Details

Time bar (total: 10.9s)

sample45.0ms

Algorithm
intervals
Results
17.0ms297×body80valid
7.0ms111×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: 12.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.7b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.3b
(/ (* M D) (* 2.0 d))
10.2b
(* (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:
6.0ms
(* 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))))
6.0ms
(/ (* 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:
419.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
367.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
33.0ms
(/ (* M D) (* 2.0 d))
696.0ms
(* (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

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.2b

localize15.0ms

Local error

Found 4 expressions with local error:

3.7b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.7b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.3b
(/ (* M D) (* 2.0 d))
6.0b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite31.0ms

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:
7.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
6.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
6.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series2.0s

Counts
4 → 12
Calls
4 calls:
703.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
371.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
28.0ms
(/ (* M D) (* 2.0 d))
921.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify69.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0576880
12585798
25001796

prune383.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.3b
(/ (* M D) (* 2.0 d))
5.3b
(/ (* M D) (* 2.0 d))
5.9b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
16×add-sqr-sqrt
12×div-exp
10×*-un-lft-identity
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt
6×unpow-prod-down
5×pow1 pow-exp sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-*r* div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l* sqr-pow
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 98
Calls
4 calls:
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)))
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.2s

Counts
4 → 12
Calls
4 calls:
371.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
27.0ms
(/ (* M D) (* 2.0 d))
34.0ms
(/ (* M D) (* 2.0 d))
724.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify55.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0457979
11916874
25001872

prune400.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.4b

localize21.0ms

Local error

Found 4 expressions with local error:

5.3b
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.3b
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.9b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.9b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
26×add-sqr-sqrt
22×prod-exp
18×associate-*l*
16×*-un-lft-identity
12×add-cube-cbrt unpow-prod-down
10×cbrt-prod pow-exp
8×div-exp add-cbrt-cube
6×associate-*r* unswap-sqr
4×pow1 expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp sqr-pow
2×pow-to-exp flip3-- times-frac pow1/3 *-commutative flip-- cbrt-unprod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 100
Calls
4 calls:
4.0ms
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
8.0ms
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series2.0s

Counts
4 → 12
Calls
4 calls:
265.0ms
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
256.0ms
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
737.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
739.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify47.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03461496
110681392
250011380

prune588.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.4b

regimes618.0ms

Accuracy

0% (1.9b remaining)

Error of 9.3b against oracle of 7.4b and baseline of 9.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02934
12934

end0.0ms

sample1.2s

Algorithm
intervals
Results
574.0ms9321×body80valid
189.0ms3034×body80nan