Details

Time bar (total: 27.6s)

sample45.0ms

Algorithm
intervals
Results
17.0ms287×body80valid
6.0ms102×body80nan

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune3.0ms

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: 12.8b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

1.7b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.8b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.5b
(/ (* M D) (* 2.0 d))
11.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite331.0ms

Algorithm
rewrite-expression-head
Rules
453×add-sqr-sqrt
342×times-frac
307×associate-*l*
186×associate-*r*
178×unpow-prod-down *-un-lft-identity
169×add-cube-cbrt
118×unswap-sqr
67×add-exp-log
52×*-commutative
41×sqrt-prod
30×difference-of-squares
27×prod-exp
23×add-cbrt-cube
19×div-exp
16×associate-/l*
15×associate-/r*
11×associate-*r/
10×pow-exp
9×pow1
7×cbrt-unprod sqr-pow
5×cbrt-undiv
4×sqrt-div distribute-lft-out-- add-log-exp
3×clear-num div-inv
2×pow-to-exp flip3-- frac-2neg pow-prod-down un-div-inv flip--
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 474
Calls
4 calls:
109.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
103.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
13.0ms
(/ (* M D) (* 2.0 d))
74.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
424.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
383.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
28.0ms
(/ (* M D) (* 2.0 d))
717.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify90.0ms

Algorithm
egg-herbie
Counts
486 → 486
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
021384007
150013944

prune1.9s

Filtered
486 candidates to 366 candidates (75.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New4779486
Fresh000
Picked101
Done000
Total4789487

Merged error: 6.1b

Counts
487 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

2.8b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
5.5b
(/ (* M D) (* 2.0 d))
5.5b
(/ (* M D) (* 2.0 d))
10.6b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite676.0ms

Algorithm
rewrite-expression-head
Rules
1113×add-sqr-sqrt
621×times-frac
417×unswap-sqr
381×associate-*l*
303×unpow-prod-down
249×*-un-lft-identity
244×add-cube-cbrt
241×associate-*r*
111×sqrt-prod
106×difference-of-squares
77×add-exp-log *-commutative
33×add-cbrt-cube
32×sqr-pow
30×prod-exp
28×associate-/l*
27×associate-/r*
23×div-exp
10×pow-exp cbrt-unprod
9×cbrt-undiv associate-*r/
7×pow1
4×clear-num div-inv add-log-exp
3×frac-2neg
2×pow-to-exp sqrt-div un-div-inv distribute-lft-out--
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 pow-prod-down flip--
Counts
4 → 710
Calls
4 calls:
502.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
18.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(/ (* M D) (* 2.0 d))
77.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.2s

Counts
4 → 12
Calls
4 calls:
396.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
29.0ms
(/ (* M D) (* 2.0 d))
37.0ms
(/ (* M D) (* 2.0 d))
730.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify150.0ms

Algorithm
egg-herbie
Counts
722 → 722
Iterations

Useful iterations: 1 (52.0ms)

IterNodesCost
030699417
150019324

prune3.4s

Filtered
722 candidates to 552 candidates (76.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New7202722
Fresh268
Picked101
Done000
Total7238731

Merged error: 5.4b

Counts
731 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

5.4b
(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
5.5b
(/ (* M D) (* 2.0 d))
5.5b
(/ (* M D) (* 2.0 d))
6.2b
(/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)

rewrite306.0ms

Algorithm
rewrite-expression-head
Rules
1529×times-frac
1276×associate-*r*
1156×add-sqr-sqrt
765×unpow-prod-down
707×add-cube-cbrt *-un-lft-identity
531×associate-*l*
227×unswap-sqr
191×associate-/l*
177×*-commutative
79×add-exp-log
35×add-cbrt-cube
30×prod-exp
27×associate-/r*
24×div-exp
10×cbrt-undiv pow-exp cbrt-unprod sqr-pow
8×div-inv
6×pow1
4×add-log-exp
3×frac-2neg clear-num
2×pow-to-exp
1×pow-prod-down
Counts
4 → 1242
Calls
4 calls:
67.0ms
(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
13.0ms
(/ (* M D) (* 2.0 d))
19.0ms
(/ (* M D) (* 2.0 d))
95.0ms
(/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)

series1.5s

Counts
4 → 12
Calls
4 calls:
889.0ms
(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
28.0ms
(/ (* M D) (* 2.0 d))
29.0ms
(/ (* M D) (* 2.0 d))
603.0ms
(/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)

simplify246.0ms

Algorithm
egg-herbie
Counts
1254 → 1254
Iterations

Useful iterations: 1 (78.0ms)

IterNodesCost
0427313599
1500113550

prune5.9s

Filtered
1254 candidates to 907 candidates (72.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New125221254
Fresh167
Picked011
Done000
Total125391262

Merged error: 5.4b

Counts
1262 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

5.4b
(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
5.5b
(/ (* M D) (* 2.0 d))
5.5b
(/ (* 2.0 d) (* M D))
6.2b
(/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)

rewrite308.0ms

Algorithm
rewrite-expression-head
Rules
1529×times-frac
1276×associate-*r*
1156×add-sqr-sqrt
765×unpow-prod-down
707×add-cube-cbrt *-un-lft-identity
531×associate-*l*
227×unswap-sqr
191×associate-/l*
177×*-commutative
79×add-exp-log
35×add-cbrt-cube
30×prod-exp
27×associate-/r*
24×div-exp
10×cbrt-undiv pow-exp cbrt-unprod sqr-pow
8×div-inv
6×pow1
4×add-log-exp
3×frac-2neg clear-num
2×pow-to-exp
1×pow-prod-down
Counts
4 → 1242
Calls
4 calls:
68.0ms
(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
13.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(/ (* 2.0 d) (* M D))
96.0ms
(/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)

series1.5s

Counts
4 → 12
Calls
4 calls:
796.0ms
(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
28.0ms
(/ (* M D) (* 2.0 d))
35.0ms
(/ (* 2.0 d) (* M D))
602.0ms
(/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)

simplify280.0ms

Algorithm
egg-herbie
Counts
1254 → 1254
Iterations

Useful iterations: 1 (93.0ms)

IterNodesCost
0479113599
1500113550

prune5.7s

Filtered
1254 candidates to 906 candidates (72.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New125311254
Fresh167
Picked101
Done011
Total125581263

Merged error: 5.4b

Counts
1263 → 8

regimes1.0s

Accuracy

-60.9% (2.2b remaining)

Error of 9.8b against oracle of 7.6b and baseline of 8.9b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04529
14529

end0.0ms

sample1.2s

Algorithm
intervals
Results
561.0ms9309×body80valid
197.0ms3109×body80nan