Details

Time bar (total: 30.8s)

sample145.0ms

Algorithm
intervals
Results
75.0ms75×body1280valid
26.0ms51×body640valid
13.0ms22×body2560valid
6.0ms81×body80valid
4.0ms15×body320valid
2.0ms12×body160valid

simplify8.0ms

Counts
1 → 1
Iterations
IterNodes
done10
110
07

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 49.9b

localize26.0ms

Local error

Found 3 expressions with local error:

1.0b
(+ (sqrt (fma x x 1.0)) x)
2.7b
(log (+ (sqrt (fma x x 1.0)) x))
13.3b
(sqrt (fma x x 1.0))

rewrite40.0ms

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:
19.0ms
(+ (sqrt (fma x x 1.0)) x)
15.0ms
(log (+ (sqrt (fma x x 1.0)) x))
3.0ms
(sqrt (fma x x 1.0))

series616.0ms

Counts
3 → 9
Calls
3 calls:
137.0ms
(+ (sqrt (fma x x 1.0)) x)
375.0ms
(log (+ (sqrt (fma x x 1.0)) x))
104.0ms
(sqrt (fma x x 1.0))

simplify3.3s

Counts
61 → 61
Iterations
IterNodes
done5004
32853
2834
1287
0125

prune542.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (/ (* (/ (* x x) 1.0) x) (sqrt 1.0)) -1/6 (+ (/ x (sqrt 1.0)) (log (sqrt 1.0))))
0.1b
(* (/ (* x x) 1.0) x)

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
11×add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×associate-*l*
5×add-cube-cbrt *-un-lft-identity
4×pow1 times-frac prod-exp cbrt-unprod
3×associate-*r*
2×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp unswap-sqr
1×pow-prod-down associate-*l/ *-commutative fma-udef div-inv
Counts
2 → 40
Calls
2 calls:
1.0ms
(fma (/ (* (/ (* x x) 1.0) x) (sqrt 1.0)) -1/6 (+ (/ x (sqrt 1.0)) (log (sqrt 1.0))))
49.0ms
(* (/ (* x x) 1.0) x)

series302.0ms

Counts
2 → 6
Calls
2 calls:
216.0ms
(fma (/ (* (/ (* x x) 1.0) x) (sqrt 1.0)) -1/6 (+ (/ x (sqrt 1.0)) (log (sqrt 1.0))))
87.0ms
(* (/ (* x x) 1.0) x)

simplify4.2s

Counts
46 → 46
Iterations
IterNodes
done5023
33022
2670
1185
083

prune348.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x 2 (- (/ 0.5 x) (/ (/ 0.125 x) (* x x))))
0.0b
(- (/ 0.5 x) (/ (/ 0.125 x) (* x x)))
0.2b
(/ (/ 0.125 x) (* x x))
8.8b
(log (fma x 2 (- (/ 0.5 x) (/ (/ 0.125 x) (* x x)))))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
488×times-frac
266×add-sqr-sqrt
251×*-un-lft-identity
249×add-cube-cbrt
221×prod-diff
47×div-inv
17×add-exp-log
16×add-cbrt-cube
13×fma-neg associate-/l*
6×cbrt-undiv div-exp add-log-exp difference-of-squares
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×log-prod
2×prod-exp cbrt-unprod
1×sub-neg flip3-- frac-2neg diff-log rem-log-exp clear-num associate-/r* log-pow frac-sub flip-- fma-udef associate-/l/ distribute-lft-out--
Counts
4 → 328
Calls
4 calls:
1.0ms
(fma x 2 (- (/ 0.5 x) (/ (/ 0.125 x) (* x x))))
93.0ms
(- (/ 0.5 x) (/ (/ 0.125 x) (* x x)))
37.0ms
(/ (/ 0.125 x) (* x x))
3.0ms
(log (fma x 2 (- (/ 0.5 x) (/ (/ 0.125 x) (* x x)))))

series684.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(fma x 2 (- (/ 0.5 x) (/ (/ 0.125 x) (* x x))))
181.0ms
(- (/ 0.5 x) (/ (/ 0.125 x) (* x x)))
74.0ms
(/ (/ 0.125 x) (* x x))
292.0ms
(log (fma x 2 (- (/ 0.5 x) (/ (/ 0.125 x) (* x x)))))

simplify3.7s

Counts
340 → 340
Iterations
IterNodes
done5001
23039
11190
0518

prune3.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 0.125 x) (* x x))
0.3b
(/ 0.0625 (pow x 5))
10.9b
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
17.5b
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

rewrite746.0ms

Algorithm
rewrite-expression-head
Rules
224×times-frac
212×*-un-lft-identity
114×add-sqr-sqrt
100×add-cube-cbrt
85×prod-diff
36×distribute-lft-out
22×add-exp-log
18×add-cbrt-cube
17×fma-neg
16×div-inv associate-/l*
12×unpow-prod-down
9×div-exp add-log-exp
8×log-prod associate-/r*
7×cbrt-undiv
6×frac-sub difference-of-squares
5×pow1 log-div
4×expm1-log1p-u log1p-expm1-u distribute-lft-out-- sqr-pow
2×flip3-- frac-2neg flip3-+ diff-log frac-add prod-exp clear-num flip-- cbrt-unprod flip-+
1×pow-to-exp sub-neg rem-log-exp pow-exp sum-log log-pow associate-/l/ associate--r+
Counts
4 → 245
Calls
4 calls:
32.0ms
(/ (/ 0.125 x) (* x x))
17.0ms
(/ 0.0625 (pow x 5))
277.0ms
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
386.0ms
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series720.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (/ 0.125 x) (* x x))
104.0ms
(/ 0.0625 (pow x 5))
408.0ms
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
108.0ms
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

simplify4.0s

Counts
257 → 257
Iterations
IterNodes
done5007
23278
11007
0412

prune2.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes99.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.4b

bsearch181.0ms

Steps
ItersRangePoint
9
2.490703692944805e-05
37.746059492850215
0.8909481582438814
9
-1.440408271564231
-1.963203309137196e-05
-1.014477909773237

simplify13.0ms

Iterations
IterNodes
done37
137
034

end0.0ms

sample5.0s

Algorithm
intervals
Results
2.3s2355×body1280valid
1.4s1483×body640valid
474.0ms808×body2560valid
248.0ms781×body320valid
235.0ms2167×body80valid
69.0ms406×body160valid