Details

Time bar (total: 19.3s)

sample82.0ms

Algorithm
intervals
Results
25.0ms506×body80nan
22.0ms259×body160nan
13.0ms256×body80valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1119
2129
done129

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.5b
(log (+ x (sqrt (- (* x x) 1.0))))
30.0b
(sqrt (- (* x x) 1.0))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×add-exp-log log-prod sqrt-prod
3×expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u
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 → 52
Calls
3 calls:
18.0ms
(+ x (sqrt (- (* x x) 1.0)))
36.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
15.0ms
(sqrt (- (* x x) 1.0))

series490.0ms

Counts
3 → 9
Calls
3 calls:
95.0ms
(+ x (sqrt (- (* x x) 1.0)))
318.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
77.0ms
(sqrt (- (* x x) 1.0))

simplify1.7s

Counts
61 → 61
Iterations

Useful iterations: done (1.7s)

IterNodesCost
0146832
1337748
2943682
33115614
done5000611

prune235.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4)))
0.2b
(- (log 2) (- (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))) (log x)))
0.6b
(/ 0.09375 (pow x 4))
0.7b
(/ 0.25 (* x x))

rewrite827.0ms

Algorithm
rewrite-expression-head
Rules
111×*-un-lft-identity
56×add-sqr-sqrt
48×prod-diff
46×add-cube-cbrt
34×pow1 distribute-lft-out--
30×log-pow
27×times-frac
19×associate--r+
17×distribute-lft-out
14×add-exp-log
12×unpow-prod-down
11×add-cbrt-cube
10×add-log-exp
8×associate-/r*
7×fma-def
6×associate-/l*
5×diff-log div-exp difference-of-squares
4×expm1-log1p-u fma-neg associate--l+ log1p-expm1-u sqr-pow
3×cbrt-undiv log-prod div-inv
2×sub-neg frac-2neg clear-num sum-log
1×+-commutative pow-to-exp flip3-- flip3-+ frac-add pow-exp prod-exp flip-- cbrt-unprod flip-+ associate--r-
Counts
4 → 178
Calls
4 calls:
52.0ms
(+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4)))
751.0ms
(- (log 2) (- (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))) (log x)))
7.0ms
(/ 0.09375 (pow x 4))
8.0ms
(/ 0.25 (* x x))

series358.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4)))
125.0ms
(- (log 2) (- (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))) (log x)))
53.0ms
(/ 0.09375 (pow x 4))
42.0ms
(/ 0.25 (* x x))

simplify1.5s

Counts
190 → 190
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02714981
15974155
216653394
done50012522

prune558.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
15×sqrt-prod
13×*-un-lft-identity
12×sqrt-div
9×add-cube-cbrt associate-*r*
8×pow1
7×associate-*l*
6×add-exp-log
5×flip3-+ add-cbrt-cube flip-+ add-log-exp
4×frac-times unswap-sqr
3×expm1-log1p-u log-prod flip3-- fma-def pow-prod-down flip-- log1p-expm1-u
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 → 76
Calls
3 calls:
11.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
79.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
7.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))

series925.0ms

Counts
3 → 9
Calls
3 calls:
222.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
285.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
418.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))

simplify3.1s

Counts
85 → 85
Iterations

Useful iterations: done (3.1s)

IterNodesCost
01971683
14651428
213541310
348551281
done50001279

prune424.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (pow (- (log 2) (+ (- (/ 0.09375 (pow x 4)) (log x)) (/ 0.25 (* x x)))) 3))
0.6b
(/ 0.09375 (pow x 4))
0.7b
(/ 0.25 (* x x))
0.7b
(pow (- (log 2) (+ (- (/ 0.09375 (pow x 4)) (log x)) (/ 0.25 (* x x)))) 3)

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
108×*-un-lft-identity
48×distribute-lft-out--
36×add-sqr-sqrt unpow-prod-down
30×cbrt-prod
29×pow1
28×add-cube-cbrt
24×times-frac cube-prod log-pow distribute-lft-out
15×add-exp-log
12×add-cbrt-cube
8×associate-/r*
6×associate-/l* sqr-pow
5×div-exp
4×cube-div expm1-log1p-u log1p-expm1-u add-log-exp difference-of-squares
3×cbrt-undiv pow-unpow
2×cube-mult pow-to-exp cbrt-div flip3-- frac-2neg unpow3 pow-exp clear-num flip-- div-inv
1×pow-pow pow1/3 prod-exp rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 158
Calls
4 calls:
970.0ms
(cbrt (pow (- (log 2) (+ (- (/ 0.09375 (pow x 4)) (log x)) (/ 0.25 (* x x)))) 3))
8.0ms
(/ 0.09375 (pow x 4))
8.0ms
(/ 0.25 (* x x))
802.0ms
(pow (- (log 2) (+ (- (/ 0.09375 (pow x 4)) (log x)) (/ 0.25 (* x x)))) 3)

series556.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(cbrt (pow (- (log 2) (+ (- (/ 0.09375 (pow x 4)) (log x)) (/ 0.25 (* x x)))) 3))
59.0ms
(/ 0.09375 (pow x 4))
39.0ms
(/ 0.25 (* x x))
295.0ms
(pow (- (log 2) (+ (- (/ 0.09375 (pow x 4)) (log x)) (/ 0.25 (* x x)))) 3)

simplify2.1s

Counts
170 → 170
Iterations

Useful iterations: done (2.1s)

IterNodesCost
03573897
19243428
233993174
done50003162

prune728.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01014
11314
done1314

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.0s7613×body160nan
991.0ms8000×body80valid
872.0ms16245×body80nan