Details

Time bar (total: 12.0s)

sample56.0ms

Algorithm
intervals
Results
25.0ms281×body80valid
8.0ms107×body80nan

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.6b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

1.5b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.1b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.6b
(/ (* M D) (* 2.0 d))
13.4b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite30.0ms

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:
6.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms
(/ (* M D) (* 2.0 d))
11.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
423.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
381.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms
(/ (* M D) (* 2.0 d))
712.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify75.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06301136
127791057
250021054

prune413.0ms

Filtered
133 candidates to 89 candidates (66.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1249133
Fresh000
Picked101
Done000
Total1259134

Merged error: 6.1b

Counts
134 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

3.1b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
4.6b
(/ (* M D) (* 2.0 d))
5.2b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
6.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite37.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 136
Calls
4 calls:
3.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
10.0ms
(/ (* M D) (* 2.0 d))
11.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series1.9s

Counts
4 → 12
Calls
4 calls:
383.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
28.0ms
(/ (* M D) (* 2.0 d))
709.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
748.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify97.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07681192
134931070
250011057

prune354.0ms

Filtered
148 candidates to 81 candidates (54.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1453148
Fresh178
Picked101
Done000
Total14710157

Merged error: 5.3b

Counts
157 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (* M D) (* 2.0 d))
4.6b
(/ (* M D) (* 2.0 d))
4.9b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.2b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
1402×add-exp-log
907×prod-exp
366×div-exp
305×pow-exp
61×pow-to-exp
57×rec-exp 1-exp
51×add-cbrt-cube
21×cbrt-unprod
19×add-sqr-sqrt
16×associate-*r*
14×add-cube-cbrt *-un-lft-identity
12×times-frac
11×cbrt-undiv
10×associate-*l*
6×pow1 unpow-prod-down
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×unswap-sqr
2×frac-2neg clear-num associate-/r* *-commutative associate-/l* sqr-pow
1×associate-*r/ pow-prod-down un-div-inv
Counts
4 → 340
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
19.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

series1.5s

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ (* M D) (* 2.0 d))
29.0ms
(/ (* M D) (* 2.0 d))
751.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
711.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

simplify124.0ms

Algorithm
egg-herbie
Counts
352 → 352
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
016044551
146393125
250013125

prune430.0ms

Filtered
352 candidates to 86 candidates (24.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New3502352
Fresh099
Picked101
Done000
Total35111362

Merged error: 5.3b

Counts
362 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

5.2b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))) (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))) (/ 1 l))
19.9b
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
19.9b
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
19.9b
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
454×add-exp-log
304×prod-exp
92×div-exp
60×pow-exp
28×add-cbrt-cube
22×rec-exp 1-exp
20×cbrt-unprod
13×associate-*r*
12×pow-to-exp
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3
1×associate-*r/ associate-*l* pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 156
Calls
4 calls:
22.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))) (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))) (/ 1 l))
4.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
4.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
4.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

series2.1s

Counts
4 → 12
Calls
4 calls:
787.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))) (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))) (/ 1 l))
454.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
467.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
436.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

simplify103.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
09084282
130932701
250022481

prune332.0ms

Filtered
168 candidates to 64 candidates (38.1%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1680168
Fresh01010
Picked011
Done000
Total16811179

Merged error: 5.3b

Counts
179 → 11

regimes1.2s

Accuracy

33.4% (1.3b remaining)

Error of 8.7b against oracle of 7.3b and baseline of 9.3b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06469
16469

end0.0ms

sample1.5s

Algorithm
intervals
Results
726.0ms9290×body80valid
251.0ms3110×body80nan