Details

Time bar (total: 27.2s)

sample120.0ms

Algorithm
intervals
Results
55.0ms75×body1280valid
25.0ms51×body640valid
13.0ms22×body2560valid
6.0ms81×body80valid
4.0ms15×body320valid
2.0ms12×body160valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done9
19
07

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 49.9b

localize27.0ms

Local error

Found 3 expressions with local error:

1.0b
(+ x (sqrt (+ (* x x) 1.0)))
2.7b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.3b
(sqrt (+ (* x x) 1.0))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod
3×flip3-+ sqrt-prod add-cbrt-cube flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
53.0ms
(+ x (sqrt (+ (* x x) 1.0)))
33.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
18.0ms
(sqrt (+ (* x x) 1.0))

series497.0ms

Counts
3 → 9
Calls
3 calls:
103.0ms
(+ x (sqrt (+ (* x x) 1.0)))
319.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
74.0ms
(sqrt (+ (* x x) 1.0))

simplify3.6s

Counts
51 → 51
Iterations
IterNodes
done5014
33574
2941
1311
0133

prune435.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* (/ (* x (* x x)) 1.0) (/ -1/6 (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
0.1b
(* x (* x x))
0.1b
(* (/ (* x (* x x)) 1.0) (/ -1/6 (sqrt 1.0)))

rewrite388.0ms

Algorithm
rewrite-expression-head
Rules
40×add-exp-log add-cbrt-cube
28×add-sqr-sqrt
23×times-frac associate-*r*
19×pow1 add-cube-cbrt *-un-lft-identity
17×prod-exp cbrt-unprod
10×cbrt-undiv div-exp associate-*l* sqrt-prod
7×add-log-exp
6×frac-add
5×pow-prod-up
4×flip3-+ pow-prod-down flip-+ unswap-sqr
3×frac-times associate-*r/ associate-*l/ sum-log
2×*-commutative div-inv
1×+-commutative pow2 associate-+r+ pow-plus cube-unmult pow-sqr
Counts
3 → 103
Calls
3 calls:
209.0ms
(+ (* (/ (* x (* x x)) 1.0) (/ -1/6 (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
35.0ms
(* x (* x x))
131.0ms
(* (/ (* x (* x x)) 1.0) (/ -1/6 (sqrt 1.0)))

series419.0ms

Counts
3 → 9
Calls
3 calls:
204.0ms
(+ (* (/ (* x (* x x)) 1.0) (/ -1/6 (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
62.0ms
(* x (* x x))
153.0ms
(* (/ (* x (* x x)) 1.0) (/ -1/6 (sqrt 1.0)))

simplify4.5s

Counts
112 → 112
Iterations
IterNodes
done5004
23672
1724
0216

prune637.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (+ x (- (/ 0.5 x) (/ (/ 0.125 x) (* x x)))))
0.0b
(- (/ 0.5 x) (/ (/ 0.125 x) (* x x)))
0.2b
(/ (/ 0.125 x) (* x x))
8.8b
(log (+ x (+ x (- (/ 0.5 x) (/ (/ 0.125 x) (* x x))))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
40×times-frac
39×*-un-lft-identity
36×add-sqr-sqrt
19×add-cube-cbrt
17×add-exp-log
16×add-cbrt-cube
15×add-log-exp
13×associate-/l*
10×distribute-lft-out
6×cbrt-undiv log-prod div-exp difference-of-squares
5×pow1 sum-log
3×div-inv distribute-lft-out--
2×associate-+r- log-div flip3-+ diff-log prod-exp cbrt-unprod flip-+
1×+-commutative sub-neg associate-+r+ flip3-- frac-2neg rem-log-exp clear-num associate-/r* log-pow frac-sub flip-- associate-/l/
Counts
4 → 101
Calls
4 calls:
505.0ms
(+ x (+ x (- (/ 0.5 x) (/ (/ 0.125 x) (* x x)))))
70.0ms
(- (/ 0.5 x) (/ (/ 0.125 x) (* x x)))
29.0ms
(/ (/ 0.125 x) (* x x))
540.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ (/ 0.125 x) (* x x))))))

series677.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(+ x (+ x (- (/ 0.5 x) (/ (/ 0.125 x) (* x x)))))
185.0ms
(- (/ 0.5 x) (/ (/ 0.125 x) (* x x)))
83.0ms
(/ (/ 0.125 x) (* x x))
325.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ (/ 0.125 x) (* x x))))))

simplify2.6s

Counts
113 → 113
Iterations
IterNodes
done5001
21717
1542
0229

prune722.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 0.125 x) (* x x))
0.3b
(/ 0.0625 (pow x 5))
10.9b
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
17.5b
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite570.0ms

Algorithm
rewrite-expression-head
Rules
58×times-frac
49×add-sqr-sqrt
45×*-un-lft-identity
35×add-cube-cbrt
22×add-exp-log
18×add-cbrt-cube
16×associate-/l*
12×unpow-prod-down
9×div-exp add-log-exp
8×log-prod associate-/r*
7×cbrt-undiv
6×frac-sub difference-of-squares
5×pow1 log-div
4×div-inv distribute-lft-out-- sqr-pow
2×flip3-- frac-2neg flip3-+ diff-log frac-add prod-exp clear-num flip-- cbrt-unprod flip-+ distribute-lft-out
1×pow-to-exp sub-neg rem-log-exp pow-exp sum-log log-pow associate-/l/ associate--r+
Counts
4 → 135
Calls
4 calls:
32.0ms
(/ (/ 0.125 x) (* x x))
16.0ms
(/ 0.0625 (pow x 5))
240.0ms
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
267.0ms
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series690.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (/ 0.125 x) (* x x))
106.0ms
(/ 0.0625 (pow x 5))
369.0ms
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
132.0ms
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify3.5s

Counts
147 → 147
Iterations
IterNodes
done5060
22832
1779
0320

prune1.0s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes203.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.4b

bsearch196.0ms

Steps
ItersRangePoint
9
2.490703692944805e-05
37.746059492850215
0.8909481582438814
9
-1.440408271564231
-1.963203309137196e-05
-1.014477909773237

simplify23.0ms

Iterations
IterNodes
done42
142
035

end0.0ms

sample5.0s

Algorithm
intervals
Results
2.8s2355×body1280valid
806.0ms1483×body640valid
487.0ms808×body2560valid
265.0ms781×body320valid
226.0ms2167×body80valid
90.0ms406×body160valid