.0b
(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))
6.0b
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
6.3b
(* (/ M 2.0) (/ D d))
6.9b
(* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
165×add-exp-log
91×prod-exp
44×add-sqr-sqrt
40×div-exp
31×times-frac
30×add-cbrt-cube
29×associate-*r*
28×add-cube-cbrt *-un-lft-identity
25×pow-exp
19×associate-*l*
11×cbrt-unprod
9×pow1
8×rec-exp 1-exp
6×cbrt-undiv unswap-sqr
5×pow-to-exp
4×add-log-exp
3×sqrt-prod *-commutative div-inv
2×sqrt-div associate-*r/ pow-prod-down sqr-pow
1×frac-times unpow-prod-down rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*l/ un-div-inv flip--
Counts
4 → 152
Calls
4 calls:
3.0ms
(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))
5.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
12.0ms
(* (/ M 2.0) (/ D d))
17.0ms
(* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))

series1.9s

Counts
4 → 12
Calls
4 calls:
390.0ms
(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))
743.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
33.0ms
(* (/ M 2.0) (/ D d))
697.0ms
(* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))

simplify104.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
08921255
139051133
250011120

prune459.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.5b

localize21.0ms

Local error

Found 4 expressions with local error:

5.3b
(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
6.3b
(* (/ M 2.0) (/ D d))
6.3b
(* (/ M 2.0) (/ D d))
6.9b
(* (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) (/ 1 l))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
1402×add-exp-log
907×prod-exp
366×div-exp
305×pow-exp
68×add-sqr-sqrt
61×pow-to-exp
57×rec-exp 1-exp
53×times-frac
51×add-cbrt-cube
42×associate-*r*
41×add-cube-cbrt *-un-lft-identity
32×associate-*l*
21×cbrt-unprod
11×cbrt-undiv
10×pow1 unswap-sqr
5×div-inv
4×*-commutative add-log-exp
3×associate-*r/ pow-prod-down
2×frac-times associate-*l/ sqr-pow
1×unpow-prod-down un-div-inv
Counts
4 → 385
Calls
4 calls:
6.0ms
(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
13.0ms
(* (/ M 2.0) (/ D d))
12.0ms
(* (/ M 2.0) (/ D d))
34.0ms
(* (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) (/ 1 l))

series1.5s

Counts
4 → 12
Calls
4 calls:
747.0ms
(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
28.0ms
(* (/ M 2.0) (/ D d))
29.0ms
(* (/ M 2.0) (/ D d))
737.0ms
(* (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) (/ 1 l))

simplify73.0ms

Algorithm
egg-herbie
Counts
397 → 397
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
016974758
150013332

prune681.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.5b

regimes752.0ms

Accuracy

31.3% (1.1b remaining)

Error of 7.8b against oracle of 6.7b and baseline of 8.3b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05945
15945

end0.0ms

sample1.1s

Algorithm
intervals
Results
506.0ms9385×body80valid
181.0ms3169×body80nan