Details

Time bar (total: 10.8s)

sample63.0ms

Algorithm
intervals
Results
21.0ms299×body80valid
7.0ms97×body80nan

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize18.0ms

Local error

Found 4 expressions with local error:

2.0b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.3b
(/ (* M D) (* 2.0 d))
5.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
8.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite71.0ms

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:
20.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
12.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
30.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.4s

Counts
4 → 12
Calls
4 calls:
393.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
30.0ms
(/ (* M D) (* 2.0 d))
359.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
645.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify72.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06091076
12742997
25002994

prune381.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

localize14.0ms

Local error

Found 4 expressions with local error:

3.9b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
4.3b
(/ (* M D) (* 2.0 d))
4.7b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.2b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

rewrite69.0ms

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:
23.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
13.0ms
(/ (* M D) (* 2.0 d))
18.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
11.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

series1.7s

Counts
4 → 12
Calls
4 calls:
692.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
25.0ms
(/ (* M D) (* 2.0 d))
656.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
361.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

simplify63.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0560829
12559746
25001744

prune328.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

localize16.0ms

Local error

Found 4 expressions with local error:

4.3b
(/ (* M D) (* 2.0 d))
4.7b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
5.2b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
6.3b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
361×add-exp-log
180×prod-exp
125×div-exp
80×pow-exp
27×add-cbrt-cube
18×add-sqr-sqrt
16×pow-to-exp
12×*-un-lft-identity
10×add-cube-cbrt
9×associate-*l*
8×cbrt-unprod
7×cbrt-undiv
6×unpow-prod-down
5×pow1 times-frac sqrt-prod
4×associate-/r* add-log-exp
3×associate-*r* div-inv unswap-sqr
2×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 → 146
Calls
4 calls:
14.0ms
(/ (* M D) (* 2.0 d))
40.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
14.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
24.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.8s

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ (* M D) (* 2.0 d))
675.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
363.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
688.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify93.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
09011943
132721558
250011548

prune359.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.7b

localize17.0ms

Local error

Found 4 expressions with local error:

4.3b
(/ (* M D) (* 2.0 d))
4.9b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
5.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
6.3b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
26×prod-exp
23×add-cbrt-cube
20×div-exp
16×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity pow-exp
9×associate-*l*
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1 times-frac
4×associate-/r* add-log-exp
3×associate-*r* sqrt-prod 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--
Counts
4 → 94
Calls
4 calls:
12.0ms
(/ (* M D) (* 2.0 d))
16.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
27.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.8s

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ (* M D) (* 2.0 d))
671.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
364.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
709.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify72.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05711022
12660912
25001911

prune357.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.7b

regimes505.0ms

Accuracy

-69.7% (2.4b remaining)

Error of 9.4b against oracle of 7.0b and baseline of 8.4b

bsearch100.0ms

Steps
ItersRangePoint
9
2.9686534244321025e+286
1.9526570868530345e+291
1.933159505335491e+291
10
3.385551585241616e-297
5.139020178807382e-287
1.855277338734028e-289

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03726
13726

end0.0ms

sample1.3s

Algorithm
intervals
Results
467.0ms9299×body80valid
168.0ms3133×body80nan