Details

Time bar (total: 3.7s)

sample333.0ms

Algorithm
intervals
Results
19.0ms735×body80nan
5.0ms256×body80valid

simplify29.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
094
1104
2104
done104

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 1 expressions with local error:

0.5b
(* (sqrt (- x 1.0)) (sqrt x))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×sqrt-prod
8×associate-*l*
7×*-un-lft-identity
6×associate-*r*
5×pow1 add-cube-cbrt
4×unswap-sqr
3×add-exp-log pow-prod-down add-cbrt-cube
2×sqrt-pow1 pow1/2 sqrt-div associate-*l/
1×flip3-- sqrt-unprod prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- add-log-exp difference-of-squares
Counts
1 → 34
Calls
1 calls:
28.0ms
(* (sqrt (- x 1.0)) (sqrt x))

series78.0ms

Counts
1 → 3
Calls
1 calls:
78.0ms
(* (sqrt (- x 1.0)) (sqrt x))

simplify73.0ms

Counts
37 → 37
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0181216
1610206
22471201
35002201
done5002201

prune67.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize6.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune4.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
66×sqrt-prod
40×add-sqr-sqrt
36×sqrt-div
24×*-un-lft-identity
22×associate-*l*
20×pow1
16×add-cube-cbrt
13×sqrt-pow1
11×add-exp-log add-cbrt-cube
10×pow-prod-down associate-*l/
9×flip3-- pow1/2 flip--
7×associate-*r*
6×unswap-sqr
4×frac-times rem-sqrt-square prod-exp cbrt-unprod distribute-lft-out-- add-log-exp difference-of-squares
3×sqrt-unprod
2×associate-*r/ *-commutative
Counts
4 → 122
Calls
4 calls:
8.0ms
(sqrt (sqrt (- x 1.0)))
8.0ms
(sqrt (sqrt (- x 1.0)))
69.0ms
(* (sqrt (sqrt (- x 1.0))) (* (sqrt (sqrt (- x 1.0))) (sqrt x)))
32.0ms
(* (sqrt (sqrt (- x 1.0))) (sqrt x))

series515.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(sqrt (sqrt (- x 1.0)))
98.0ms
(sqrt (sqrt (- x 1.0)))
64.0ms
(* (sqrt (sqrt (- x 1.0))) (* (sqrt (sqrt (- x 1.0))) (sqrt x)))
259.0ms
(* (sqrt (sqrt (- x 1.0))) (sqrt x))

simplify57.0ms

Counts
134 → 134
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05611080
12009976
25002947
done5002947

prune288.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b
(sqrt (sqrt (- x 1.0)))
0.3b
(* (sqrt (sqrt (- x 1.0))) (* (pow (- x 1.0) 1/4) (sqrt x)))
0.3b
(* (pow (- x 1.0) 1/4) (sqrt x))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
33×sqrt-prod
30×add-sqr-sqrt
20×associate-*l*
18×add-exp-log *-un-lft-identity
12×add-cube-cbrt
10×prod-exp add-cbrt-cube
8×sqrt-div
7×pow1 unpow-prod-down associate-*r*
6×unswap-sqr
4×sqrt-pow1 cbrt-unprod
3×distribute-lft-out-- add-log-exp difference-of-squares sqr-pow
2×pow-to-exp rem-sqrt-square flip3-- pow1/2 associate-*l/ pow-exp *-commutative flip--
1×pow-prod-down
Counts
3 → 85
Calls
3 calls:
9.0ms
(sqrt (sqrt (- x 1.0)))
67.0ms
(* (sqrt (sqrt (- x 1.0))) (* (pow (- x 1.0) 1/4) (sqrt x)))
39.0ms
(* (pow (- x 1.0) 1/4) (sqrt x))

series499.0ms

Counts
3 → 9
Calls
3 calls:
99.0ms
(sqrt (sqrt (- x 1.0)))
170.0ms
(* (sqrt (sqrt (- x 1.0))) (* (pow (- x 1.0) 1/4) (sqrt x)))
229.0ms
(* (pow (- x 1.0) 1/4) (sqrt x))

simplify63.0ms

Counts
94 → 94
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0613811
12310756
25001749
done5001749

prune218.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes13.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0124
1124
done124

end0.0ms

sample1.1s

Algorithm
intervals
Results
532.0ms23430×body80nan
148.0ms7990×body80valid
0.0ms10×body160valid