Details

Time bar (total: 12.9s)

sample45.0ms

Algorithm
intervals
Results
17.0ms300×body80valid
5.0ms92×body80nan

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize18.0ms

Local error

Found 4 expressions with local error:

2.6b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.3b
(/ (* M D) (* 2.0 d))
4.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
9.7b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite81.0ms

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:
20.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
17.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
33.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.4s

Counts
4 → 12
Calls
4 calls:
395.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
32.0ms
(/ (* M D) (* 2.0 d))
355.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
660.0ms
(* (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

prune867.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.1b

localize15.0ms

Local error

Found 4 expressions with local error:

3.3b
(/ (* M D) (* 2.0 d))
4.2b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
4.9b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
165×add-exp-log
91×prod-exp
40×div-exp
30×add-cbrt-cube
25×pow-exp
21×add-sqr-sqrt
16×associate-*r*
15×add-cube-cbrt *-un-lft-identity
11×times-frac cbrt-unprod
10×associate-*l*
8×rec-exp 1-exp
7×pow1
6×cbrt-undiv unpow-prod-down
5×pow-to-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod div-inv unswap-sqr
2×sqrt-div *-commutative sqr-pow
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num associate-/r* un-div-inv flip-- associate-/l*
Counts
4 → 136
Calls
4 calls:
15.0ms
(/ (* M D) (* 2.0 d))
8.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
42.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
27.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series1.7s

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ (* M D) (* 2.0 d))
351.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
637.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
669.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify91.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07681192
134931070
250011057

prune611.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize18.0ms

Local error

Found 4 expressions with local error:

3.3b
(/ (* M D) (* 2.0 d))
3.7b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.2b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
4.9b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
1390×add-exp-log
903×prod-exp
362×div-exp
305×pow-exp
61×pow-to-exp
57×rec-exp 1-exp
39×add-cbrt-cube
21×add-sqr-sqrt
17×cbrt-unprod
16×associate-*r*
15×add-cube-cbrt *-un-lft-identity
11×times-frac
10×associate-*l*
7×pow1 cbrt-undiv
6×unpow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod div-inv unswap-sqr
2×sqrt-div *-commutative sqr-pow
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num associate-/r* un-div-inv flip-- associate-/l*
Counts
4 → 334
Calls
4 calls:
14.0ms
(/ (* M D) (* 2.0 d))
26.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
9.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
130.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

series1.7s

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ (* M D) (* 2.0 d))
676.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
344.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
658.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

simplify130.0ms

Algorithm
egg-herbie
Counts
346 → 346
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
016664789
148373400
250013400

prune849.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.0b

localize18.0ms

Local error

Found 4 expressions with local error:

3.3b
(/ (* M D) (* 2.0 d))
3.7b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
6.5b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
165×add-exp-log
91×prod-exp
40×div-exp
30×add-cbrt-cube
25×pow-exp
21×add-sqr-sqrt
16×associate-*r*
15×add-cube-cbrt *-un-lft-identity
11×times-frac cbrt-unprod
10×associate-*l*
8×rec-exp 1-exp
7×pow1
6×cbrt-undiv unpow-prod-down
5×pow-to-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod div-inv unswap-sqr
2×sqrt-div *-commutative sqr-pow
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num associate-/r* un-div-inv flip-- associate-/l*
Counts
4 → 136
Calls
4 calls:
13.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
7.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
48.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

series1.7s

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ (* M D) (* 2.0 d))
693.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
340.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
651.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

simplify93.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07861471
135511321
250021303

prune726.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.0b

regimes1.1s

Accuracy

0% (1.1b remaining)

Error of 8.7b against oracle of 7.5b and baseline of 8.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03236
13236

end0.0ms

sample1.1s

Algorithm
intervals
Results
503.0ms9265×body80valid
179.0ms3146×body80nan