Details

Time bar (total: 13.1s)

sample118.0ms

Algorithm
intervals
Results
60.0ms78×body1280valid
18.0ms43×body640valid
13.0ms27×body2560valid
6.0ms27×body320valid
4.0ms65×body80valid
2.0ms16×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
079
1108
done108

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.7b
(+ x (sqrt (+ (* x x) 1.0)))
3.6b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.5b
(sqrt (+ (* x x) 1.0))

rewrite66.0ms

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
3×expm1-log1p-u fma-def flip3-+ sqrt-prod add-cbrt-cube flip-+ log1p-expm1-u
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow hypot-def
Counts
3 → 52
Calls
3 calls:
31.0ms
(+ x (sqrt (+ (* x x) 1.0)))
23.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
11.0ms
(sqrt (+ (* x x) 1.0))

series371.0ms

Counts
3 → 9
Calls
3 calls:
102.0ms
(+ x (sqrt (+ (* x x) 1.0)))
223.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify1.0s

Counts
61 → 61
Iterations

Useful iterations: done (1.0s)

IterNodesCost
0139813
1342677
21454609
done5001597

prune362.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series233.0ms

Counts
1 → 3
Calls
1 calls:
233.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify1.2s

Counts
13 → 13
Iterations

Useful iterations: done (1.2s)

IterNodesCost
025295
151295
2177256
31271256
done5002255

prune87.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.7b
(+ x (hypot x (sqrt 1.0)))
3.6b
(log (+ x (hypot x (sqrt 1.0))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
4×add-sqr-sqrt add-cube-cbrt log-prod add-log-exp
3×pow1 add-exp-log fma-def
2×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
1×+-commutative rem-log-exp sum-log log-pow
Counts
2 → 34
Calls
2 calls:
6.0ms
(+ x (hypot x (sqrt 1.0)))
5.0ms
(log (+ x (hypot x (sqrt 1.0))))

series671.0ms

Counts
2 → 6
Calls
2 calls:
178.0ms
(+ x (hypot x (sqrt 1.0)))
493.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify540.0ms

Counts
40 → 40
Iterations

Useful iterations: done (539.0ms)

IterNodesCost
0102509
1243487
2999433
done5001431

prune146.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.0625 (pow x 5))
0.3b
(/ 0.125 (pow x 3))
12.4b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
17.1b
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite658.0ms

Algorithm
rewrite-expression-head
Rules
480×*-un-lft-identity
367×times-frac
244×add-sqr-sqrt
218×add-cube-cbrt
200×prod-diff
84×distribute-lft-out
80×unpow-prod-down
68×cube-prod
40×fma-neg
28×sqr-pow
22×cube-mult unpow3
19×associate-/r*
15×add-exp-log
11×log-prod
10×difference-of-squares
9×add-log-exp
8×add-cbrt-cube div-inv
6×div-exp frac-sub associate-/l* distribute-lft-out--
5×pow1 log-div
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv pow-to-exp flip3-- frac-2neg flip3-+ diff-log frac-add pow-exp clear-num flip-- flip-+
1×sub-neg rem-log-exp sum-log log-pow associate--r+
Counts
4 → 408
Calls
4 calls:
8.0ms
(/ 0.0625 (pow x 5))
17.0ms
(/ 0.125 (pow x 3))
284.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
304.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series523.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ 0.0625 (pow x 5))
69.0ms
(/ 0.125 (pow x 3))
287.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
91.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify2.6s

Counts
420 → 420
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
046617336
1108012011
245999527
done50009527

prune977.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.0b

bsearch82.0ms

Steps
ItersRangePoint
7
0.0004583402999225959
0.01136632641909174
0.0005593634739476161
10
-1950712569354.648
-0.00015980627971116164
-1.0227411808047386

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03249
13549
done3549

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.4s2328×body1280valid
960.0ms1549×body640valid
335.0ms819×body2560valid
292.0ms797×body320valid
108.0ms2085×body80valid
50.0ms422×body160valid