Details

Time bar (total: 18.9s)

sample68.0ms

Algorithm
intervals
Results
23.0ms220×body160nan
14.0ms461×body80nan
9.0ms256×body80valid

simplify13.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1109
2119
done119

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
31.0b
(sqrt (- (* x x) 1.0))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod sqrt-prod
3×add-cbrt-cube
2×log-div flip3-+ sqrt-div flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square flip3-- sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow flip-- difference-of-squares
Counts
3 → 43
Calls
3 calls:
48.0ms
(+ x (sqrt (- (* x x) 1.0)))
17.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
10.0ms
(sqrt (- (* x x) 1.0))

series411.0ms

Counts
3 → 9
Calls
3 calls:
95.0ms
(+ x (sqrt (- (* x x) 1.0)))
244.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
72.0ms
(sqrt (- (* x x) 1.0))

simplify2.1s

Counts
52 → 52
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0140780
1315710
2860637
32835619
done5001613

prune199.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.2b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×sqrt-prod
12×*-un-lft-identity sqrt-div
9×associate-*r*
8×pow1 add-cube-cbrt
7×associate-*l*
6×add-exp-log
5×flip3-+ add-cbrt-cube flip-+ add-log-exp
4×frac-times unswap-sqr
3×log-prod flip3-- pow-prod-down flip--
2×log-div sqrt-pow1 pow1/2 associate-*r/ associate-*l/ difference-of-squares
1×+-commutative sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
3 → 67
Calls
3 calls:
8.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
4.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
56.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series847.0ms

Counts
3 → 9
Calls
3 calls:
192.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
399.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
255.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify3.1s

Counts
76 → 76
Iterations

Useful iterations: done (3.1s)

IterNodesCost
01911601
14381358
212481272
344401242
done50011240

prune305.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(log (+ x (* (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))))))
0.5b
(* (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))))
0.5b
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
0.5b
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))

rewrite426.0ms

Algorithm
rewrite-expression-head
Rules
480×sqrt-div
144×frac-times
90×sqrt-prod
88×pow1
80×sqrt-pow1
63×pow-prod-down
61×add-sqr-sqrt flip3-+ flip-+
60×flip3-- flip--
48×associate-*r/ associate-*l/
40×pow1/2
25×*-un-lft-identity associate-*r*
21×add-exp-log associate-*l*
20×add-cbrt-cube
18×unswap-sqr
17×add-cube-cbrt
12×pow-prod-up
10×prod-exp cbrt-unprod
8×pow-sqr
7×sqrt-unprod
4×add-log-exp difference-of-squares
3×log-prod *-commutative
2×log-div pow-plus distribute-lft-out distribute-lft-out--
1×pow2 swap-sqr rem-log-exp rem-square-sqrt log-pow
Counts
4 → 256
Calls
4 calls:
4.0ms
(log (+ x (* (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))))))
230.0ms
(* (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))))
80.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
78.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))

series1.8s

Counts
4 → 12
Calls
4 calls:
458.0ms
(log (+ x (* (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))))))
341.0ms
(* (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))))
521.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
480.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))

simplify2.1s

Counts
268 → 268
Iterations

Useful iterations: done (2.1s)

IterNodesCost
044910254
111777413
232666723
done50006657

prune1.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 3/32 (/ (* 1.0 1.0) (pow x 4)))
0.2b
(- (log 2) (- (+ (* (/ 1.0 (pow x 2)) 1/4) (* 3/32 (/ (* 1.0 1.0) (pow x 4)))) (log x)))
0.3b
(/ 1.0 (pow x 2))
0.4b
(/ (* 1.0 1.0) (pow x 4))

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
43×add-exp-log
41×*-un-lft-identity times-frac
39×add-sqr-sqrt
30×add-cube-cbrt
22×unpow-prod-down
20×add-cbrt-cube
15×div-exp associate-/r*
13×prod-exp
11×pow1 associate-*r*
10×distribute-lft-out--
8×add-log-exp sqr-pow
5×cbrt-undiv pow-to-exp diff-log pow-exp log-pow cbrt-unprod
4×associate--l+ associate-/l* unpow2 unswap-sqr
3×log-prod associate-*l* div-inv associate--r+
2×sub-neg frac-2neg clear-num
1×flip3-- associate-*r/ pow-prod-down sum-log *-commutative flip-- associate--r- difference-of-squares
Counts
4 → 148
Calls
4 calls:
45.0ms
(* 3/32 (/ (* 1.0 1.0) (pow x 4)))
157.0ms
(- (log 2) (- (+ (* (/ 1.0 (pow x 2)) 1/4) (* 3/32 (/ (* 1.0 1.0) (pow x 4)))) (log x)))
13.0ms
(/ 1.0 (pow x 2))
15.0ms
(/ (* 1.0 1.0) (pow x 4))

series319.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* 3/32 (/ (* 1.0 1.0) (pow x 4)))
146.0ms
(- (log 2) (- (+ (* (/ 1.0 (pow x 2)) 1/4) (* 3/32 (/ (* 1.0 1.0) (pow x 4)))) (log x)))
47.0ms
(/ 1.0 (pow x 2))
75.0ms
(/ (* 1.0 1.0) (pow x 4))

simplify1.3s

Counts
160 → 160
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02492330
15372160
214801937
done50011861

prune679.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01330
11630
done1630

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.2s16579×body80nan
868.0ms7766×body160nan
579.0ms8000×body80valid