Details

Time bar (total: 3.4s)

sample19.0ms

Algorithm
intervals
Results
4.0ms44×body1280valid
3.0ms38×body640valid
3.0ms134×body80valid
1.0ms24×body320valid
1.0ms16×body160valid

simplify21.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0126
1166
2196
3216
4276
5396
6586
7796
81076
91606
102776
113036
123036

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.6b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
4.4b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
52×times-frac
45×add-sqr-sqrt
23×add-cube-cbrt
18×distribute-lft-out distribute-lft-out--
9×associate-/r* difference-of-squares
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
4×associate-/r/
3×pow1
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num flip-- flip-+ div-inv associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 104
Calls
3 calls:
5.0ms
(/ x (+ x 1.0))
7.0ms
(/ (+ x 1.0) (- x 1.0))
32.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series204.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(/ x (+ x 1.0))
37.0ms
(/ (+ x 1.0) (- x 1.0))
130.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify44.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0392760
11379726
25001716

prune190.0ms

Filtered
113 candidates to 76 candidates (67.3%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1085113
Fresh000
Picked101
Done000
Total1095114

Merged error: 0.0b

Counts
114 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ x 1.0) (- x 1.0))
0.0b
(exp (/ x (+ x 1.0)))
2.3b
(log (exp (/ x (+ x 1.0))))
4.4b
(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
48×add-sqr-sqrt
45×times-frac
36×exp-prod
33×add-cube-cbrt
20×log-pow
12×distribute-lft-out
7×distribute-lft-out-- difference-of-squares
6×pow1 add-exp-log log-prod associate-/r/ add-cbrt-cube add-log-exp
5×associate-/r*
4×associate-/l*
3×flip3-+ associate--l+ flip-+ div-inv
2×flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp rem-log-exp clear-num rem-exp-log
Counts
4 → 120
Calls
4 calls:
7.0ms
(/ (+ x 1.0) (- x 1.0))
6.0ms
(exp (/ x (+ x 1.0)))
7.0ms
(log (exp (/ x (+ x 1.0))))
38.0ms
(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ (+ x 1.0) (- x 1.0))
54.0ms
(exp (/ x (+ x 1.0)))
34.0ms
(log (exp (/ x (+ x 1.0))))
130.0ms
(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

simplify44.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0432839
11356774
25001761

prune223.0ms

Filtered
132 candidates to 97 candidates (73.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1311132
Fresh044
Picked011
Done000
Total1316137

Merged error: 0.0b

Counts
137 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))
20.8b
(- (/ (/ x (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
35×*-un-lft-identity
25×times-frac
16×cbrt-prod
10×difference-of-squares
7×add-cube-cbrt distribute-lft-out--
6×cbrt-div add-log-exp
5×distribute-lft-out
4×pow1 add-exp-log add-cbrt-cube
3×flip3-+ pow1/3 flip-+
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 70
Calls
4 calls:
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
125.0ms
(- (/ (/ x (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(cbrt (+ x 1.0))
87.0ms
(cbrt (+ x 1.0))
87.0ms
(cbrt (+ x 1.0))
130.0ms
(- (/ (/ x (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

simplify101.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 3 (90.0ms)

IterNodesCost
03521028
1953958
23729920
35002914

prune187.0ms

Filtered
82 candidates to 64 candidates (78.0%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New81182
Fresh134
Picked011
Done011
Total82688

Merged error: 0.0b

Counts
88 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))
20.8b
(+ (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (/ (* (/ (/ x (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (+ x 1.0))) x) (+ x 1.0)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
12×cbrt-prod
8×add-log-exp
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+ distribute-lft-out
3×pow1/3 frac-add distribute-neg-frac
2×sum-log
1×+-commutative neg-sub0 frac-times associate-+l- associate-*r/ neg-log associate-*l/
Counts
4 → 59
Calls
4 calls:
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
9.0ms
(+ (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (/ (* (/ (/ x (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (+ x 1.0))) x) (+ x 1.0)))

series475.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(cbrt (+ x 1.0))
89.0ms
(cbrt (+ x 1.0))
89.0ms
(cbrt (+ x 1.0))
209.0ms
(+ (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (/ (* (/ (/ x (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (+ x 1.0))) x) (+ x 1.0)))

simplify44.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0409906
11320812
25002770

prune231.0ms

Filtered
71 candidates to 61 candidates (85.9%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New68371
Fresh033
Picked101
Done112
Total70777

Merged error: 0.0b

Counts
77 → 7

regimes47.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.4b

bsearch99.0ms

Steps
ItersRangePoint
9
860.9547529914067
28642596122.821114
8391.566280727506
10
-43540924890.08803
-0.0051836583041924315
-9397.35870742111

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04738
14938
24938

end0.0ms

sample515.0ms

Algorithm
intervals
Results
175.0ms1732×body1280valid
106.0ms1213×body640valid
92.0ms4091×body80valid
42.0ms650×body320valid
13.0ms314×body160valid