Details

Time bar (total: 18.5s)

sample160.0ms

Algorithm
intervals
Results
70.0ms681×body80nan
11.0ms256×body80valid

simplify184.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
067
197
2107
done107

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite42.0ms

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×expm1-log1p-u flip3-- sqrt-unprod prod-exp *-commutative flip-- cbrt-unprod log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
Counts
1 → 36
Calls
1 calls:
39.0ms
(* (sqrt (- x 1.0)) (sqrt x))

series218.0ms

Counts
1 → 3
Calls
1 calls:
217.0ms
(* (sqrt (- x 1.0)) (sqrt x))

simplify4.4s

Counts
39 → 39
Iterations

Useful iterations: done (4.4s)

IterNodesCost
085403
1188370
2451354
31053351
42875350
done5002348

prune147.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune8.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
55×sqrt-prod
46×add-sqr-sqrt
28×*-un-lft-identity
20×associate-*l*
18×pow1 sqrt-div
12×add-cube-cbrt
11×add-exp-log add-cbrt-cube
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-+ prod-exp cbrt-unprod flip-+ hypot-def 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 → 122
Calls
4 calls:
18.0ms
(sqrt (+ (sqrt x) (sqrt 1.0)))
28.0ms
(sqrt (- (sqrt x) (sqrt 1.0)))
130.0ms
(* (sqrt (+ (sqrt x) (sqrt 1.0))) (* (sqrt (- (sqrt x) (sqrt 1.0))) (sqrt x)))
75.0ms
(* (sqrt (- (sqrt x) (sqrt 1.0))) (sqrt x))

series2.2s

Counts
4 → 12
Calls
4 calls:
192.0ms
(sqrt (+ (sqrt x) (sqrt 1.0)))
230.0ms
(sqrt (- (sqrt x) (sqrt 1.0)))
1.3s
(* (sqrt (+ (sqrt x) (sqrt 1.0))) (* (sqrt (- (sqrt x) (sqrt 1.0))) (sqrt x)))
564.0ms
(* (sqrt (- (sqrt x) (sqrt 1.0))) (sqrt x))

simplify3.1s

Counts
134 → 134
Iterations

Useful iterations: done (3.1s)

IterNodesCost
03762746
110382316
231742180
done50012159

prune531.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 1 expressions with local error:

31.0b
(pow (* (- x 1.0) x) 1/2)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log
3×pow-unpow
2×add-sqr-sqrt add-cube-cbrt pow-pow *-un-lft-identity pow-exp
1×expm1-log1p-u pow-to-exp unpow-prod-down pow-prod-down prod-exp add-cbrt-cube log1p-expm1-u unpow1/2 add-log-exp sqr-pow
Counts
1 → 20
Calls
1 calls:
13.0ms
(pow (* (- x 1.0) x) 1/2)

series149.0ms

Counts
1 → 3
Calls
1 calls:
149.0ms
(pow (* (- x 1.0) x) 1/2)

simplify3.7s

Counts
23 → 23
Iterations

Useful iterations: 4 (1.8s)

IterNodesCost
064264
1154226
2360205
31053189
44460182
done5000182

prune57.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes19.0ms

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
067
done67

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.7s24345×body80nan
752.0ms7991×body80valid
1.0ms9×body160valid