Details

Time bar (total: 6.9s)

sample108.0ms

Algorithm
intervals
Results
32.0ms73×body10240exit
30.0ms72×body1280valid
15.0ms284×body80valid
8.0ms35×body640valid
4.0ms25×body320valid
2.0ms17×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (36.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 eps) x)
0.0b
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
3.9b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite285.0ms

Algorithm
rewrite-expression-head
Rules
122×*-un-lft-identity
106×times-frac
96×add-sqr-sqrt
36×add-cube-cbrt
27×distribute-lft-out--
18×difference-of-squares
10×add-cbrt-cube distribute-lft-out associate-/l*
8×add-exp-log
6×pow1 associate-/r* add-log-exp
5×associate-*l*
4×div-inv associate-/l/
3×flip3-- div-sub associate-*r* flip--
2×cbrt-undiv frac-2neg div-exp associate-*l/ clear-num
1×sub-neg distribute-rgt-out-- flip3-+ diff-log pow-prod-down prod-exp *-commutative frac-sub cbrt-unprod flip-+ sub-div associate--r- unswap-sqr
Counts
4 → 138
Calls
4 calls:
10.0ms
(* (- 1.0 eps) x)
26.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
20.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
222.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series297.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (- 1.0 eps) x)
44.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
45.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
178.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify69.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06841993
121761881
250021880

prune435.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.33333333333333337 (pow x 3))
6.0b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite33.0ms

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
(* 0.33333333333333337 (pow x 3))
26.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series78.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(* 0.33333333333333337 (pow x 3))
38.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify34.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0207270
1894242
25002238

prune114.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 0.33333333333333337 x) x)
0.6b
(cbrt x)
0.7b
(pow (cbrt x) 3)
6.0b
(- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2)))

rewrite210.0ms

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:
6.0ms
(* (* 0.33333333333333337 x) x)
0.0ms
(cbrt x)
2.0ms
(pow (cbrt x) 3)
200.0ms
(- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2)))

series492.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (* 0.33333333333333337 x) x)
188.0ms
(cbrt x)
222.0ms
(pow (cbrt x) 3)
57.0ms
(- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2)))

simplify73.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
0311379
11784317
25003303

prune186.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize23.0ms

Local error

Found 4 expressions with local error:

6.0b
(- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2)))
9.5b
(cbrt (- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2))))
9.5b
(cbrt (- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2))))
9.5b
(cbrt (- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2))))

rewrite447.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-log-exp
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×pow1 add-exp-log flip3-- add-cbrt-cube flip--
3×pow1/3
2×diff-log
1×sub-neg associate--l+ sum-log
Counts
4 → 53
Calls
4 calls:
197.0ms
(- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2)))
82.0ms
(cbrt (- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2))))
83.0ms
(cbrt (- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2))))
84.0ms
(cbrt (- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2))))

series556.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2)))
168.0ms
(cbrt (- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2))))
167.0ms
(cbrt (- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2))))
163.0ms
(cbrt (- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2))))

simplify43.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02741247
110961152
250011049

prune303.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

regimes68.0ms

Accuracy

95.8% (0.7b remaining)

Error of 1.2b against oracle of 0.5b and baseline of 16.8b

bsearch92.0ms

Steps
ItersRangePoint
6
1.2499789889099044
12.952944841197453
2.2371703346309433

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04840
14840

end0.0ms

sample2.9s

Algorithm
intervals
Results
871.0ms1856×body10240exit
750.0ms1774×body1280valid
537.0ms9956×body80valid
305.0ms1245×body640valid
108.0ms641×body320valid
31.0ms298×body160valid