Details

Time bar (total: 9.4s)

sample41.0ms

Algorithm
intervals
Results
15.0ms295×body80valid
6.0ms110×body80nan

simplify56.0ms

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: 14.8b

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.5b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.9b
(/ (* M D) (* 2.0 d))
12.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite38.0ms

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))))
7.0ms
(/ (* 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:
401.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
370.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
28.0ms
(/ (* M D) (* 2.0 d))
687.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify75.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06301135
127791057
250021054

prune440.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.7b

localize15.0ms

Local error

Found 4 expressions with local error:

3.5b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
4.9b
(/ (* M D) (* 2.0 d))
5.1b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
6.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite40.0ms

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:
3.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
4.0ms
(/ (* M D) (* 2.0 d))
17.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series1.8s

Counts
4 → 12
Calls
4 calls:
373.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
28.0ms
(/ (* M D) (* 2.0 d))
705.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
732.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify91.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07681192
134931070
250011057

prune412.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.0b

localize17.0ms

Local error

Found 4 expressions with local error:

3.5b
(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
(/ (* M D) (* 2.0 d))
4.9b
(/ (* M D) (* 2.0 d))
5.1b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
1381×add-exp-log
896×prod-exp
362×div-exp
300×pow-exp
60×pow-to-exp
57×rec-exp 1-exp
49×add-cbrt-cube
20×cbrt-unprod
13×add-sqr-sqrt associate-*r*
12×add-cube-cbrt *-un-lft-identity
11×cbrt-undiv times-frac
7×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod div-inv
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ associate-*l* pow-prod-down un-div-inv *-commutative flip--
Counts
4 → 324
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)) (/ 1 l))))
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))
53.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

series1.1s

Counts
4 → 12
Calls
4 calls:
376.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
28.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))
702.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

simplify125.0ms

Algorithm
egg-herbie
Counts
336 → 336
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
015374620
142093218
250013206

prune402.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.8b

localize17.0ms

Local error

Found 4 expressions with local error:

3.5b
(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
(/ (* M D) (* 2.0 d))
4.9b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
156×add-exp-log
84×prod-exp
40×div-exp add-cbrt-cube
20×pow-exp
14×cbrt-unprod
13×add-sqr-sqrt associate-*r*
12×add-cube-cbrt *-un-lft-identity
11×times-frac
10×cbrt-undiv
8×rec-exp 1-exp
7×pow1
4×expm1-log1p-u pow-to-exp log1p-expm1-u add-log-exp
3×sqrt-prod div-inv
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ associate-*l* pow-prod-down un-div-inv *-commutative flip--
Counts
4 → 126
Calls
4 calls:
4.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
5.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))
21.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

series1.1s

Counts
4 → 12
Calls
4 calls:
377.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
28.0ms
(/ (* M D) (* 2.0 d))
34.0ms
(/ (* M D) (* 2.0 d))
697.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

simplify80.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06851303
130251139
250021121

prune380.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

regimes414.0ms

Accuracy

0% (0.9b remaining)

Error of 8.3b against oracle of 7.3b and baseline of 8.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03418
13418

end0.0ms

sample1.1s

Algorithm
intervals
Results
478.0ms9368×body80valid
162.0ms3045×body80nan