Details

Time bar (total: 2.5m)

sample124.0ms

Algorithm
intervals
Results
40.0ms494×body80valid
31.0ms46×body1280valid
11.0ms131×body80overflowed
9.0ms24×body640valid
4.0ms16×body320valid
2.0ms10×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (36.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune14.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 21.7b

Counts
2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(exp (neg (* (- 1.0 eps) x)))
0.0b
(exp (neg (* (+ 1.0 eps) x)))
1.7b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
74×exp-neg
72×frac-times
56×neg-sub0 exp-diff
38×associate-*l/
36×associate-*r/
28×flip3-- flip3-+ flip-- flip-+
18×un-div-inv
12×exp-prod
10×add-sqr-sqrt *-un-lft-identity add-log-exp
8×add-cube-cbrt
6×pow1 add-exp-log add-cbrt-cube
4×associate-*l* rem-exp-log
3×associate-*r*
2×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in neg-log
1×sub-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
4 → 148
Calls
4 calls:
6.0ms
(* (+ 1.0 eps) x)
3.0ms
(exp (neg (* (- 1.0 eps) x)))
3.0ms
(exp (neg (* (+ 1.0 eps) x)))
17.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series65.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (+ 1.0 eps) x)
6.0ms
(exp (neg (* (- 1.0 eps) x)))
6.0ms
(exp (neg (* (+ 1.0 eps) x)))
49.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify137.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
011773664
143803403
250013392

prune288.0ms

Filtered
160 candidates to 81 candidates (49.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1573160
Fresh101
Picked101
Done000
Total1593162

Merged error: 0.0b

Counts
162 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 0.6666666666666667 (pow x 3))
7.8b
(- (+ (* 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)))

series8.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(* 0.6666666666666667 (pow x 3))
4.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify34.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0207270
1894242
25002238

prune77.0ms

Filtered
51 candidates to 31 candidates (39.2%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New51051
Fresh022
Picked011
Done000
Total51354

Merged error: 0.0b

Counts
54 → 3

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 eps) x)
0.0b
(* (+ 1.0 eps) x)
0.0b
(exp (neg (* (+ 1.0 eps) x)))
1.7b
(- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
72×frac-times
55×neg-sub0
40×associate-*l/
37×exp-neg
36×pow-neg associate-*r/
29×flip3-- flip--
28×flip3-+ exp-diff flip-+
27×pow-sub
18×un-div-inv
15×add-sqr-sqrt
13×*-un-lft-identity
9×add-cube-cbrt associate-*l*
8×pow1 add-exp-log add-cbrt-cube add-log-exp
6×exp-prod associate-*r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 153
Calls
4 calls:
6.0ms
(* (- 1.0 eps) x)
6.0ms
(* (+ 1.0 eps) x)
3.0ms
(exp (neg (* (+ 1.0 eps) x)))
15.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series73.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (- 1.0 eps) x)
4.0ms
(* (+ 1.0 eps) x)
6.0ms
(exp (neg (* (+ 1.0 eps) x)))
58.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify144.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
012173685
147503460
250013460

prune275.0ms

Filtered
165 candidates to 81 candidates (50.9%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1641165
Fresh011
Picked101
Done011
Total1653168

Merged error: 0.0b

Counts
168 → 3

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (neg (* (+ 1.0 eps) x)))
0.4b
(* (sqrt (- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))) (sqrt (- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))))
1.7b
(- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))
1.7b
(- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
19129×frac-times
13944×sqrt-div
13770×frac-sub
9181×neg-sub0
6203×associate-*r/ associate-*l/
6121×exp-neg
6120×pow-neg
4760×flip3-- flip--
4591×exp-diff
4590×flip3-+ flip-+ pow-sub
3060×un-div-inv
25×add-sqr-sqrt
19×pow1
18×sqrt-prod
13×add-cube-cbrt *-un-lft-identity
10×add-log-exp
8×sqrt-pow1 pow1/2 swap-sqr
6×add-exp-log exp-prod associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×unswap-sqr
3×pow-prod-down pow-sqr
2×sub-neg diff-log rem-exp-log
1×pow2 distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in pow-plus sqrt-unprod neg-log prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 7307
Calls
4 calls:
3.0ms
(exp (neg (* (+ 1.0 eps) x)))
196.0ms
(* (sqrt (- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))) (sqrt (- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))))
18.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))
16.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series175.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(exp (neg (* (+ 1.0 eps) x)))
56.0ms
(* (sqrt (- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))) (sqrt (- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))))
58.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))
55.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (pow E (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify5.3s

Algorithm
egg-herbie
Counts
7319 → 7319
Iterations

Useful iterations: 0 (114.0ms)

IterNodesCost
08258614064

prune2.3m

Filtered
7319 candidates to 7289 candidates (0.4%)

Profiling

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