Details

Time bar (total: 5.9s)

sample1.0s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 48.260498%

Guaranteed chance to sample good point: 93.234635%

Results
28.0ms52×body1280valid
14.0ms41×body640valid
11.0ms133×body80valid
5.0ms19×body320valid
2.0ms11×body160valid
0.0ms2×body80invalid
0.0ms1×body80overflowed

simplify35.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (34.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune7.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 28.5b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
81×exp-neg frac-sub
80×frac-times
61×neg-sub0 exp-diff
40×associate-*r/ associate-*l/
31×flip3-- flip--
30×flip3-+ flip-+
20×un-div-inv
18×add-sqr-sqrt
13×*-un-lft-identity
10×associate-*l*
9×add-cube-cbrt
8×pow1 add-cbrt-cube add-log-exp
6×add-exp-log exp-prod associate-*r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log difference-of-squares unswap-sqr
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in times-frac diff-log neg-log distribute-lft-out distribute-lft-out--
Counts
4 → 168
Calls
4 calls:
3.0ms
(exp (neg (* (- 1.0 eps) x)))
13.0ms
(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
11.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
16.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series76.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(exp (neg (* (- 1.0 eps) x)))
12.0ms
(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
10.0ms
(* (+ 1.0 (/ 1.0 eps)) (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)))))

simplify144.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
012014059
144003786
250023771

prune357.0ms

Filtered
96 candidates to 180 candidates (-87.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1773180
Fresh000
Picked101
Done000
Total1783181

Merged error: 0.8b

Counts
181 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* 0.6666666666666667 (pow x 3)) 2.0)
0.1b
(* 0.6666666666666667 (pow x 3))
7.6b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×associate-*r*
10×add-log-exp
8×add-exp-log
7×add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube
4×unpow-prod-down cube-prod unswap-sqr
3×pow1 associate-*l* prod-exp
2×diff-log sum-log sqr-pow
1×+-commutative cube-mult pow-to-exp sub-neg flip3-- flip3-+ unpow3 pow-exp associate--l+ *-commutative flip-- cbrt-unprod flip-+
Counts
3 → 56
Calls
3 calls:
4.0ms
(+ (* 0.6666666666666667 (pow x 3)) 2.0)
6.0ms
(* 0.6666666666666667 (pow x 3))
7.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series15.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(+ (* 0.6666666666666667 (pow x 3)) 2.0)
4.0ms
(* 0.6666666666666667 (pow x 3))
4.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify38.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0251336
11024311
25002307

prune111.0ms

Filtered
41 candidates to 65 candidates (-58.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New62365
Fresh022
Picked101
Done000
Total63568

Merged error: 0.8b

Counts
68 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 0.6666666666666667 x) x)
0.6b
(cbrt x)
0.7b
(pow (cbrt x) 3)
7.6b
(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
10×pow1 add-exp-log
9×cbrt-prod add-cbrt-cube add-log-exp
6×unpow-prod-down cube-prod
3×pow-unpow associate-*r* pow-prod-down prod-exp cbrt-unprod
2×pow-pow pow1/3 diff-log
1×cube-mult pow-to-exp sub-neg flip3-- unpow3 associate-*l* pow-exp associate--l+ sum-log *-commutative flip-- rem-cube-cbrt sqr-pow
Counts
4 → 73
Calls
4 calls:
5.0ms
(* (* 0.6666666666666667 x) x)
1.0ms
(cbrt x)
3.0ms
(pow (cbrt x) 3)
11.0ms
(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

series64.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (* 0.6666666666666667 x) x)
25.0ms
(cbrt x)
29.0ms
(pow (cbrt x) 3)
7.0ms
(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

simplify68.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0351412
11878356
25001322

prune116.0ms

Filtered
46 candidates to 85 candidates (-84.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New84185
Fresh044
Picked101
Done000
Total85590

Merged error: 0.8b

Counts
90 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.7b
(pow (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) 3)
7.6b
(- (+ (* (* (* 0.6666666666666667 x) x) (pow (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) 3)) 2.0) (* 1.0 (pow x 2)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×add-log-exp
7×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube
4×pow-pow pow1/3
3×pow-unpow
2×diff-log pow-prod-down pow-exp rem-cube-cbrt
1×cube-mult pow-to-exp sub-neg unpow-prod-down flip3-- unpow3 cube-prod pow3 prod-exp associate--l+ sum-log flip-- cbrt-unprod sqr-pow
Counts
4 → 60
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
6.0ms
(pow (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) 3)
10.0ms
(- (+ (* (* (* 0.6666666666666667 x) x) (pow (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) 3)) 2.0) (* 1.0 (pow x 2)))

series81.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(cbrt x)
21.0ms
(cbrt x)
31.0ms
(pow (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) 3)
7.0ms
(- (+ (* (* (* 0.6666666666666667 x) x) (pow (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) 3)) 2.0) (* 1.0 (pow x 2)))

simplify41.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0266632
11067528
25002369

prune112.0ms

Filtered
53 candidates to 72 candidates (-35.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New71172
Fresh044
Picked101
Done000
Total72577

Merged error: 0.8b

Counts
77 → 5

regimes185.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 17.8b

bsearch97.0ms

Steps
ItersRangePoint
8
0.01526814401880452
49.41739978793382
1.677411260115744

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05137
16337
26337

end0.0ms

sample3.2s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 48.260498%

Guaranteed chance to sample good point: 93.234635%

Results
957.0ms1722×body1280valid
427.0ms1193×body640valid
347.0ms4208×body80valid
152.0ms606×body320valid
43.0ms271×body160valid
9.0ms114×body80overflowed
9.0ms96×body80invalid
8.0ms15×body1280invalid
3.0ms10×body320invalid
3.0ms7×body640invalid
0.0ms1×body160invalid

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