Details

Time bar (total: 8.8s)

sample63.0ms

Algorithm
intervals
Results
32.0ms77×body1280valid
12.0ms54×body640valid
6.0ms21×body2560valid
2.0ms78×body80valid
2.0ms16×body320valid
1.0ms10×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
079
1108
done108

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ (sqrt (fma x x 1.0)) x)
2.2b
(log (+ (sqrt (fma x x 1.0)) x))
15.5b
(sqrt (fma x x 1.0))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
6×fma-def sqrt-prod
5×pow1 add-log-exp
4×add-exp-log log-prod
3×expm1-log1p-u add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 52
Calls
3 calls:
5.0ms
(+ (sqrt (fma x x 1.0)) x)
4.0ms
(log (+ (sqrt (fma x x 1.0)) x))
1.0ms
(sqrt (fma x x 1.0))

series303.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(+ (sqrt (fma x x 1.0)) x)
178.0ms
(log (+ (sqrt (fma x x 1.0)) x))
55.0ms
(sqrt (fma x x 1.0))

simplify1.5s

Counts
61 → 61
Iterations

Useful iterations: 3 (364.0ms)

IterNodesCost
0125701
1284639
2867573
33907523
done5000523

prune193.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 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))))

series149.0ms

Counts
1 → 3
Calls
1 calls:
149.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify333.0ms

Counts
13 → 13
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
025295
151295
2168259
3949256
done5001256

prune46.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (hypot (sqrt 1.0) x))
0.3b
(* (cbrt (hypot (sqrt 1.0) x)) (cbrt (hypot (sqrt 1.0) x)))
2.2b
(log (+ (* (* (cbrt (hypot (sqrt 1.0) x)) (cbrt (hypot (sqrt 1.0) x))) (cbrt (hypot (sqrt 1.0) x))) x))
10.1b
(+ (* (* (cbrt (hypot (sqrt 1.0) x)) (cbrt (hypot (sqrt 1.0) x))) (cbrt (hypot (sqrt 1.0) x))) x)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×cbrt-prod
14×add-cube-cbrt *-un-lft-identity
12×pow1
7×add-exp-log pow1/3
6×swap-sqr associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u unswap-sqr
3×log-prod
2×log-div flip3-+ pow-prod-down pow-sqr pow-prod-up flip-+
1×+-commutative pow2 fma-def pow-plus rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
0.0ms
(cbrt (hypot (sqrt 1.0) x))
6.0ms
(* (cbrt (hypot (sqrt 1.0) x)) (cbrt (hypot (sqrt 1.0) x)))
13.0ms
(log (+ (* (* (cbrt (hypot (sqrt 1.0) x)) (cbrt (hypot (sqrt 1.0) x))) (cbrt (hypot (sqrt 1.0) x))) x))
15.0ms
(+ (* (* (cbrt (hypot (sqrt 1.0) x)) (cbrt (hypot (sqrt 1.0) x))) (cbrt (hypot (sqrt 1.0) x))) x)

series1.1s

Counts
4 → 12
Calls
4 calls:
335.0ms
(cbrt (hypot (sqrt 1.0) x))
359.0ms
(* (cbrt (hypot (sqrt 1.0) x)) (cbrt (hypot (sqrt 1.0) x)))
288.0ms
(log (+ (* (* (cbrt (hypot (sqrt 1.0) x)) (cbrt (hypot (sqrt 1.0) x))) (cbrt (hypot (sqrt 1.0) x))) x))
132.0ms
(+ (* (* (cbrt (hypot (sqrt 1.0) x)) (cbrt (hypot (sqrt 1.0) x))) (cbrt (hypot (sqrt 1.0) x))) x)

simplify618.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (178.0ms)

IterNodesCost
02162022
15261884
219301181
done50001181

prune259.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (hypot (sqrt 1.0) x) x)
0.5b
(+ (hypot (sqrt 1.0) x) x)
2.2b
(log (+ (hypot (sqrt 1.0) x) x))
2.2b
(log (+ (hypot (sqrt 1.0) x) x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt log-prod add-log-exp
6×pow1 add-exp-log fma-def
4×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
2×+-commutative rem-log-exp sum-log log-pow
Counts
4 → 68
Calls
4 calls:
2.0ms
(+ (hypot (sqrt 1.0) x) x)
2.0ms
(+ (hypot (sqrt 1.0) x) x)
2.0ms
(log (+ (hypot (sqrt 1.0) x) x))
3.0ms
(log (+ (hypot (sqrt 1.0) x) x))

series846.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(+ (hypot (sqrt 1.0) x) x)
135.0ms
(+ (hypot (sqrt 1.0) x) x)
293.0ms
(log (+ (hypot (sqrt 1.0) x) x))
289.0ms
(log (+ (hypot (sqrt 1.0) x) x))

simplify899.0ms

Counts
80 → 80
Iterations

Useful iterations: 3 (268.0ms)

IterNodesCost
01021018
1241986
2722878
33077862
done5000862

prune263.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes34.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.2b

bsearch268.0ms

Steps
ItersRangePoint
10
3.2824798326487284e-15
0.08347146558812443
0.0013723653044277859
9
-5.7596417613087905
-6.7357437175194845e-09
-1.03811431304858

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03562
13862
done3862

end0.0ms

sample1.9s

Algorithm
intervals
Results
951.0ms2308×body1280valid
375.0ms1563×body640valid
218.0ms786×body2560valid
106.0ms767×body320valid
68.0ms2171×body80valid
33.0ms405×body160valid