Details

Time bar (total: 12.6s)

sample63.0ms

Algorithm
intervals
Results
32.0ms308×body80valid
10.0ms96×body80nan

simplify55.0ms

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: 15.3b

localize17.0ms

Local error

Found 4 expressions with local error:

3.1b
(* 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))))
4.0b
(/ (* M D) (* 2.0 d))
11.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite34.0ms

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:
8.0ms
(* 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))
14.0ms
(* (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)))))
363.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms
(/ (* M D) (* 2.0 d))
679.0ms
(* (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

prune428.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize17.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
4.0b
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
4.0b
(/ (* M D) (* 2.0 d))
6.2b
(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
210×add-exp-log
85×div-exp
79×prod-exp
57×times-frac
55×add-sqr-sqrt
33×add-cbrt-cube
30×pow-exp
25×add-cube-cbrt *-un-lft-identity
22×associate-*r*
18×unpow-prod-down
13×cbrt-undiv cbrt-prod associate-*l* cbrt-unprod
12×unswap-sqr
10×associate-/l*
7×pow1 div-inv
6×pow-to-exp sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×frac-2neg sqrt-div clear-num associate-/r*
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 184
Calls
4 calls:
10.0ms
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
3.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
4.0ms
(/ (* M D) (* 2.0 d))
37.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

series1.6s

Counts
4 → 12
Calls
4 calls:
472.0ms
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
413.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
28.0ms
(/ (* M D) (* 2.0 d))
719.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

simplify116.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
010642411
149532226
250012226

prune700.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.3b

localize19.0ms

Local error

Found 4 expressions with local error:

4.0b
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l))))))
4.0b
(/ (* M D) (* 2.0 d))
4.0b
(/ (* M D) (* 2.0 d))
6.3b
(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
118×add-sqr-sqrt
112×times-frac
96×add-exp-log
58×associate-*l*
52×cbrt-prod
49×add-cube-cbrt *-un-lft-identity
38×div-exp
36×unpow-prod-down add-cbrt-cube
32×prod-exp
22×associate-*r*
21×unswap-sqr
12×cbrt-undiv cbrt-unprod sqr-pow
10×pow-exp div-inv
7×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 198
Calls
4 calls:
3.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l))))))
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))
47.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l)))

series1.3s

Counts
4 → 12
Calls
4 calls:
410.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l))))))
27.0ms
(/ (* M D) (* 2.0 d))
33.0ms
(/ (* M D) (* 2.0 d))
871.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l)))

simplify117.0ms

Algorithm
egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
010972706
146702542
250012542

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.3b

localize29.0ms

Local error

Found 4 expressions with local error:

4.0b
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ (* (cbrt h) (cbrt h)) (cbrt (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt (cbrt l)))))))
4.0b
(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ (* (cbrt h) (cbrt h)) (cbrt (* (cbrt l) (cbrt l)))))
4.0b
(/ (* M D) (* 2.0 d))
4.0b
(/ (* M D) (* 2.0 d))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
142×add-exp-log
98×times-frac
86×add-sqr-sqrt
58×associate-*l*
57×div-exp
52×prod-exp
44×cbrt-prod
38×add-cube-cbrt *-un-lft-identity add-cbrt-cube
36×unpow-prod-down
21×unswap-sqr
16×cbrt-unprod
15×cbrt-undiv pow-exp
12×sqr-pow
10×div-inv
8×associate-*r*
7×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp sqrt-prod
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 194
Calls
4 calls:
3.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ (* (cbrt h) (cbrt h)) (cbrt (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt (cbrt l)))))))
42.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ (* (cbrt h) (cbrt h)) (cbrt (* (cbrt l) (cbrt l)))))
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))

series1.0s

Counts
4 → 12
Calls
4 calls:
372.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ (* (cbrt h) (cbrt h)) (cbrt (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt (cbrt l)))))))
595.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ (* (cbrt h) (cbrt h)) (cbrt (* (cbrt l) (cbrt l)))))
27.0ms
(/ (* M D) (* 2.0 d))
32.0ms
(/ (* M D) (* 2.0 d))

simplify121.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
010913738
146293492
250033492

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.3b

regimes1.0s

Accuracy

0% (1.2b remaining)

Error of 8.2b against oracle of 6.9b and baseline of 8.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03532
13532

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.0s9334×body80valid
350.0ms3241×body80nan