Details

Time bar (total: 2.8s)

sample95.0ms

Algorithm
intervals
Results
34.0ms63×body1280valid
22.0ms316×body80valid
13.0ms42×body640valid
4.0ms64×body80overflowed
4.0ms19×body320valid
1.0ms10×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (36.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 31.4b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(* (- 1.0 eps) x)
0.0b
(- (/ 1.0 eps) 1.0)
3.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
72×exp-neg frac-times
54×neg-sub0 exp-diff
40×associate-*l/
36×associate-*r/
30×flip3-- flip--
28×flip3-+ flip-+
19×add-sqr-sqrt
18×un-div-inv
14×*-un-lft-identity
9×associate-*l*
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube add-log-exp
6×associate-*r*
3×difference-of-squares
2×sub-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out-- unswap-sqr
1×times-frac distribute-lft-out
Counts
4 → 151
Calls
4 calls:
6.0ms
(* (+ 1.0 eps) x)
6.0ms
(* (- 1.0 eps) x)
7.0ms
(- (/ 1.0 eps) 1.0)
19.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (+ 1.0 eps) x)
28.0ms
(* (- 1.0 eps) x)
36.0ms
(- (/ 1.0 eps) 1.0)
192.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify149.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
012053664
145823401
250013392

prune339.0ms

Filtered
163 candidates to 80 candidates (49.1%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1612163
Fresh000
Picked101
Done000
Total1622164

Merged error: 0.5b

Counts
164 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
6.6b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log add-log-exp
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 diff-log sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- unpow3 pow-exp associate--l+ sum-log *-commutative flip-- cbrt-unprod
Counts
2 → 45
Calls
2 calls:
6.0ms
(* 0.6666666666666667 (pow x 3))
7.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series77.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(* 0.6666666666666667 (pow x 3))
42.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify40.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0207270
1894242
25002238

prune159.0ms

Filtered
51 candidates to 31 candidates (60.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New49251
Fresh011
Picked101
Done000
Total50353

Merged error: 0.5b

Counts
53 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
0.1b
(* 0.6666666666666667 (pow x 3))
10.2b
(+ (* (neg (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))
11.3b
(/ (+ (* (neg (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
20×add-cube-cbrt *-un-lft-identity
16×add-exp-log
10×add-cbrt-cube
9×times-frac
8×unpow-prod-down cube-prod unswap-sqr
6×associate-*l* prod-exp add-log-exp
4×pow1 sqr-pow
3×flip3-+ associate-/r* flip-+ associate-/l*
2×cube-mult pow-to-exp associate-+r+ unpow3 pow-exp associate-/r/ *-commutative cbrt-unprod associate-/l/
1×cbrt-undiv +-commutative distribute-rgt-in frac-2neg distribute-lft-in div-exp clear-num sum-log div-inv
Counts
4 → 106
Calls
4 calls:
9.0ms
(* 0.6666666666666667 (pow x 3))
6.0ms
(* 0.6666666666666667 (pow x 3))
5.0ms
(+ (* (neg (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))
14.0ms
(/ (+ (* (neg (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

series234.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* 0.6666666666666667 (pow x 3))
34.0ms
(* 0.6666666666666667 (pow x 3))
51.0ms
(+ (* (neg (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))
110.0ms
(/ (+ (* (neg (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

simplify67.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04121398
119941258
250031248

prune352.0ms

Filtered
118 candidates to 82 candidates (69.5%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1162118
Fresh022
Picked101
Done000
Total1174121

Merged error: 0.4b

Counts
121 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow x 2) (+ (* 0.6666666666666667 x) 1.0))
0.1b
(* 2.666666666666667 (pow x 3))
11.6b
(- (+ (* 2.666666666666667 (pow x 3)) 4.0) (* 1.0 (pow x 4)))
12.8b
(/ (- (+ (* 2.666666666666667 (pow x 3)) 4.0) (* 1.0 (pow x 4))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
16×add-exp-log
15×associate-*r*
11×associate-*l*
10×add-cbrt-cube
9×times-frac add-log-exp
8×unpow-prod-down unswap-sqr
6×prod-exp
4×pow1 cube-prod sqr-pow
3×associate-/r* associate-/l*
2×pow-to-exp flip3-- flip3-+ diff-log associate-*r/ pow-exp associate-/r/ *-commutative flip-- cbrt-unprod flip-+ associate-/l/ unpow2
1×cbrt-undiv distribute-rgt-in cube-mult sub-neg frac-2neg distribute-lft-in unpow3 div-sub div-exp associate--l+ clear-num sum-log div-inv
Counts
4 → 108
Calls
4 calls:
7.0ms
(* (pow x 2) (+ (* 0.6666666666666667 x) 1.0))
6.0ms
(* 2.666666666666667 (pow x 3))
10.0ms
(- (+ (* 2.666666666666667 (pow x 3)) 4.0) (* 1.0 (pow x 4)))
15.0ms
(/ (- (+ (* 2.666666666666667 (pow x 3)) 4.0) (* 1.0 (pow x 4))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

series242.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* (pow x 2) (+ (* 0.6666666666666667 x) 1.0))
39.0ms
(* 2.666666666666667 (pow x 3))
51.0ms
(- (+ (* 2.666666666666667 (pow x 3)) 4.0) (* 1.0 (pow x 4)))
81.0ms
(/ (- (+ (* 2.666666666666667 (pow x 3)) 4.0) (* 1.0 (pow x 4))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

simplify86.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
05661098
126151007
250021000

prune312.0ms

Filtered
120 candidates to 81 candidates (67.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1173120
Fresh123
Picked101
Done000
Total1195124

Merged error: 0.4b

Counts
124 → 5

regimes83.0ms

bsearch6.0ms

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