Details

Time bar (total: 1.1m)

sample265.0ms

Algorithm
intervals
Results
137.0ms1158×body80nan
60.0ms400×body80valid

simplify244.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

prune12.0ms

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: 24.9b

Counts
2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

7.2b
(* (* (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))))
11.4b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.6b
(pow (/ d l) (/ 1.0 2.0))
11.9b
(pow (/ d h) (/ 1.0 2.0))

rewrite479.0ms

Algorithm
rewrite-expression-head
Rules
680×add-sqr-sqrt
344×associate-*l*
337×times-frac
291×associate-*r*
282×unpow-prod-down
243×unswap-sqr
205×add-exp-log
186×*-un-lft-identity
179×add-cube-cbrt
107×prod-exp
99×associate-*l/
81×frac-times
61×associate-/l*
60×associate-/r*
55×div-exp
40×pow-exp
31×difference-of-squares sqr-pow
30×add-cbrt-cube
28×*-commutative
26×pow-unpow
21×clear-num
20×frac-2neg
16×pow1
14×pow-to-exp
13×cbrt-unprod
11×associate-*r/
9×div-inv
6×pow-prod-down
5×cbrt-undiv
4×add-log-exp
3×distribute-lft-out--
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in un-div-inv
1×flip3-- flip--
Counts
4 → 594
Calls
4 calls:
255.0ms
(* (* (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))))
146.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
7.0ms
(pow (/ d l) (/ 1.0 2.0))
8.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
652.0ms
(* (* (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))))
930.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
91.0ms
(pow (/ d l) (/ 1.0 2.0))
81.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify128.0ms

Algorithm
egg-herbie
Counts
606 → 606
Iterations

Useful iterations: 1 (62.0ms)

IterNodesCost
035947501
150017368

prune2.9s

Filtered
606 candidates to 459 candidates (75.7%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New58620606
Fresh000
Picked101
Done000
Total58720607

Merged error: 7.9b

Counts
607 → 20

localize43.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (* M D) (* 2.0 d))
7.2b
(* (* (* (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))))
11.4b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.6b
(pow (/ d l) (/ 1.0 2.0))

rewrite4.5s

Algorithm
rewrite-expression-head
Rules
31159×add-sqr-sqrt
17333×unswap-sqr
12299×unpow-prod-down
10728×cbrt-prod
10508×times-frac
6537×associate-*l*
2592×swap-sqr
2012×sqr-pow
1243×*-commutative
757×*-un-lft-identity
750×add-cube-cbrt
738×add-exp-log
737×associate-*r*
487×prod-exp
216×pow-exp
171×div-exp
99×associate-*l/
81×frac-times
78×pow-to-exp
73×associate-/l*
72×associate-/r*
46×add-cbrt-cube
31×difference-of-squares
22×clear-num
21×frac-2neg
20×cbrt-unprod
19×pow1
13×pow-unpow
11×associate-*r/
9×cbrt-undiv pow-prod-down div-inv
4×add-log-exp
3×distribute-lft-out--
2×distribute-rgt-in sub-neg distribute-lft-in un-div-inv
1×flip3-- pow-pow flip--
Counts
4 → 6881
Calls
4 calls:
12.0ms
(/ (* M D) (* 2.0 d))
2.9s
(* (* (* (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))))
120.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
640.0ms
(* (* (* (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))))
828.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
64.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify2.8s

Algorithm
egg-herbie
Counts
6893 → 6893
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
06653297823

prune32.1s

Filtered
6893 candidates to 3702 candidates (53.7%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New688676893
Fresh31619
Picked101
Done000
Total6890236913

Merged error: 5.9b

Counts
6913 → 23

localize54.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (* M D) (* 2.0 d))
11.6b
(pow (/ d l) (/ 1.0 2.0))
15.5b
(sqrt (/ h l))
15.5b
(sqrt (/ h l))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
182×times-frac
172×add-sqr-sqrt
114×add-cube-cbrt *-un-lft-identity
78×associate-*r* associate-*l*
26×sqrt-prod *-commutative unswap-sqr
19×add-exp-log
18×sqrt-div associate-/r* associate-/l*
16×add-cbrt-cube
13×unpow-prod-down pow-unpow
7×pow1
5×div-exp div-inv
4×cbrt-undiv rem-sqrt-square prod-exp cbrt-unprod add-log-exp
3×frac-2neg clear-num
2×sqrt-pow1 pow1/2 pow-exp
1×pow-to-exp pow-pow sqr-pow
Counts
4 → 290
Calls
4 calls:
16.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(pow (/ d l) (/ 1.0 2.0))
4.0ms
(sqrt (/ h l))
4.0ms
(sqrt (/ h l))

series195.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
66.0ms
(pow (/ d l) (/ 1.0 2.0))
54.0ms
(sqrt (/ h l))
47.0ms
(sqrt (/ h l))

simplify57.0ms

Algorithm
egg-herbie
Counts
302 → 302
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
012201918
150011851

prune2.3s

Filtered
302 candidates to 220 candidates (72.8%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New2948302
Fresh41822
Picked101
Done000
Total29926325

Merged error: 5.8b

Counts
325 → 26

localize70.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (* M D) (* 2.0 d))
4.6b
(/ (* M D) (* 2.0 d))
15.5b
(sqrt (/ h l))
15.5b
(sqrt (/ h l))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
308×times-frac
288×add-sqr-sqrt
178×add-cube-cbrt *-un-lft-identity
156×associate-*r* associate-*l*
52×*-commutative unswap-sqr
30×associate-/r* associate-/l*
28×add-exp-log add-cbrt-cube
26×sqrt-prod
18×sqrt-div
8×cbrt-undiv div-exp prod-exp cbrt-unprod
6×pow1
4×rem-sqrt-square frac-2neg clear-num div-inv add-log-exp
2×sqrt-pow1 pow1/2
Counts
4 → 438
Calls
4 calls:
14.0ms
(/ (* M D) (* 2.0 d))
14.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(sqrt (/ h l))
4.0ms
(sqrt (/ h l))

series164.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ (* M D) (* 2.0 d))
30.0ms
(/ (* M D) (* 2.0 d))
54.0ms
(sqrt (/ h l))
48.0ms
(sqrt (/ h l))

simplify159.0ms

Algorithm
egg-herbie
Counts
450 → 450
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
09802968
148112872
250012872

prune3.6s

Filtered
450 candidates to 318 candidates (70.7%)
Pruning

27 alts after pruning (27 fresh and 0 done)

PrunedKeptTotal
New4482450
Fresh02525
Picked101
Done000
Total44927476

Merged error: 5.8b

Counts
476 → 27

regimes1.4s

Accuracy

-15% (7.7b remaining)

Error of 14.5b against oracle of 6.7b and baseline of 13.5b

bsearch730.0ms

Steps
ItersRangePoint
3
9.487713136033044e+221
1.2941430525931866e+222
1.0135285146639071e+222
10
3.4132628554713364e-121
8.654977733661828e-110
1.835147891625137e-120
6
-2.757039247511383e-289
-5.0696558361627677e-290
-5.117098412144494e-290

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0124159
1124159

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.1s38777×body80nan
1.8s12765×body80valid