Details

Time bar (total: 1.6m)

sample4.7s

Algorithm
intervals
Results
3.9s415×body10240exit
455.0ms2333×body80nan
132.0ms392×body80valid

simplify195.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize28.0ms

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))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow-exp
30×add-cbrt-cube
26×unpow-prod-down pow-unpow
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 176
Calls
4 calls:
36.0ms
(* (* (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))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
4.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
625.0ms
(* (* (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))))
58.0ms
(pow (/ d h) (/ 1.0 2.0))
721.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
64.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify46.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
012282042
150011847

prune708.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.8b

localize40.0ms

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))

rewrite181.0ms

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×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
20×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
9×pow1 cbrt-undiv
4×div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in 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 → 292
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
121.0ms
(* (* (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))))
7.0ms
(pow (/ d h) (/ 1.0 2.0))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.9s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
943.0ms
(* (* (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))))
58.0ms
(pow (/ d h) (/ 1.0 2.0))
898.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify79.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
018495801
150015529

prune722.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.3b

localize54.0ms

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))

rewrite495.0ms

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
32×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
4×pow-prod-down div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 1229
Calls
4 calls:
6.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.0ms
(/ (* M D) (* 2.0 d))
260.0ms
(* (* (* (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))))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.7s

Counts
4 → 12
Calls
4 calls:
178.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
28.0ms
(/ (* M D) (* 2.0 d))
718.0ms
(* (* (* (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))))
737.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify344.0ms

Algorithm
egg-herbie
Counts
1241 → 1241
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0500139400

prune1.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.8b

localize57.0ms

Local error

Found 4 expressions with local error:

7.1b
(cbrt (- 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))
11.0b
(* (* (/ 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))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
439×add-exp-log
222×prod-exp
135×div-exp
67×add-cbrt-cube
60×pow-exp
39×associate-*r*
30×cbrt-unprod
27×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×cbrt-undiv
12×pow-to-exp
10×pow1
9×associate-*l/
4×add-log-exp
3×cbrt-prod frac-times associate-*r/ associate-*l* pow-prod-down *-commutative div-inv
2×cbrt-div
1×flip3-- pow1/3 flip--
Counts
4 → 199
Calls
4 calls:
1.0ms
(cbrt (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
25.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.5s

Counts
4 → 12
Calls
4 calls:
247.0ms
(cbrt (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
734.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
740.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
736.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify78.0ms

Algorithm
egg-herbie
Counts
211 → 211
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06052264
124871991
250021988

prune864.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 10.8b

regimes1.3s

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0102118
1102118

end0.0ms

sample1.3m

Algorithm
intervals
Results
1.1m6763×body10240exit
7.6s40319×body80nan
2.2s6534×body80valid