Details

Time bar (total: 11.5s)

sample63.0ms

Algorithm
intervals
Results
32.0ms294×body80valid
10.0ms101×body80nan

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize13.0ms

Local error

Found 4 expressions with local error:

1.9b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.1b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.1b
(/ (* M D) (* 2.0 d))
10.0b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite39.0ms

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:
9.0ms
(* 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))
15.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
406.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
366.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms
(/ (* M D) (* 2.0 d))
682.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify81.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06301135
127791057
250021054

prune444.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize14.0ms

Local error

Found 4 expressions with local error:

3.1b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.1b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.1b
(/ (* M D) (* 2.0 d))

rewrite34.0ms

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)
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
4.0ms
(/ (* M D) (* 2.0 d))

series1.8s

Counts
4 → 12
Calls
4 calls:
366.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
695.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
719.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
28.0ms
(/ (* M D) (* 2.0 d))

simplify67.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0576881
12585798
25001796

prune568.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
4.2b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.1b
(/ (* M D) (* 2.0 d))
6.1b
(/ (* M D) (* 2.0 d))

rewrite49.0ms

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:
19.0ms
(/ (* (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)
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))

series1.4s

Counts
4 → 12
Calls
4 calls:
672.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
687.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
26.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))

simplify81.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
08821759
131701336
250021332

prune442.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 expressions with local error:

4.2b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.4b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
6.1b
(/ (* M D) (* 2.0 d))
6.1b
(/ (* M D) (* 2.0 d))

rewrite31.0ms

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:
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
5.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
721.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
685.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
26.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))

simplify61.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0512859
12386728
25001728

prune398.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

regimes886.0ms

Accuracy

-8% (1.6b remaining)

Error of 8.8b against oracle of 7.2b and baseline of 8.7b

bsearch207.0ms

Steps
ItersRangePoint
9
6.008254652834628e-204
1.5252088610619315e-195
2.1109490795691675e-203
9
-1.682790079631386e-84
-1.0289575753963934e-93
-6.873603463407481e-86

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05452
15452

end0.0ms

sample1.8s

Algorithm
intervals
Results
986.0ms9316×body80valid
320.0ms3066×body80nan