Details

Time bar (total: 1.6m)

sample4.7s

Algorithm
intervals
Results
4.0s415×body10240exit
468.0ms2333×body80nan
136.0ms392×body80valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05417
117417
272017
3500117

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize33.0ms

Local error

Found 4 expressions with local error:

7.7b
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.0b
(pow (/ d h) (/ 1.0 2.0))
11.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.5b
(pow (/ d l) (/ 1.0 2.0))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
42×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
40×pow-exp
30×add-cbrt-cube
26×unpow-prod-down pow-unpow
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
6×prod-diff
5×cbrt-undiv distribute-rgt-in distribute-lft-in div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 190
Calls
4 calls:
172.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
4.0ms
(pow (/ d h) (/ 1.0 2.0))
24.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
5.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
632.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
68.0ms
(pow (/ d h) (/ 1.0 2.0))
726.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
62.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify61.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
012872382
150012125

prune743.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.8b

localize46.0ms

Local error

Found 4 expressions with local error:

5.7b
(/ (* M D) (* 2.0 d))
7.7b
(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.0b
(pow (/ d h) (/ 1.0 2.0))
11.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
818×add-exp-log
567×prod-exp
280×pow-exp
187×div-exp
94×pow-to-exp
46×add-cbrt-cube
32×rec-exp 1-exp
28×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
20×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
9×pow1 cbrt-undiv
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg associate-*l* pow-prod-down *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 306
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
132.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
5.0ms
(pow (/ d h) (/ 1.0 2.0))
23.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.8s

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (* M D) (* 2.0 d))
975.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
70.0ms
(pow (/ d h) (/ 1.0 2.0))
748.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify79.0ms

Algorithm
egg-herbie
Counts
318 → 318
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
019736253
150025937

prune800.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.3b

localize51.0ms

Local error

Found 4 expressions with local error:

3.0b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
5.7b
(/ (* M D) (* 2.0 d))
7.7b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite513.0ms

Algorithm
rewrite-expression-head
Rules
6373×add-exp-log
4949×prod-exp
2614×pow-exp
1626×div-exp
789×pow-to-exp
528×1-exp
232×rec-exp
55×add-cbrt-cube
37×times-frac
34×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×cbrt-unprod
22×unpow-prod-down
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-undiv cbrt-prod
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u pow-prod-down log1p-expm1-u div-inv add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 1243
Calls
4 calls:
7.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.0ms
(/ (* M D) (* 2.0 d))
278.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
26.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.7s

Counts
4 → 12
Calls
4 calls:
181.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
27.0ms
(/ (* M D) (* 2.0 d))
728.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
747.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify340.0ms

Algorithm
egg-herbie
Counts
1255 → 1255
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
0500139782

prune1.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 8.9b

localize60.0ms

Local error

Found 4 expressions with local error:

5.7b
(/ (* M D) (* 2.0 d))
7.7b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (exp (+ (log (/ 1.0 2.0)) (+ (* (log (/ (* M D) (* 2.0 d))) 2.0) (log (/ h l)))))))
11.9b
(log (/ (* M D) (* 2.0 d)))
13.7b
(log (/ h l))

rewrite664.0ms

Algorithm
rewrite-expression-head
Rules
6241×add-exp-log
4879×prod-exp
2592×pow-exp
1585×div-exp
784×pow-to-exp
528×1-exp
232×rec-exp
34×add-cbrt-cube
29×add-sqr-sqrt *-un-lft-identity
27×add-cube-cbrt
24×prod-diff
18×log-prod
17×cbrt-unprod
14×distribute-rgt-in distribute-lft-in
11×pow1 times-frac
7×rem-log-exp
6×exp-sum
5×associate-*r*
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down div-inv
2×sub-neg log-div associate-*r/ log-pow
1×flip3-- frac-2neg associate-*l* clear-num associate-/r* *-commutative flip-- associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 1197
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
457.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (exp (+ (log (/ 1.0 2.0)) (+ (* (log (/ (* M D) (* 2.0 d))) 2.0) (log (/ h l)))))))
3.0ms
(log (/ (* M D) (* 2.0 d)))
2.0ms
(log (/ h l))

series775.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
646.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (exp (+ (log (/ 1.0 2.0)) (+ (* (log (/ (* M D) (* 2.0 d))) 2.0) (log (/ h l)))))))
66.0ms
(log (/ (* M D) (* 2.0 d)))
35.0ms
(log (/ h l))

simplify375.0ms

Algorithm
egg-herbie
Counts
1209 → 1209
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0479244532
1500343457

prune1.1s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 8.2b

regimes1.8s

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05343
15343

end0.0ms

sample1.3m

Algorithm
intervals
Results
1.1m6763×body10240exit
7.9s40319×body80nan
2.3s6534×body80valid