Details

Time bar (total: 10.4s)

sample48.0ms

Algorithm
intervals
Results
18.0ms302×body80valid
6.0ms96×body80nan

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize16.0ms

Local error

Found 4 expressions with local error:

2.2b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.2b
(/ (* M D) (* 2.0 d))
5.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
8.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite34.0ms

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:
9.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0ms
(/ (* M D) (* 2.0 d))
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
15.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
407.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
31.0ms
(/ (* M D) (* 2.0 d))
361.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
672.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify71.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06091075
12742997
25002994

prune356.0ms

Filtered
125 candidates to 81 candidates (64.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.5b

localize14.0ms

Local error

Found 4 expressions with local error:

4.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.1b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.2b
(/ (* M D) (* 2.0 d))
5.9b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
26×prod-exp
23×add-cbrt-cube
20×div-exp
18×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt pow-exp
9×associate-*l*
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1 times-frac sqrt-prod
4×associate-/r* add-log-exp
3×associate-*r* div-inv unswap-sqr
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/l* sqr-pow
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 96
Calls
4 calls:
15.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
7.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

series1.8s

Counts
4 → 12
Calls
4 calls:
713.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
666.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
27.0ms
(/ (* M D) (* 2.0 d))
372.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

simplify71.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0560828
12559746
25001744

prune337.0ms

Filtered
108 candidates to 71 candidates (65.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.8b

localize16.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ (* M D) (* 2.0 d))
5.2b
(/ (* M D) (* 2.0 d))
5.9b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
6.6b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
16×add-sqr-sqrt
12×div-exp
10×*-un-lft-identity
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt
6×unpow-prod-down
5×pow1 pow-exp sqrt-prod
4×add-log-exp
3×times-frac associate-*r* div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l* sqr-pow
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 90
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.2s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
32.0ms
(/ (* M D) (* 2.0 d))
375.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
738.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify52.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0443917
11894812
25001810

prune349.0ms

Filtered
102 candidates to 65 candidates (63.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.8b

localize25.0ms

Local error

Found 4 expressions with local error:

6.6b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.6b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
8.1b
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
8.1b
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
26×add-sqr-sqrt
22×prod-exp
18×associate-*l*
16×*-un-lft-identity
12×add-cube-cbrt unpow-prod-down
10×cbrt-prod pow-exp
8×div-exp add-cbrt-cube
6×associate-*r* unswap-sqr
4×pow1 cbrt-div add-log-exp sqr-pow
2×pow-to-exp flip3-- times-frac pow1/3 *-commutative flip-- cbrt-unprod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 92
Calls
4 calls:
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.0ms
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
4.0ms
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))

series2.0s

Counts
4 → 12
Calls
4 calls:
749.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
746.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
241.0ms
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
255.0ms
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))

simplify45.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03341404
110481300
250011288

prune530.0ms

Filtered
104 candidates to 78 candidates (75.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.8b

regimes538.0ms

Accuracy

-33.1% (3.0b remaining)

Error of 10.1b against oracle of 7.2b and baseline of 9.4b

bsearch197.0ms

Steps
ItersRangePoint
9
1.402363006301505e+53
1.723905641708485e+60
1.1020729799525435e+54
11
-2.0422903935287356e-243
-1.8087304515288067e-277
-1.1248613893079875e-247

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04425
14425

end0.0ms

sample1.1s

Algorithm
intervals
Results
493.0ms9265×body80valid
168.0ms3037×body80nan