Details

Time bar (total: 17.8s)

sample106.0ms

Algorithm
intervals
Results
46.0ms75×body1280valid
17.0ms43×body640valid
14.0ms30×body2560valid
8.0ms31×body320valid
3.0ms61×body80valid
2.0ms16×body160valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
done10
110
07

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.6b

localize38.0ms

Local error

Found 3 expressions with local error:

0.9b
(+ x (sqrt (fma x x 1.0)))
3.4b
(log (+ x (sqrt (fma x x 1.0))))
16.6b
(sqrt (fma x x 1.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
7×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×log-prod add-exp-log
3×expm1-log1p-u fma-def add-cbrt-cube sqrt-prod log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
3 → 49
Calls
3 calls:
10.0ms
(+ x (sqrt (fma x x 1.0)))
10.0ms
(log (+ x (sqrt (fma x x 1.0))))
3.0ms
(sqrt (fma x x 1.0))

series488.0ms

Counts
3 → 9
Calls
3 calls:
126.0ms
(+ x (sqrt (fma x x 1.0)))
291.0ms
(log (+ x (sqrt (fma x x 1.0))))
71.0ms
(sqrt (fma x x 1.0))

simplify630.0ms

Counts
58 → 58
Iterations
IterNodes
done5001
21087
1289
0126

prune353.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma (/ (/ (pow x 3) 1.0) (sqrt 1.0)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

rewrite1.0ms

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

series151.0ms

Counts
1 → 3
Calls
1 calls:
151.0ms
(fma (/ (/ (pow x 3) 1.0) (sqrt 1.0)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify3.1s

Counts
13 → 13
Iterations
IterNodes
done5000
44906
3569
2144
149
027

prune95.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 0.0625 (pow x 5))
0.1b
(/ 0.125 (pow x 3))
10.7b
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
15.6b
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
1674×add-sqr-sqrt
1602×times-frac
1026×*-un-lft-identity
895×prod-diff
848×add-cube-cbrt
522×associate--l+
330×unpow-prod-down
268×difference-of-squares
181×cube-prod
146×sqr-pow
70×div-inv
62×distribute-lft-out--
43×cube-mult unpow3
19×associate-/r*
15×fma-neg add-exp-log
10×log-prod
9×add-log-exp
8×add-cbrt-cube frac-sub
6×div-exp associate-/l*
5×pow1 log-div
4×expm1-log1p-u flip3-- log1p-expm1-u flip--
3×diff-log
2×pow-to-exp cbrt-undiv clear-num sub-neg frac-2neg pow-exp
1×associate--l- rem-log-exp log-pow
Counts
4 → 1078
Calls
4 calls:
7.0ms
(/ 0.0625 (pow x 5))
7.0ms
(/ 0.125 (pow x 3))
417.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
688.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series578.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ 0.0625 (pow x 5))
69.0ms
(/ 0.125 (pow x 3))
310.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
113.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify1.1s

Counts
1090 → 1090
Iterations
IterNodes
done5000
11918
0810

prune6.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x 2 (/ 0.5 x))
0.0b
(- (fma x 2 (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.1b
(/ 0.125 (pow x 3))
8.3b
(log (- (fma x 2 (/ 0.5 x)) (/ 0.125 (pow x 3))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
163×add-sqr-sqrt
152×times-frac
141×*-un-lft-identity
137×add-cube-cbrt
120×prod-diff
41×unpow-prod-down cube-prod
15×sqr-pow
13×cube-mult unpow3
12×associate-/r*
10×add-exp-log difference-of-squares
9×log-prod
6×add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv
3×fma-neg div-exp associate-/l*
2×log-div flip3-- fma-udef flip-- distribute-lft-out--
1×pow-to-exp cbrt-undiv clear-num sub-neg frac-2neg diff-log rem-log-exp pow-exp associate--l+ log-pow
Counts
4 → 243
Calls
4 calls:
0.0ms
(fma x 2 (/ 0.5 x))
23.0ms
(- (fma x 2 (/ 0.5 x)) (/ 0.125 (pow x 3)))
6.0ms
(/ 0.125 (pow x 3))
28.0ms
(log (- (fma x 2 (/ 0.5 x)) (/ 0.125 (pow x 3))))

series326.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(fma x 2 (/ 0.5 x))
56.0ms
(- (fma x 2 (/ 0.5 x)) (/ 0.125 (pow x 3)))
41.0ms
(/ 0.125 (pow x 3))
166.0ms
(log (- (fma x 2 (/ 0.5 x)) (/ 0.125 (pow x 3))))

simplify373.0ms

Counts
255 → 255
Iterations
IterNodes
done5001
11050
0418

prune550.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes49.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.0b

bsearch78.0ms

Steps
ItersRangePoint
8
0.00104763160503943
5.1212688054922095
0.8884086436842497
9
-205.8624528279525
-0.0007095347148853646
-1.0022756540898416

simplify3.0ms

Iterations
IterNodes
done34
134
033

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.1s2252×body1280valid
488.0ms1576×body640valid
273.0ms762×body2560valid
164.0ms836×body320valid
81.0ms2144×body80valid
74.0ms430×body160valid