Details

Time bar (total: 8.8s)

sample46.0ms

Algorithm
intervals
Results
18.0ms306×body80valid
6.0ms104×body80nan

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize19.0ms

Local error

Found 4 expressions with local error:

2.2b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.6b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.4b
(/ (* M D) (* 2.0 d))
11.9b
(* (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×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)))))
3.0ms
(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))

series1.5s

Counts
4 → 12
Calls
4 calls:
400.0ms
(* w0 (sqrt (- 1.0 (* (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))))
33.0ms
(/ (* M D) (* 2.0 d))
677.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify72.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
06301135
127791057
250021057

prune437.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize16.0ms

Local error

Found 4 expressions with local error:

3.6b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
6.4b
(/ (* M D) (* 2.0 d))
6.4b
(/ (* M D) (* 2.0 d))
8.2b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
33×add-cbrt-cube
30×prod-exp
28×add-sqr-sqrt
23×div-exp
15×times-frac
14×add-cube-cbrt *-un-lft-identity
13×associate-*r*
10×pow-exp cbrt-unprod
9×cbrt-undiv associate-*l*
7×unpow-prod-down
6×unswap-sqr
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×sqrt-prod sqr-pow
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ *-commutative flip--
Counts
4 → 118
Calls
4 calls:
3.0ms
(sqrt (- 1.0 (* (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))
7.0ms
(/ (* M D) (* 2.0 d))
14.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.1s

Counts
4 → 12
Calls
4 calls:
362.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
32.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
678.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify71.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
05951197
126181077
250011076

prune449.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

localize17.0ms

Local error

Found 4 expressions with local error:

5.2b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.4b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
6.4b
(/ (* M D) (* 2.0 d))
6.4b
(/ (* 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:
9.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0ms
(/ (* (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:
713.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
685.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
29.0ms
(/ (* M D) (* 2.0 d))
31.0ms
(/ (* M D) (* 2.0 d))

simplify60.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0512859
12386728
25001728

prune412.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

localize28.0ms

Local error

Found 4 expressions with local error:

6.4b
(/ (* M D) (* 2.0 d))
17.6b
(cbrt (/ (* M D) (* 2.0 d)))
17.6b
(cbrt (/ (* M D) (* 2.0 d)))
17.6b
(cbrt (/ (* M D) (* 2.0 d)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log add-cbrt-cube
15×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 cbrt-undiv expm1-log1p-u times-frac div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×cbrt-div pow1/3
1×frac-2neg clear-num associate-/r* associate-/l*
Counts
4 → 71
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
2.0ms
(cbrt (/ (* M D) (* 2.0 d)))
2.0ms
(cbrt (/ (* M D) (* 2.0 d)))
3.0ms
(cbrt (/ (* M D) (* 2.0 d)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
102.0ms
(cbrt (/ (* M D) (* 2.0 d)))
103.0ms
(cbrt (/ (* M D) (* 2.0 d)))
104.0ms
(cbrt (/ (* M D) (* 2.0 d)))

simplify227.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0250540
11148478
25002472

prune413.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.3b

regimes743.0ms

Accuracy

-30.2% (2.0b remaining)

Error of 9.3b against oracle of 7.3b and baseline of 8.8b

bsearch48.0ms

Steps
ItersRangePoint
0
-6.0706316482279e-314
-1.976262583365e-323
-3.0353158251021e-314
6
-4.4879316068299356e+294
-6.981255098223496e+293
-4.434769257142831e+294

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03938
13938

end0.0ms

sample1.2s

Algorithm
intervals
Results
571.0ms9329×body80valid
197.0ms3112×body80nan