Details

Time bar (total: 5.2s)

sample23.0ms

Algorithm
intervals
Results
6.0ms63×body640valid
4.0ms124×body80valid
3.0ms33×body320valid
2.0ms15×body1280valid
1.0ms21×body160valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1317
2437
3577
4737
5927
61267
71587
82077
92097
102097

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b
(/ 1.0 (- x 1.0))
3.0b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
83×*-un-lft-identity
47×times-frac
43×add-sqr-sqrt
23×add-cube-cbrt
14×distribute-lft-out--
13×distribute-lft-out
11×add-log-exp
9×associate-/r*
8×add-exp-log add-cbrt-cube difference-of-squares
6×associate-/l*
4×pow1 associate-/r/
3×flip3-- frac-add flip--
2×cbrt-undiv sub-neg associate-+l+ frac-2neg flip3-+ diff-log div-exp clear-num sum-log frac-sub flip-+ div-inv
1×+-commutative associate-+l-
Counts
4 → 114
Calls
4 calls:
5.0ms
(/ 1.0 (+ x 1.0))
36.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms
(/ 1.0 (- x 1.0))
182.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ 1.0 (+ x 1.0))
48.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
27.0ms
(/ 1.0 (- x 1.0))
222.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify49.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0496865
11681827
25001816

prune276.0ms

Filtered
126 candidates to 92 candidates (73.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.2b
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
7.6b
(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
12.6b
(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
16×add-exp-log add-cbrt-cube
13×flip3-+ flip-+
12×frac-times
11×associate-/r/ associate-/l/
10×add-log-exp
9×times-frac
8×frac-add distribute-lft-out
6×associate-*l/
4×pow1 cbrt-undiv add-sqr-sqrt add-cube-cbrt associate-+r+ flip3-- associate-*r/ div-exp prod-exp flip-- cbrt-unprod
3×+-commutative sum-log
2×distribute-rgt-in sub-neg distribute-lft-in
1×frac-2neg clear-num associate-/r* div-inv associate-/l*
Counts
4 → 88
Calls
4 calls:
31.0ms
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
29.0ms
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
20.0ms
(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
66.0ms
(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))

series544.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
66.0ms
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
128.0ms
(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
309.0ms
(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))

simplify85.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
06271549
132301162
250021152

prune248.0ms

Filtered
100 candidates to 78 candidates (78.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0))) (- (* x x) (* 1.0 1.0)))
0.1b
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0))
2.6b
(* (/ (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0))) (- (* x x) (* 1.0 1.0))) (+ x 1.0))
7.6b
(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))

rewrite262.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
39×*-un-lft-identity
33×times-frac
28×associate-*l*
24×add-cube-cbrt
13×add-exp-log add-cbrt-cube
12×difference-of-squares
9×flip3-- associate-*r* flip--
8×pow1 frac-times
6×add-log-exp
5×distribute-rgt-in distribute-lft-in
4×sub-neg associate-+r+ flip3-+ associate-*r/ associate-*l/ associate-/r* associate-/r/ flip-+ distribute-lft-out--
3×prod-exp frac-sub cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv associate-/l/ distribute-lft-out
1×+-commutative frac-2neg clear-num sum-log
Counts
4 → 136
Calls
4 calls:
86.0ms
(/ (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0))) (- (* x x) (* 1.0 1.0)))
122.0ms
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0))
27.0ms
(* (/ (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0))) (- (* x x) (* 1.0 1.0))) (+ x 1.0))
23.0ms
(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))

series841.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(/ (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0))) (- (* x x) (* 1.0 1.0)))
125.0ms
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0))
390.0ms
(* (/ (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0))) (- (* x x) (* 1.0 1.0))) (+ x 1.0))
128.0ms
(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))

simplify101.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
08682030
138591863
250011861

prune410.0ms

Filtered
148 candidates to 115 candidates (77.7%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (+ x 1.0) x) (- x 1.0))
0.0b
(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.0b
(- (* 1.0 x) (* (+ x 1.0) 2.0))
19.0b
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
88×associate-*l/
32×frac-add
31×flip3-- flip--
24×frac-times flip3-+ flip-+
18×add-exp-log add-cbrt-cube associate-/l/
12×associate-*r/
9×pow1 add-sqr-sqrt *-un-lft-identity
8×associate-/r/ add-log-exp
7×add-cube-cbrt
6×prod-exp cbrt-unprod
5×sub-neg associate-*r*
4×distribute-rgt-in associate-+l+ distribute-lft-in
3×cbrt-undiv times-frac div-exp pow-prod-down associate-/l*
1×+-commutative frac-2neg diff-log associate-*l* clear-num associate-/r* sum-log *-commutative div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 124
Calls
4 calls:
20.0ms
(* (* (+ x 1.0) x) (- x 1.0))
37.0ms
(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
2.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
10.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series225.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (* (+ x 1.0) x) (- x 1.0))
90.0ms
(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
37.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
1.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09972264
150012129

prune460.0ms

Filtered
136 candidates to 108 candidates (79.4%)
Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 10.9b

bsearch92.0ms

Steps
ItersRangePoint
8
0.8818080259852756
19555.519105776155
449.06402820041797
7
-4240874295.0135207
-33514344.933988083
-133358930.129605

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04924
14924

end0.0ms

sample595.0ms

Algorithm
intervals
Results
201.0ms1880×body640valid
121.0ms4142×body80valid
77.0ms945×body320valid
73.0ms540×body1280valid
26.0ms496×body160valid