Details

Time bar (total: 15.6s)

sample64.0ms

Algorithm
intervals
Results
21.0ms482×body80nan
12.0ms218×body160nan
9.0ms256×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

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×*-un-lft-identity
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-- difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log rem-log-exp log-pow flip-+ distribute-lft-out
Counts
3 → 44
Calls
3 calls:
47.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
15.0ms
(- (* x x) 1.0)
13.0ms
(sqrt (- (* x x) 1.0))

series384.0ms

Counts
3 → 9
Calls
3 calls:
261.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
55.0ms
(- (* x x) 1.0)
67.0ms
(sqrt (- (* x x) 1.0))

simplify651.0ms

Counts
53 → 53
Iterations

Useful iterations: done (648.0ms)

IterNodesCost
0133692
1296628
21180569
done5001561

prune179.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 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))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×sqrt-prod
15×*-un-lft-identity
14×sqrt-div
9×pow1 add-cube-cbrt associate-*r*
7×associate-*l*
6×add-exp-log
5×flip3-+ add-cbrt-cube flip-+
4×frac-times unswap-sqr
3×log-prod flip3-- sqrt-pow1 pow1/2 pow-prod-down flip-- add-log-exp
2×log-div associate-*r/ associate-*l/ distribute-lft-out difference-of-squares
1×rem-sqrt-square sqrt-unprod rem-log-exp prod-exp log-pow *-commutative cbrt-unprod distribute-lft-out--
Counts
3 → 72
Calls
3 calls:
10.0ms
(sqrt (+ x (sqrt 1.0)))
4.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
58.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series694.0ms

Counts
3 → 9
Calls
3 calls:
86.0ms
(sqrt (+ x (sqrt 1.0)))
359.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
249.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify937.0ms

Counts
81 → 81
Iterations

Useful iterations: 2 (308.0ms)

IterNodesCost
02011529
14531321
216491235
done50011235

prune320.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (sqrt x) (sqrt (sqrt 1.0))))
0.1b
(sqrt (+ (sqrt x) (sqrt (sqrt 1.0))))
0.3b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (+ (sqrt x) (sqrt (sqrt 1.0)))))
0.3b
(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (+ (sqrt x) (sqrt (sqrt 1.0))))) (sqrt (- (sqrt x) (sqrt (sqrt 1.0)))))

rewrite335.0ms

Algorithm
rewrite-expression-head
Rules
70×sqrt-div
66×sqrt-prod
46×add-sqr-sqrt
32×frac-times
30×*-un-lft-identity
25×flip3-+ flip-+
22×associate-*r*
18×pow1
16×associate-*l/
12×add-cube-cbrt difference-of-squares
11×add-exp-log add-cbrt-cube
10×flip3-- associate-*r/ pow-prod-down flip--
8×associate-*l*
7×sqrt-pow1 pow1/2
5×distribute-lft-out
4×prod-exp cbrt-unprod distribute-lft-out-- add-log-exp unswap-sqr
3×sqrt-unprod
2×rem-sqrt-square *-commutative
Counts
4 → 139
Calls
4 calls:
29.0ms
(sqrt (- (sqrt x) (sqrt (sqrt 1.0))))
18.0ms
(sqrt (+ (sqrt x) (sqrt (sqrt 1.0))))
96.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (+ (sqrt x) (sqrt (sqrt 1.0)))))
178.0ms
(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (+ (sqrt x) (sqrt (sqrt 1.0))))) (sqrt (- (sqrt x) (sqrt (sqrt 1.0)))))

series2.2s

Counts
4 → 12
Calls
4 calls:
249.0ms
(sqrt (- (sqrt x) (sqrt (sqrt 1.0))))
281.0ms
(sqrt (+ (sqrt x) (sqrt (sqrt 1.0))))
481.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (+ (sqrt x) (sqrt (sqrt 1.0)))))
1.2s
(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (+ (sqrt x) (sqrt (sqrt 1.0))))) (sqrt (- (sqrt x) (sqrt (sqrt 1.0)))))

simplify602.0ms

Counts
151 → 151
Iterations

Useful iterations: done (590.0ms)

IterNodesCost
03874606
110673858
done50003615

prune1.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (+ 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
(cbrt (pow (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) 3))
0.7b
(pow (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) 3)

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
19×*-un-lft-identity
15×add-cube-cbrt sqrt-prod
14×pow1 cbrt-prod
12×sqrt-div
9×associate-*r*
8×add-exp-log unpow-prod-down cube-prod
7×associate-*l* add-cbrt-cube
5×log-pow
4×frac-times flip3-+ flip-+ add-log-exp unswap-sqr
3×pow-unpow log-prod flip3-- pow-prod-down flip--
2×cube-mult log-div sqrt-pow1 pow1/2 unpow3 associate-*r/ associate-*l/ difference-of-squares sqr-pow
1×pow-to-exp pow-pow pow1/3 sqrt-unprod rem-log-exp pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod distribute-lft-out distribute-lft-out-- rem-cube-cbrt
Counts
4 → 104
Calls
4 calls:
4.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
92.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
5.0ms
(cbrt (pow (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) 3))
7.0ms
(pow (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) 3)

series1.9s

Counts
4 → 12
Calls
4 calls:
487.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
301.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
480.0ms
(cbrt (pow (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) 3))
604.0ms
(pow (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) 3)

simplify2.8s

Counts
116 → 116
Iterations

Useful iterations: 2 (899.0ms)

IterNodesCost
03333063
19172634
245362376
done50012376

prune490.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes15.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01524
12024
done2024

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.0s7633×body160nan
717.0ms16242×body80nan
355.0ms8000×body80valid