Details

Time bar (total: 16.5s)

sample108.0ms

Algorithm
intervals
Results
51.0ms73×body1280valid
20.0ms51×body640valid
15.0ms34×body2560valid
6.0ms27×body320valid
3.0ms62×body80valid
1.0ms9×body160valid

simplify3.0ms

Counts
1 → 1
Iterations
IterNodes
done9
19
07

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.8b
(+ x (sqrt (+ (* x x) 1.0)))
2.9b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.4b
(sqrt (+ (* x x) 1.0))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod flip3-+ add-cbrt-cube flip-+
3×sqrt-prod
2×+-commutative log-div sum-log sqrt-div distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
4 → 53
Calls
4 calls:
8.0ms
(+ (* x x) 1.0)
27.0ms
(+ x (sqrt (+ (* x x) 1.0)))
16.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
7.0ms
(sqrt (+ (* x x) 1.0))

series459.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(+ (* x x) 1.0)
73.0ms
(+ x (sqrt (+ (* x x) 1.0)))
250.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
76.0ms
(sqrt (+ (* x x) 1.0))

simplify2.3s

Counts
65 → 65
Iterations
IterNodes
done5017
34032
21026
1342
0142

prune450.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 2 expressions with local error:

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

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
52×add-cbrt-cube add-exp-log
35×add-sqr-sqrt
29×times-frac
25×associate-*r*
23×prod-exp cbrt-unprod
18×*-un-lft-identity add-cube-cbrt
14×cbrt-undiv div-exp
11×sqrt-prod
9×pow1
8×associate-*l*
6×unswap-sqr
5×associate-*l/
4×pow-prod-down
2×frac-times associate-*r/ *-commutative div-inv add-log-exp
1×pow3
Counts
2 → 91
Calls
2 calls:
49.0ms
(* (/ (* x x) 1.0) (/ x (sqrt 1.0)))
92.0ms
(* (* (/ (* x x) 1.0) (/ x (sqrt 1.0))) -1/6)

series269.0ms

Counts
2 → 6
Calls
2 calls:
140.0ms
(* (/ (* x x) 1.0) (/ x (sqrt 1.0)))
129.0ms
(* (* (/ (* x x) 1.0) (/ x (sqrt 1.0))) -1/6)

simplify2.0s

Counts
97 → 97
Iterations
IterNodes
done5000
21883
1491
0157

prune436.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.4b
(/ 0.125 (* x (* x x)))
11.4b
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
18.3b
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
27×add-sqr-sqrt
24×times-frac
23×add-cube-cbrt
19×add-exp-log
15×add-cbrt-cube
12×unpow-prod-down
9×add-log-exp
8×associate-/r*
6×log-prod div-exp frac-sub associate-/l*
5×pow1 log-div
4×cbrt-undiv distribute-lft-out-- sqr-pow
3×prod-exp cbrt-unprod
2×clear-num frac-2neg flip3-+ flip3-- diff-log frac-add flip-+ div-inv flip-- distribute-lft-out difference-of-squares
1×pow-to-exp sum-log sub-neg rem-log-exp pow-exp log-pow associate--r+
Counts
4 → 108
Calls
4 calls:
7.0ms
(/ 0.0625 (pow x 5))
24.0ms
(/ 0.125 (* x (* x x)))
140.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
129.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series501.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ 0.0625 (pow x 5))
75.0ms
(/ 0.125 (* x (* x x)))
272.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
78.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

simplify1.9s

Counts
120 → 120
Iterations
IterNodes
done5067
22547
1637
0268

prune665.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 0.125 (* x (* x x))) x)
0.1b
(* x (* x x))
0.4b
(/ 0.125 (* x (* x x)))
9.7b
(log (+ x (- (/ 0.5 x) (- (/ 0.125 (* x (* x x))) x))))

rewrite441.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1 *-un-lft-identity add-exp-log
18×add-cbrt-cube
11×add-sqr-sqrt
8×add-cube-cbrt
6×log-prod prod-exp cbrt-unprod add-log-exp
5×pow-prod-up
4×distribute-lft-out--
3×cbrt-undiv times-frac div-exp associate-*l* pow-prod-down distribute-lft-out associate-/l*
2×log-div
1×pow2 clear-num associate-/r* sub-neg frac-2neg flip3-+ pow-plus flip3-- diff-log cube-unmult rem-log-exp associate-*r* pow-sqr log-pow *-commutative flip-+ div-inv flip-- difference-of-squares unswap-sqr
Counts
4 → 78
Calls
4 calls:
76.0ms
(- (/ 0.125 (* x (* x x))) x)
26.0ms
(* x (* x x))
25.0ms
(/ 0.125 (* x (* x x)))
309.0ms
(log (+ x (- (/ 0.5 x) (- (/ 0.125 (* x (* x x))) x))))

series472.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(- (/ 0.125 (* x (* x x))) x)
43.0ms
(* x (* x x))
61.0ms
(/ 0.125 (* x (* x x)))
225.0ms
(log (+ x (- (/ 0.5 x) (- (/ 0.125 (* x (* x x))) x))))

simplify1.6s

Counts
90 → 90
Iterations
IterNodes
done5010
21170
1359
0160

prune363.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes186.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.3b

bsearch127.0ms

Steps
ItersRangePoint
7
0.778402845272117
28.34319947931986
0.8904362184089252
8
-2980.3304644899954
-0.1501579911863904
-1.01308332610721

simplify12.0ms

Iterations
IterNodes
done41
141
034

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.9s2287×body1280valid
579.0ms1570×body640valid
477.0ms840×body2560valid
211.0ms767×body320valid
128.0ms2109×body80valid
53.0ms427×body160valid