Details

Time bar (total: 10.7s)

sample40.0ms

Algorithm
intervals
Results
15.0ms290×body80valid
5.0ms87×body80nan

simplify59.0ms

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: 15.8b

localize14.0ms

Local error

Found 4 expressions with local error:

2.6b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.9b
(/ (* M D) (* 2.0 d))
13.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite40.0ms

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:
13.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0ms
(/ (* M D) (* 2.0 d))
16.0ms
(* (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)))))
356.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms
(/ (* M D) (* 2.0 d))
671.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify73.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06301136
127791057
250021054

prune415.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.2b

localize13.0ms

Local error

Found 4 expressions with local error:

4.0b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.9b
(/ (* M D) (* 2.0 d))
6.0b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.9b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

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:
11.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

series1.8s

Counts
4 → 12
Calls
4 calls:
367.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
27.0ms
(/ (* M D) (* 2.0 d))
722.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
688.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify69.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0576880
12585798
25001796

prune389.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.9b

localize14.0ms

Local error

Found 4 expressions with local error:

4.0b
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
6.0b
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
6.3b
(* (/ M 2.0) (/ D d))
6.9b
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
41×add-sqr-sqrt
26×prod-exp
25×*-un-lft-identity times-frac
23×add-cube-cbrt add-cbrt-cube
20×div-exp
18×associate-*l*
16×associate-*r*
10×pow-exp
7×pow1
6×cbrt-undiv cbrt-unprod unswap-sqr
5×sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* div-inv
2×pow-to-exp sqrt-div *-commutative sqr-pow
1×frac-times unpow-prod-down rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ clear-num flip-- associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 128
Calls
4 calls:
14.0ms
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
6.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
13.0ms
(* (/ M 2.0) (/ D d))
6.0ms
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)

series1.8s

Counts
4 → 12
Calls
4 calls:
374.0ms
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
722.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
27.0ms
(* (/ M 2.0) (/ D d))
699.0ms
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)

simplify79.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
07171000
13046917
25001915

prune470.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.5b

localize16.0ms

Local error

Found 4 expressions with local error:

5.3b
(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
6.3b
(* (/ M 2.0) (/ D d))
6.3b
(* (/ M 2.0) (/ D d))
6.9b
(/ (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) l)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
373×add-exp-log
184×prod-exp
129×div-exp
80×pow-exp
63×add-sqr-sqrt
47×times-frac
39×add-cbrt-cube
36×add-cube-cbrt *-un-lft-identity
31×associate-*l*
29×associate-*r*
16×pow-to-exp
12×cbrt-unprod
11×cbrt-undiv
10×unswap-sqr
8×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* *-commutative
2×frac-times associate-*r/ pow-prod-down associate-*l/ sqr-pow
1×unpow-prod-down frac-2neg clear-num associate-/l*
Counts
4 → 211
Calls
4 calls:
6.0ms
(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
13.0ms
(* (/ M 2.0) (/ D d))
14.0ms
(* (/ M 2.0) (/ D d))
18.0ms
(/ (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) l)

series1.5s

Counts
4 → 12
Calls
4 calls:
737.0ms
(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
27.0ms
(* (/ M 2.0) (/ D d))
27.0ms
(* (/ M 2.0) (/ D d))
704.0ms
(/ (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) l)

simplify96.0ms

Algorithm
egg-herbie
Counts
223 → 223
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
010222026
136151603
250011599

prune649.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.5b

regimes428.0ms

Accuracy

0% (3.7b remaining)

Error of 10.5b against oracle of 6.7b and baseline of 10.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02712
12712

end0.0ms

sample1.1s

Algorithm
intervals
Results
503.0ms9385×body80valid
176.0ms3169×body80nan