Details

Time bar (total: 18.2s)

sample147.0ms

Algorithm
intervals
Results
48.0ms808×body80nan
13.0ms255×body80valid
0.0ms1×body160valid

simplify48.0ms

Counts
1 → 1
Iterations
IterNodes
311
211
110
06

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 1 expressions with local error:

0.5b
(* (sqrt (- x 1)) (sqrt x))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×sqrt-prod
10×associate-*l*
8×*-un-lft-identity
6×associate-*r*
5×pow1 add-cube-cbrt
4×unswap-sqr
3×add-cbrt-cube pow-prod-down add-exp-log
2×sqrt-pow1 pow1/2 sqrt-div associate-*l/ difference-of-squares
1×expm1-log1p-u flip3-- sqrt-unprod difference-of-sqr-1 prod-exp *-commutative cbrt-unprod insert-posit16 log1p-expm1-u flip-- distribute-lft-out-- add-log-exp
Counts
1 → 39
Calls
1 calls:
21.0ms
(* (sqrt (- x 1)) (sqrt x))

series232.0ms

Counts
1 → 3
Calls
1 calls:
232.0ms
(* (sqrt (- x 1)) (sqrt x))

simplify2.1s

Counts
42 → 42
Iterations
IterNodes
42318
3969
2413
1192
087

prune222.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (+ -1/2 x) (/ -1/8 x))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-log-exp
4×fma-def distribute-lft-out
3×sum-log
2×add-sqr-sqrt flip3-+ frac-add add-cube-cbrt flip-+
1×expm1-log1p-u pow1 +-commutative associate-+l+ add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
Counts
1 → 24
Calls
1 calls:
22.0ms
(+ (+ -1/2 x) (/ -1/8 x))

series17.0ms

Counts
1 → 3
Calls
1 calls:
17.0ms
(+ (+ -1/2 x) (/ -1/8 x))

simplify702.0ms

Counts
27 → 27
Iterations
IterNodes
32037
2490
1171
060

prune121.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (sqrt x) 1))
0.1b
(sqrt (+ (sqrt x) 1))
0.3b
(* (sqrt (+ (sqrt x) 1)) (* (sqrt (- (sqrt x) 1)) (sqrt x)))
0.3b
(* (sqrt (- (sqrt x) 1)) (sqrt x))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
51×sqrt-prod
48×add-sqr-sqrt
30×*-un-lft-identity
22×associate-*l*
18×pow1 sqrt-div
12×add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×pow-prod-down associate-*l/
8×difference-of-squares
7×sqrt-pow1 pow1/2 associate-*r*
5×flip3-- flip--
4×expm1-log1p-u frac-times flip3-+ difference-of-sqr-1 prod-exp cbrt-unprod flip-+ hypot-def insert-posit16 log1p-expm1-u distribute-lft-out distribute-lft-out-- add-log-exp unswap-sqr
3×sqrt-unprod
2×rem-sqrt-square associate-*r/ *-commutative
Counts
4 → 130
Calls
4 calls:
9.0ms
(sqrt (- (sqrt x) 1))
7.0ms
(sqrt (+ (sqrt x) 1))
85.0ms
(* (sqrt (+ (sqrt x) 1)) (* (sqrt (- (sqrt x) 1)) (sqrt x)))
50.0ms
(* (sqrt (- (sqrt x) 1)) (sqrt x))

series740.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(sqrt (- (sqrt x) 1))
83.0ms
(sqrt (+ (sqrt x) 1))
326.0ms
(* (sqrt (+ (sqrt x) 1)) (* (sqrt (- (sqrt x) 1)) (sqrt x)))
226.0ms
(* (sqrt (- (sqrt x) 1)) (sqrt x))

simplify2.2s

Counts
142 → 142
Iterations
IterNodes
33714
21291
1485
0201

prune831.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 1 expressions with local error:

30.2b
(sqrt (* (- x 1) x))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1
2×sqrt-pow1 sqrt-div associate-*l/
1×add-sqr-sqrt expm1-log1p-u *-un-lft-identity flip3-- add-cbrt-cube pow1/2 pow-prod-down add-exp-log add-cube-cbrt sqrt-prod insert-posit16 log1p-expm1-u flip-- add-log-exp
Counts
1 → 16
Calls
1 calls:
16.0ms
(sqrt (* (- x 1) x))

series46.0ms

Counts
1 → 3
Calls
1 calls:
46.0ms
(sqrt (* (- x 1) x))

simplify6.4s

Counts
19 → 19
Iterations
IterNodes
54200
41606
3629
2250
1113
053

prune137.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes45.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
28
18
06

end0.0ms

sample3.9s

Algorithm
intervals
Results
2.7s24425×body80nan
731.0ms7997×body80valid
0.0ms3×body160valid