Details

Time bar (total: 22.7s)

sample237.0ms

Algorithm
intervals
Results
118.0ms1134×body80nan
58.0ms409×body80valid

simplify29.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05417
117417
272017
3500117

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize29.0ms

Local error

Found 4 expressions with local error:

7.4b
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.8b
(pow (/ d h) (/ 1.0 2.0))
12.0b
(pow (/ d l) (/ 1.0 2.0))
13.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
42×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
40×pow-exp
30×add-cbrt-cube
26×unpow-prod-down pow-unpow
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
6×prod-diff
5×cbrt-undiv distribute-rgt-in distribute-lft-in div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 190
Calls
4 calls:
14.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
6.0ms
(pow (/ d h) (/ 1.0 2.0))
9.0ms
(pow (/ d l) (/ 1.0 2.0))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
615.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
59.0ms
(pow (/ d h) (/ 1.0 2.0))
68.0ms
(pow (/ d l) (/ 1.0 2.0))
711.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify46.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
012872382
150022125

prune709.0ms

Filtered
202 candidates to 119 candidates (58.9%)
Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.4b

localize41.0ms

Local error

Found 4 expressions with local error:

7.2b
(/ (* M D) (* 2.0 d))
7.4b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.0b
(pow (/ d l) (/ 1.0 2.0))
13.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
738×add-exp-log
487×prod-exp
216×pow-exp
171×div-exp
78×pow-to-exp
46×add-cbrt-cube
28×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
20×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
9×pow1 cbrt-undiv
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg associate-*l* pow-prod-down *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 274
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
32.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
6.0ms
(pow (/ d l) (/ 1.0 2.0))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.4s

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ (* M D) (* 2.0 d))
623.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
63.0ms
(pow (/ d l) (/ 1.0 2.0))
714.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify71.0ms

Algorithm
egg-herbie
Counts
286 → 286
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
017106060
150015717

prune847.0ms

Filtered
286 candidates to 104 candidates (36.4%)
Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.9b

localize56.0ms

Local error

Found 4 expressions with local error:

3.5b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
7.2b
(/ (* M D) (* 2.0 d))
7.4b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
6965×add-exp-log
5245×prod-exp
2614×pow-exp
1626×div-exp
789×pow-to-exp
232×rec-exp 1-exp
55×add-cbrt-cube
37×times-frac
34×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×cbrt-unprod
22×unpow-prod-down
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-undiv cbrt-prod
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u pow-prod-down log1p-expm1-u div-inv add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 1243
Calls
4 calls:
7.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
81.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.9s

Counts
4 → 12
Calls
4 calls:
171.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
32.0ms
(/ (* M D) (* 2.0 d))
934.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
729.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify362.0ms

Algorithm
egg-herbie
Counts
1255 → 1255
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
0500145180

prune1.6s

Filtered
1255 candidates to 145 candidates (11.6%)
Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 10.3b

localize56.0ms

Local error

Found 4 expressions with local error:

5.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
5.2b
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
7.2b
(/ (* M D) (* 2.0 d))
7.4b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))

rewrite335.0ms

Algorithm
rewrite-expression-head
Rules
6964×add-exp-log
5245×prod-exp
2612×pow-exp
1626×div-exp
788×pow-to-exp
232×rec-exp 1-exp
57×add-cbrt-cube
42×prod-diff
36×add-sqr-sqrt *-un-lft-identity
34×add-cube-cbrt
27×cbrt-unprod
23×distribute-rgt-in distribute-lft-in
22×times-frac
11×pow1
10×cbrt-undiv
8×associate-*r* div-inv
4×expm1-log1p-u pow-prod-down associate-*l/ associate-/r* log1p-expm1-u add-log-exp
2×sub-neg frac-2neg associate-*r/ associate-*l* clear-num *-commutative associate-/l*
1×flip3-- flip-- associate-/l/ distribute-lft-out-- difference-of-squares
Counts
4 → 1242
Calls
4 calls:
10.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
12.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
6.0ms
(/ (* M D) (* 2.0 d))
88.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))

series2.4s

Counts
4 → 12
Calls
4 calls:
734.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
723.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
33.0ms
(/ (* M D) (* 2.0 d))
935.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))

simplify391.0ms

Algorithm
egg-herbie
Counts
1254 → 1254
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0500148577

prune1.3s

Filtered
1254 candidates to 143 candidates (11.4%)
Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 10.0b

regimes1.3s

Accuracy

-9.4% (6.2b remaining)

Error of 16.6b against oracle of 10.4b and baseline of 16.1b

bsearch167.0ms

Steps
ItersRangePoint
6
2.1481558930268566e+158
1.4957174130964848e+159
1.4768637021576945e+159

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06760
16760

end0.0ms

sample7.5s

Algorithm
intervals
Results
4.1s38730×body80nan
1.8s12709×body80valid