Details

Time bar (total: 17.9s)

sample251.0ms

Algorithm
intervals
Results
170.0ms265×body10240exit
27.0ms298×body80valid
17.0ms199×body80nan

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize13.0ms

Local error

Found 4 expressions with local error:

2.3b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.3b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.1b
(/ (* M D) (* 2.0 d))
9.3b
(* (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×expm1-log1p-u sqrt-div log1p-expm1-u 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 → 121
Calls
4 calls:
8.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
6.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0ms
(/ (* M D) (* 2.0 d))
14.0ms
(* (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)))))
348.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
32.0ms
(/ (* M D) (* 2.0 d))
667.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify71.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06301135
127791057
250021054

prune416.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.7b

localize13.0ms

Local error

Found 4 expressions with local error:

3.3b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.6b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.1b
(/ (* M D) (* 2.0 d))
5.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

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×expm1-log1p-u associate-/r* log1p-expm1-u 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 → 104
Calls
4 calls:
10.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series1.8s

Counts
4 → 12
Calls
4 calls:
362.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
680.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
35.0ms
(/ (* M D) (* 2.0 d))
709.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify63.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0576880
12585798
25001796

prune380.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize20.0ms

Local error

Found 4 expressions with local error:

4.4b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.6b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
5.1b
(/ (* M D) (* 2.0 d))
5.1b
(/ (* M D) (* 2.0 d))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
373×add-exp-log
184×prod-exp
129×div-exp
80×pow-exp
39×add-cbrt-cube
16×pow-to-exp
14×add-sqr-sqrt
12×cbrt-unprod
11×cbrt-undiv
9×add-cube-cbrt *-un-lft-identity associate-*l*
6×unpow-prod-down times-frac
5×associate-/r*
4×pow1 expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×frac-2neg associate-*r* clear-num associate-/l* unswap-sqr
2×sqr-pow
1×*-commutative
Counts
4 → 158
Calls
4 calls:
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
16.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
722.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
689.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
27.0ms
(/ (* M D) (* 2.0 d))
34.0ms
(/ (* M D) (* 2.0 d))

simplify86.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
08821759
131701336
250021332

prune425.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize20.0ms

Local error

Found 4 expressions with local error:

4.3b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
4.4b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.1b
(/ (* M D) (* 2.0 d))
5.1b
(/ (* M D) (* 2.0 d))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
79×add-exp-log
35×add-cbrt-cube
30×prod-exp
24×div-exp
14×add-sqr-sqrt
10×cbrt-undiv pow-exp cbrt-unprod
9×add-cube-cbrt *-un-lft-identity associate-*l*
6×unpow-prod-down times-frac
5×associate-/r*
4×pow1 expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×frac-2neg associate-*r* clear-num associate-/l* unswap-sqr
2×pow-to-exp sqr-pow
1×*-commutative
Counts
4 → 108
Calls
4 calls:
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
692.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
722.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
33.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))

simplify58.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0512859
12388728
25001728

prune398.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.1b

regimes696.0ms

Accuracy

0% (1.5b remaining)

Error of 8.4b against oracle of 6.9b and baseline of 8.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03117
13117

end0.0ms

sample8.6s

Algorithm
intervals
Results
6.2s9142×body10240exit
747.0ms6102×body80nan
710.0ms9332×body80valid