Details

Time bar (total: 10.8s)

sample68.0ms

Algorithm
intervals
Results
36.0ms300×body80valid
11.0ms96×body80nan

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize14.0ms

Local error

Found 4 expressions with local error:

2.7b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.8b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
3.8b
(/ (* M D) (* 2.0 d))
13.7b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite37.0ms

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:
8.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0ms
(/ (* M D) (* 2.0 d))
18.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
398.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
362.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
33.0ms
(/ (* M D) (* 2.0 d))
669.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify70.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06091076
12742997
25003994

prune382.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.7b

localize13.0ms

Local error

Found 4 expressions with local error:

3.8b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
3.8b
(/ (* M D) (* 2.0 d))
4.3b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.0b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

rewrite32.0ms

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:
7.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

series1.8s

Counts
4 → 12
Calls
4 calls:
366.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
33.0ms
(/ (* M D) (* 2.0 d))
707.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
672.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify63.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0560828
12559746
25001744

prune339.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.5b

localize19.0ms

Local error

Found 4 expressions with local error:

5.0b
(/ (* (pow (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) 2.0) (* (pow (cbrt (/ (* M D) (* 2.0 d))) 2.0) h)) l)
19.1b
(cbrt (/ (* M D) (* 2.0 d)))
19.1b
(cbrt (/ (* M D) (* 2.0 d)))
19.1b
(cbrt (/ (* M D) (* 2.0 d)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
32×prod-exp
17×div-exp
15×cbrt-prod
13×add-cbrt-cube
12×pow-exp
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×pow-to-exp
6×times-frac
4×pow1 div-inv add-log-exp
3×cbrt-undiv cbrt-div pow1/3 associate-/r* cbrt-unprod
1×frac-2neg clear-num associate-/l*
Counts
4 → 79
Calls
4 calls:
19.0ms
(/ (* (pow (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) 2.0) (* (pow (cbrt (/ (* M D) (* 2.0 d))) 2.0) h)) l)
3.0ms
(cbrt (/ (* M D) (* 2.0 d)))
3.0ms
(cbrt (/ (* M D) (* 2.0 d)))
3.0ms
(cbrt (/ (* M D) (* 2.0 d)))

series1.2s

Counts
4 → 12
Calls
4 calls:
891.0ms
(/ (* (pow (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) 2.0) (* (pow (cbrt (/ (* M D) (* 2.0 d))) 2.0) h)) l)
103.0ms
(cbrt (/ (* M D) (* 2.0 d)))
104.0ms
(cbrt (/ (* M D) (* 2.0 d)))
104.0ms
(cbrt (/ (* M D) (* 2.0 d)))

simplify48.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04311230
116911042
250011009

prune387.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize19.0ms

Local error

Found 4 expressions with local error:

4.6b
(* (pow (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) 2.0) (/ (* (pow (cbrt (/ (* M D) (* 2.0 d))) 2.0) h) l))
19.1b
(cbrt (/ (* M D) (* 2.0 d)))
19.1b
(cbrt (/ (* M D) (* 2.0 d)))
19.1b
(cbrt (/ (* M D) (* 2.0 d)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
68×add-exp-log
37×prod-exp
16×div-exp
15×cbrt-prod
14×add-sqr-sqrt pow-exp
13×add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
9×pow-to-exp
7×associate-*r*
6×times-frac
5×associate-*l*
4×pow1 cbrt-unprod div-inv add-log-exp
3×cbrt-div pow1/3 unswap-sqr
2×cbrt-undiv unpow-prod-down sqr-pow
1×associate-*r/ *-commutative
Counts
4 → 89
Calls
4 calls:
18.0ms
(* (pow (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) 2.0) (/ (* (pow (cbrt (/ (* M D) (* 2.0 d))) 2.0) h) l))
3.0ms
(cbrt (/ (* M D) (* 2.0 d)))
3.0ms
(cbrt (/ (* M D) (* 2.0 d)))
3.0ms
(cbrt (/ (* M D) (* 2.0 d)))

series1.4s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (pow (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) 2.0) (/ (* (pow (cbrt (/ (* M D) (* 2.0 d))) 2.0) h) l))
100.0ms
(cbrt (/ (* M D) (* 2.0 d)))
102.0ms
(cbrt (/ (* M D) (* 2.0 d)))
130.0ms
(cbrt (/ (* M D) (* 2.0 d)))

simplify51.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04381457
117381268
250011106

prune389.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.3b

regimes654.0ms

Accuracy

-17.5% (2.2b remaining)

Error of 10.0b against oracle of 7.8b and baseline of 9.7b

bsearch216.0ms

Steps
ItersRangePoint
11
1.2651223916331688e+203
4.006133005282483e+228
4.304770401463899e+222
9
-4.10435513107876e+257
-1.8117190500510915e+249
-4.039376954921309e+257

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03720
13720

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.1s9334×body80valid
382.0ms3060×body80nan