Details

Time bar (total: 33.1s)

sample132.0ms

Algorithm
intervals
Results
63.0ms75×body1280valid
24.0ms57×body640valid
14.0ms24×body2560valid
8.0ms26×body320valid
5.0ms59×body80valid
3.0ms15×body160valid

simplify24.0ms

Counts
1 → 1
Iterations
IterNodes
done9
19
07

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.3b

localize94.0ms

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))))
13.6b
(sqrt (+ (* x x) 1.0))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×log-prod add-exp-log
3×flip3-+ add-cbrt-cube sqrt-prod flip-+ insert-posit16
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
3 → 45
Calls
3 calls:
38.0ms
(+ x (sqrt (+ (* x x) 1.0)))
43.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
41.0ms
(sqrt (+ (* x x) 1.0))

series450.0ms

Counts
3 → 9
Calls
3 calls:
78.0ms
(+ x (sqrt (+ (* x x) 1.0)))
295.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
77.0ms
(sqrt (+ (* x x) 1.0))

simplify5.4s

Counts
54 → 54
Iterations
IterNodes
done5049
33422
2934
1315
0137

prune528.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize100.0ms

Local error

Found 3 expressions with local error:

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

rewrite887.0ms

Algorithm
rewrite-expression-head
Rules
53×add-cbrt-cube add-exp-log
27×prod-exp cbrt-unprod
21×associate-*l/
17×pow1
16×associate-*r*
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×cbrt-undiv div-exp
9×times-frac pow-prod-down
7×add-log-exp
6×frac-add
4×frac-times flip3-+ associate-*r/ flip-+
3×sum-log insert-posit16
2×associate-*l* *-commutative
1×+-commutative associate-+l+ div-inv
Counts
3 → 93
Calls
3 calls:
313.0ms
(+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (* (* (/ x (sqrt 1.0)) x) (/ x 1.0)) -1/6))
126.0ms
(* (* (/ x (sqrt 1.0)) x) (/ x 1.0))
431.0ms
(* (* (* (/ x (sqrt 1.0)) x) (/ x 1.0)) -1/6)

series502.0ms

Counts
3 → 9
Calls
3 calls:
186.0ms
(+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (* (* (/ x (sqrt 1.0)) x) (/ x 1.0)) -1/6))
168.0ms
(* (* (/ x (sqrt 1.0)) x) (/ x 1.0))
148.0ms
(* (* (* (/ x (sqrt 1.0)) x) (/ x 1.0)) -1/6)

simplify6.0s

Counts
102 → 102
Iterations
IterNodes
done5000
22710
1606
0192

prune795.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize136.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.2b
(/ 0.125 (* (* x x) x))
14.6b
(log (- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
19.2b
(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
33×*-un-lft-identity
30×times-frac
23×add-cube-cbrt
19×add-exp-log
15×add-cbrt-cube
14×unpow-prod-down
9×log-prod add-log-exp
8×associate-/r* frac-sub difference-of-squares
6×div-exp associate-/l* distribute-lft-out-- sqr-pow
5×pow1 log-div
4×cbrt-undiv flip3-- insert-posit16 flip--
3×diff-log prod-exp cbrt-unprod
2×clear-num sub-neg frac-2neg associate--l+ div-inv
1×associate--l- pow-to-exp rem-log-exp pow-exp log-pow
Counts
4 → 120
Calls
4 calls:
26.0ms
(/ 0.0625 (pow x 5))
38.0ms
(/ 0.125 (* (* x x) x))
478.0ms
(log (- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
1.1s
(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series590.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ 0.0625 (pow x 5))
64.0ms
(/ 0.125 (* (* x x) x))
330.0ms
(log (- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
98.0ms
(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify4.4s

Counts
132 → 132
Iterations
IterNodes
done5000
22247
1628
0283

prune1.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize108.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 0.5 x) (/ 0.125 (* (* x x) x)))
0.1b
(* (* x x) x)
0.2b
(/ 0.125 (* (* x x) x))
11.4b
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (* (* x x) x))))))

rewrite740.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
19×*-un-lft-identity add-exp-log
18×add-cbrt-cube
14×add-sqr-sqrt
8×add-cube-cbrt
6×log-prod pow-plus prod-exp pow-prod-up cbrt-unprod add-log-exp
5×distribute-lft-out
4×times-frac insert-posit16
3×cbrt-undiv div-exp associate-*r* pow-prod-down associate-/l*
2×pow2 log-div pow-sqr distribute-lft-out-- difference-of-squares
1×clear-num associate-/r* sub-neg frac-2neg flip3-+ flip3-- diff-log rem-log-exp associate-*l* pow3 log-pow *-commutative frac-sub flip-+ div-inv flip-- unswap-sqr
Counts
4 → 88
Calls
4 calls:
75.0ms
(- (/ 0.5 x) (/ 0.125 (* (* x x) x)))
50.0ms
(* (* x x) x)
54.0ms
(/ 0.125 (* (* x x) x))
551.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (* (* x x) x))))))

series574.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(- (/ 0.5 x) (/ 0.125 (* (* x x) x)))
70.0ms
(* (* x x) x)
80.0ms
(/ 0.125 (* (* x x) x))
268.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (* (* x x) x))))))

simplify3.7s

Counts
100 → 100
Iterations
IterNodes
done5001
21524
1434
0175

prune542.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes233.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.6b

bsearch137.0ms

Steps
ItersRangePoint
10
4.3052657707541446e-11
1.874259372897972
0.8927244562157713
9
-209901990.47645873
-0.28008678268591264
-0.994661063828435

simplify34.0ms

Iterations
IterNodes
done43
143
035

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.7s2308×body1280valid
790.0ms822×body2560valid
647.0ms1548×body640valid
228.0ms779×body320valid
141.0ms2129×body80valid
86.0ms414×body160valid