Details

Time bar (total: 9.3s)

sample48.0ms

Algorithm
intervals
Results
11.0ms242×body160nan
11.0ms523×body80nan
7.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1109
2119
done119

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (+ x (sqrt (- (* x x) 1.0))))
0.0b
(- (* x x) 1.0)
0.0b
(+ x (sqrt (- (* x x) 1.0)))
30.6b
(sqrt (- (* x x) 1.0))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×add-sqr-sqrt
8×add-log-exp
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod sqrt-prod add-cbrt-cube
2×log-div flip3-- flip3-+ sqrt-div flip-- flip-+ distribute-lft-out difference-of-squares
1×+-commutative sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log rem-log-exp sum-log log-pow
Counts
4 → 56
Calls
4 calls:
16.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
8.0ms
(- (* x x) 1.0)
19.0ms
(+ x (sqrt (- (* x x) 1.0)))
10.0ms
(sqrt (- (* x x) 1.0))

series346.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
44.0ms
(- (* x x) 1.0)
61.0ms
(+ x (sqrt (- (* x x) 1.0)))
52.0ms
(sqrt (- (* x x) 1.0))

simplify1.2s

Counts
68 → 68
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0148916
1325835
2897750
33020732
done5001726

prune148.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x (sqrt 1.0)))
0.0b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.6b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×sqrt-prod
16×*-un-lft-identity
14×sqrt-div
10×pow1 add-cube-cbrt
9×associate-*r*
7×add-exp-log associate-*l*
6×flip3-+ add-cbrt-cube flip-+ add-log-exp
4×frac-times unswap-sqr
3×log-prod flip3-- sqrt-pow1 pow1/2 pow-prod-down flip--
2×log-div associate-*r/ associate-*l/ distribute-lft-out difference-of-squares
1×+-commutative rem-sqrt-square sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out--
Counts
4 → 83
Calls
4 calls:
9.0ms
(sqrt (+ x (sqrt 1.0)))
3.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
5.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
50.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series673.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(sqrt (+ x (sqrt 1.0)))
275.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
144.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
191.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify2.0s

Counts
95 → 95
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02141846
14891570
213671473
348321429
done50001427

prune243.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (log (+ (pow x 3) (pow (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) 3))) (log (- (* 2 (* x x)) (+ 1.0 (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))))
26.2b
(- (* 2 (* x x)) (+ 1.0 (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))
31.8b
(log (- (* 2 (* x x)) (+ 1.0 (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))))
43.3b
(log (+ (pow x 3) (pow (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) 3)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
16×log-prod *-un-lft-identity
10×pow1 add-sqr-sqrt
9×add-log-exp
8×add-cube-cbrt log-div
6×add-exp-log log-pow
5×associate--l+
4×flip3-- add-cbrt-cube flip-- associate--r+ distribute-lft-out--
3×diff-log
2×associate--l- sub-neg flip3-+ rem-log-exp sum-cubes flip-+ distribute-lft-out associate--r-
1×sum-log difference-of-squares
Counts
4 → 73
Calls
4 calls:
40.0ms
(- (log (+ (pow x 3) (pow (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) 3))) (log (- (* 2 (* x x)) (+ 1.0 (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))))
25.0ms
(- (* 2 (* x x)) (+ 1.0 (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))
26.0ms
(log (- (* 2 (* x x)) (+ 1.0 (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))))
13.0ms
(log (+ (pow x 3) (pow (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) 3)))

series1.6s

Counts
4 → 12
Calls
4 calls:
704.0ms
(- (log (+ (pow x 3) (pow (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) 3))) (log (- (* 2 (* x x)) (+ 1.0 (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))))
186.0ms
(- (* 2 (* x x)) (+ 1.0 (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))
289.0ms
(log (- (* 2 (* x x)) (+ 1.0 (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))))
464.0ms
(log (+ (pow x 3) (pow (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) 3)))

simplify836.0ms

Counts
85 → 85
Iterations

Useful iterations: done (826.0ms)

IterNodesCost
02423588
16233325
219453057
done50002921

prune371.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes13.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01014
11314
done1314

end0.0ms

sample1.5s

Algorithm
intervals
Results
371.0ms7804×body160nan
353.0ms16496×body80nan
237.0ms8000×body80valid