Details

Time bar (total: 12.3s)

sample106.0ms

Algorithm
intervals
Results
30.0ms60×body1280valid
26.0ms63×body10240exit
17.0ms304×body80valid
9.0ms32×body640valid
5.0ms26×body320valid
2.0ms15×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (37.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune10.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 29.9b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
0.0b
(* (- 1.0 eps) x)
0.0b
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
2.2b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite443.0ms

Algorithm
rewrite-expression-head
Rules
1802×associate-/l*
1682×add-sqr-sqrt
1638×*-un-lft-identity
1428×frac-sub
1358×times-frac
1136×associate-/l/
942×add-cube-cbrt
470×associate-/r*
290×difference-of-squares
178×distribute-lft-out
163×distribute-lft-out--
156×frac-2neg
154×clear-num
80×div-inv
43×flip3-+ flip-+
37×flip3-- flip--
12×add-exp-log
10×add-cbrt-cube
7×sub-div
6×pow1 add-log-exp
5×associate-*l*
4×div-exp
3×div-sub associate-*r*
2×cbrt-undiv associate-*l/
1×sub-neg distribute-rgt-out-- diff-log pow-prod-down prod-exp *-commutative cbrt-unprod associate--r- unswap-sqr
Counts
4 → 1573
Calls
4 calls:
16.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
6.0ms
(* (- 1.0 eps) x)
18.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
227.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series315.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
30.0ms
(* (- 1.0 eps) x)
49.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
188.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify736.0ms

Algorithm
egg-herbie
Counts
1585 → 1585
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
0500163430

prune4.6s

Filtered
1585 candidates to 939 candidates (59.2%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New158321585
Fresh000
Picked101
Done000
Total158421586

Merged error: 0.8b

Counts
1586 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
0.1b
(* 0.33333333333333337 (pow x 3))
4.0b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
25×*-un-lft-identity
16×associate-*r*
13×add-exp-log
11×associate-*l* unswap-sqr
9×add-cube-cbrt unpow-prod-down
8×add-log-exp
7×pow1 add-cbrt-cube
6×prod-exp distribute-lft-out--
5×difference-of-squares sqr-pow
4×distribute-lft-out
3×unpow2
2×pow-to-exp diff-log pow-prod-down pow-exp associate--l+ *-commutative cbrt-unprod
1×+-commutative sub-neg flip3-- unpow3 sum-log flip--
Counts
3 → 81
Calls
3 calls:
6.0ms
(* 0.5 (pow x 2))
6.0ms
(* 0.33333333333333337 (pow x 3))
22.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series106.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(* 0.5 (pow x 2))
37.0ms
(* 0.33333333333333337 (pow x 3))
44.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify47.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0298488
11202442
25002428

prune152.0ms

Filtered
90 candidates to 53 candidates (58.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New87390
Fresh011
Picked101
Done000
Total88492

Merged error: 0.8b

Counts
92 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

4.0b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
6.2b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
6.2b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
6.2b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
55×add-sqr-sqrt
42×cbrt-prod
24×distribute-lft-out--
20×associate-*l* difference-of-squares
16×distribute-lft-out unswap-sqr
9×add-log-exp
7×add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log unpow-prod-down flip3-- add-cbrt-cube flip-- unpow2 sqr-pow
3×pow1/3
2×diff-log associate--l+
1×+-commutative sub-neg sum-log
Counts
4 → 98
Calls
4 calls:
25.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
27.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
25.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
25.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series540.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
159.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
163.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
175.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify173.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03051518
19191443
245311351
350011351

prune322.0ms

Filtered
110 candidates to 73 candidates (66.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1082110
Fresh033
Picked101
Done000
Total1095114

Merged error: 0.8b

Counts
114 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

6.2b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
6.2b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
6.2b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
6.2b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
72×*-un-lft-identity
56×cbrt-prod add-sqr-sqrt
24×distribute-lft-out--
20×associate-*l* difference-of-squares
16×distribute-lft-out unswap-sqr
8×add-cube-cbrt cbrt-div
4×pow1 add-exp-log unpow-prod-down flip3-- pow1/3 add-cbrt-cube flip-- unpow2 add-log-exp sqr-pow
Counts
4 → 96
Calls
4 calls:
28.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
22.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
22.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
22.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series600.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
149.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
150.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
151.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify145.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
02791656
18511580
240221476
350021476

prune364.0ms

Filtered
108 candidates to 76 candidates (70.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1071108
Fresh044
Picked101
Done000
Total1085113

Merged error: 0.8b

Counts
113 → 5

regimes75.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.3b

bsearch124.0ms

Steps
ItersRangePoint
8
0.01411020868224607
10.386911891746092
1.5359688028823746

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04328
14328

end0.0ms

sample3.0s

Algorithm
intervals
Results
820.0ms1790×body1280valid
811.0ms1895×body10240exit
577.0ms9976×body80valid
354.0ms1325×body640valid
117.0ms648×body320valid
34.0ms301×body160valid