Details

Time bar (total: 12.4s)

sample80.0ms

Algorithm
intervals
Results
37.0ms77×body1280valid
15.0ms46×body640valid
9.0ms23×body2560valid
6.0ms30×body320valid
3.0ms70×body80valid
1.0ms10×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
079
1108
done108

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.1b

localize7.0ms

Local error

Found 3 expressions with local error:

1.1b
(+ x (sqrt (+ (* x x) 1.0)))
2.2b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.3b
(sqrt (+ (* x x) 1.0))

rewrite61.0ms

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:
21.0ms
(+ x (sqrt (+ (* x x) 1.0)))
29.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
10.0ms
(sqrt (+ (* x x) 1.0))

series378.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(+ x (sqrt (+ (* x x) 1.0)))
250.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
56.0ms
(sqrt (+ (* x x) 1.0))

simplify1.6s

Counts
61 → 61
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0139813
1329677
2938609
33024595
done5000593

prune222.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 1 expressions with local error:

0.1b
(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))))

series164.0ms

Counts
1 → 3
Calls
1 calls:
164.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify811.0ms

Counts
13 → 13
Iterations

Useful iterations: done (810.0ms)

IterNodesCost
025295
151295
2171256
3989256
done5000255

prune53.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))))
19.5b
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
19.5b
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
19.5b
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
16.0ms
(* (cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))))
1.0ms
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
1.0ms
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
1.0ms
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

series2.3s

Counts
4 → 12
Calls
4 calls:
693.0ms
(* (cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))))
483.0ms
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
544.0ms
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
553.0ms
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

simplify689.0ms

Counts
93 → 93
Iterations

Useful iterations: done (684.0ms)

IterNodesCost
01603869
14013618
214053305
done50002518

prune567.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

1.1b
(+ x (hypot x (sqrt 1.0)))
2.2b
(log (+ x (hypot x (sqrt 1.0))))

rewrite11.0ms

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))))

series575.0ms

Counts
2 → 6
Calls
2 calls:
149.0ms
(+ x (hypot x (sqrt 1.0)))
426.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify1.1s

Counts
40 → 40
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0102509
1240487
2668433
32329430
done5001427

prune140.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.9b

bsearch128.0ms

Steps
ItersRangePoint
10
8.937283511995443e-05
28405617999702.24
0.8904752561288425
9
-7465.585501010854
-0.008005822963963436
-1.0042810433581868

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03960
14260
done4260

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.6s2405×body1280valid
599.0ms1512×body640valid
520.0ms803×body320valid
360.0ms770×body2560valid
106.0ms2109×body80valid
48.0ms401×body160valid