Details

Time bar (total: 19.4s)

sample92.0ms

Algorithm
intervals
Results
53.0ms87×body1280valid
15.0ms46×body640valid
8.0ms23×body2560valid
5.0ms28×body320valid
3.0ms65×body80valid
1.0ms7×body160valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
done13
213
112
07

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot 1 x)
0.9b
(+ x (hypot 1 x))
1.7b
(log (+ x (hypot 1 x)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
5×add-sqr-sqrt add-cube-cbrt add-log-exp
4×pow1 log-prod add-exp-log
3×expm1-log1p-u fma-def add-cbrt-cube insert-posit16 log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative hypot-udef sum-log rem-log-exp log-pow
Counts
3 → 47
Calls
3 calls:
0.0ms
(hypot 1 x)
5.0ms
(+ x (hypot 1 x))
3.0ms
(log (+ x (hypot 1 x)))

series779.0ms

Counts
3 → 9
Calls
3 calls:
87.0ms
(hypot 1 x)
107.0ms
(+ x (hypot 1 x))
585.0ms
(log (+ x (hypot 1 x)))

simplify1.8s

Counts
56 → 56
Iterations
IterNodes
done5010
32035
2666
1244
0108

prune255.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b
(fma (* (* x x) x) -1/6 x)
0.1b
(* (* x x) x)
18.0b
(fma (pow x 5) 3/40 (fma (* (* x x) x) -1/6 x))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
22×pow1
8×add-cbrt-cube add-exp-log
6×pow-plus pow-prod-up
5×add-sqr-sqrt
4×*-un-lft-identity add-cube-cbrt
3×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×pow2 pow-sqr fma-udef
1×associate-*l* pow3 *-commutative unswap-sqr
Counts
3 → 53
Calls
3 calls:
0.0ms
(fma (* (* x x) x) -1/6 x)
17.0ms
(* (* x x) x)
0.0ms
(fma (pow x 5) 3/40 (fma (* (* x x) x) -1/6 x))

series194.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(fma (* (* x x) x) -1/6 x)
38.0ms
(* (* x x) x)
71.0ms
(fma (pow x 5) 3/40 (fma (* (* x x) x) -1/6 x))

simplify1.6s

Counts
62 → 62
Iterations
IterNodes
done5001
31430
2359
1134
071

prune192.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1/8 (* x x)) x)
0.4b
(/ 1/8 (* x x))
11.4b
(log (+ (/ -1/2 x) (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))))
22.3b
(- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
1367×times-frac
775×add-sqr-sqrt
754×*-un-lft-identity
737×add-cube-cbrt
625×prod-diff
228×unpow-prod-down
135×div-inv
78×sqr-pow
25×fma-neg
19×add-exp-log
18×add-cbrt-cube
12×difference-of-squares
10×associate-/l*
7×cbrt-undiv div-exp
6×log-prod add-log-exp
5×pow1 log-div
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u distribute-lft-out--
3×frac-add distribute-lft-out
2×clear-num frac-2neg flip3-- prod-exp frac-sub cbrt-unprod flip--
1×sub-neg flip3-+ diff-log rem-log-exp log-pow flip-+ associate-/l/
Counts
4 → 778
Calls
4 calls:
11.0ms
(/ (/ 1/8 (* x x)) x)
6.0ms
(/ 1/8 (* x x))
55.0ms
(log (+ (/ -1/2 x) (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))))
39.0ms
(- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ (/ 1/8 (* x x)) x)
27.0ms
(/ 1/8 (* x x))
161.0ms
(log (+ (/ -1/2 x) (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))))
198.0ms
(- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))

simplify2.0s

Counts
790 → 790
Iterations
IterNodes
done5000
12307
01032

prune4.5s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (hypot 1 x) x)
1.7b
(log (/ (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)) (fma (- (hypot 1 x) x) (hypot 1 x) (* x x))))
9.6b
(/ (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)) (fma (- (hypot 1 x) x) (hypot 1 x) (* x x)))
14.9b
(fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt *-un-lft-identity
26×add-cube-cbrt
18×times-frac
13×log-prod
9×prod-diff add-exp-log
6×add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg associate-/l*
2×div-exp rem-log-exp div-inv
1×cbrt-undiv log-div clear-num sub-neg frac-2neg flip3-- diff-log log-pow fma-udef flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 97
Calls
4 calls:
7.0ms
(- (hypot 1 x) x)
3.0ms
(log (/ (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)) (fma (- (hypot 1 x) x) (hypot 1 x) (* x x))))
5.0ms
(/ (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)) (fma (- (hypot 1 x) x) (hypot 1 x) (* x x)))
0.0ms
(fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
65.0ms
(- (hypot 1 x) x)
470.0ms
(log (/ (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)) (fma (- (hypot 1 x) x) (hypot 1 x) (* x x))))
383.0ms
(/ (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)) (fma (- (hypot 1 x) x) (hypot 1 x) (* x x)))
195.0ms
(fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x))

simplify2.2s

Counts
109 → 109
Iterations
IterNodes
done5026
33226
21138
1452
0208

prune437.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch113.0ms

Steps
ItersRangePoint
11
4.21785760657603e-35
57.56933376468871
0.007778482819478155
9
-34.11472770615283
-3.67231414207575e-08
-1.0840635159626253

simplify4.0ms

Iterations
IterNodes
done34
134
029

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.6s2352×body1280valid
638.0ms1515×body640valid
510.0ms773×body320valid
381.0ms786×body2560valid
146.0ms2138×body80valid
56.0ms436×body160valid