Details

Time bar (total: 11.8s)

sample45.0ms

Algorithm
intervals
Results
15.0ms299×body80valid
5.0ms97×body80nan

simplify54.0ms

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: 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))

rewrite77.0ms

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:
21.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
13.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
32.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.8s

Counts
4 → 12
Calls
4 calls:
629.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
31.0ms
(/ (* M D) (* 2.0 d))
396.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
722.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify74.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06301135
127791057
250011054

prune411.0ms

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)))

rewrite80.0ms

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:
25.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
13.0ms
(/ (* M D) (* 2.0 d))
16.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
20.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
757.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
29.0ms
(/ (* M D) (* 2.0 d))
715.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
397.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

simplify73.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0576880
12585798
25002796

prune369.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

localize23.0ms

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)

rewrite112.0ms

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×expm1-log1p-u associate-/r* log1p-expm1-u 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 → 154
Calls
4 calls:
13.0ms
(/ (* M D) (* 2.0 d))
46.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
17.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
26.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.9s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
726.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
403.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
766.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify94.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
09522025
133361640
250011630

prune417.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.7b

localize16.0ms

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)

rewrite71.0ms

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×expm1-log1p-u associate-/r* log1p-expm1-u 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 → 102
Calls
4 calls:
13.0ms
(/ (* M D) (* 2.0 d))
17.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
7.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
30.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.9s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
727.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
403.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
762.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify72.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05871092
12692982
25001981

prune391.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.7b

regimes493.0ms

Accuracy

-69.6% (2.4b remaining)

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

bsearch96.0ms

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
488.0ms9299×body80valid
166.0ms3133×body80nan