Details

Time bar (total: 6.1s)

sample81.0ms

Algorithm
intervals
Results
28.0ms59×body1280valid
19.0ms331×body80valid
7.0ms26×body640valid
5.0ms82×body80overflowed
3.0ms19×body320valid
1.0ms7×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (35.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize20.0ms

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)))
1.2b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite275.0ms

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:
11.0ms
(* (- 1.0 eps) x)
24.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
19.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
214.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series292.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (- 1.0 eps) x)
47.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
39.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
177.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify65.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06841993
121761881
250021880

prune565.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
0.1b
(* 0.33333333333333337 (pow x 3))
7.2b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
20×associate-*r*
13×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp unswap-sqr
7×add-cbrt-cube
6×associate-*l* prod-exp
4×cube-prod sqr-pow
3×pow1
2×pow-to-exp diff-log pow-exp *-commutative cbrt-unprod unpow2
1×cube-mult sub-neg flip3-- unpow3 associate--l+ sum-log flip--
Counts
3 → 72
Calls
3 calls:
5.0ms
(* 0.5 (pow x 2))
7.0ms
(* 0.33333333333333337 (pow x 3))
26.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series101.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(* 0.5 (pow x 2))
39.0ms
(* 0.33333333333333337 (pow x 3))
38.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify47.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0281367
11210327
25001314

prune160.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

7.2b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
10.8b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.8b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.8b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite63.0ms

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:
25.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
12.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
11.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
14.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series486.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (+ (* 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))))
149.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify136.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0253983
1904924
24251839
35001839

prune274.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

7.2b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
7.2b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
10.8b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.8b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
14×add-log-exp
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log cbrt-div flip3-- diff-log add-cbrt-cube flip--
2×sub-neg pow1/3 associate--l+ sum-log
Counts
4 → 54
Calls
4 calls:
24.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
24.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
14.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
12.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series379.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
38.0ms
(- (+ (* 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))))
148.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify132.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0253862
1904804
24251738
35001738

prune312.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

regimes70.0ms

Accuracy

96.9% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.6b

bsearch176.0ms

Steps
ItersRangePoint
11
4.127477794865454e-14
104248118811.33417
199.99672138679333

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06347
16347

end0.0ms

sample2.3s

Algorithm
intervals
Results
752.0ms1664×body1280valid
582.0ms9979×body80valid
345.0ms1296×body640valid
113.0ms627×body320valid
112.0ms1936×body80overflowed
39.0ms344×body160valid