Details

Time bar (total: 13.4s)

sample91.0ms

Algorithm
intervals
Results
37.0ms71×body1280valid
24.0ms124×body80valid
11.0ms32×body640valid
5.0ms19×body320valid
2.0ms10×body160valid

simplify825.0ms

Counts
1 → 1
Iterations
IterNodes
done2001
7682
6240
5101
451
330
222
118
09

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1 (exp (* -2 x)))
0.0b
(/ 2 (+ 1 (exp (* -2 x))))
2.7b
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
101×*-un-lft-identity
74×add-sqr-sqrt
63×times-frac add-cube-cbrt
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
8×add-exp-log
7×add-log-exp
6×flip3-+ flip-+
5×add-cbrt-cube div-inv
4×associate-/r* difference-of-squares
3×expm1-log1p-u pow1 fma-def insert-posit16 log1p-expm1-u associate-/l*
2×expm1-def difference-of-sqr-1 div-exp
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-- diff-log flip-- distribute-lft-out--
Counts
3 → 150
Calls
3 calls:
6.0ms
(+ 1 (exp (* -2 x)))
11.0ms
(/ 2 (+ 1 (exp (* -2 x))))
107.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series191.0ms

Counts
3 → 9
Calls
3 calls:
18.0ms
(+ 1 (exp (* -2 x)))
31.0ms
(/ 2 (+ 1 (exp (* -2 x))))
141.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify939.0ms

Counts
159 → 159
Iterations
IterNodes
done2000
2930
1426
0183

prune458.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (pow x 5) 2/15 x)
0.1b
(* x (* x x))
18.1b
(fma -1/3 (* x (* x x)) (fma (pow x 5) 2/15 x))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
8×add-cbrt-cube add-exp-log
5×add-sqr-sqrt pow-prod-up
4×*-un-lft-identity add-cube-cbrt
3×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×pow2 pow-plus cube-unmult associate-*r* pow-sqr *-commutative unswap-sqr
Counts
3 → 49
Calls
3 calls:
0.0ms
(fma (pow x 5) 2/15 x)
28.0ms
(* x (* x x))
1.0ms
(fma -1/3 (* x (* x x)) (fma (pow x 5) 2/15 x))

series326.0ms

Counts
3 → 9
Calls
3 calls:
180.0ms
(fma (pow x 5) 2/15 x)
41.0ms
(* x (* x x))
105.0ms
(fma -1/3 (* x (* x x)) (fma (pow x 5) 2/15 x))

simplify953.0ms

Counts
58 → 58
Iterations
IterNodes
done2009
31429
2365
1122
071

prune220.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1 (exp (* -2 x))))
0.0b
(/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x)))))
0.5b
(/ 2 (sqrt (+ 1 (exp (* -2 x)))))
2.7b
(- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)

rewrite362.0ms

Algorithm
rewrite-expression-head
Rules
1752×times-frac
1504×*-un-lft-identity
1059×add-sqr-sqrt
1011×sqrt-prod
996×add-cube-cbrt
585×prod-diff
249×distribute-lft-out
195×fma-neg
86×sqrt-div
84×associate-/r/
43×flip3-+ flip-+
42×div-inv
30×associate-/l*
17×add-exp-log
14×associate-/r* difference-of-squares
11×add-cbrt-cube
7×difference-of-sqr-1 div-exp
6×add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u
3×expm1-def
2×clear-num frac-2neg hypot-def
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log hypot-1-def flip-- distribute-lft-out-- associate-/l/
Counts
4 → 1133
Calls
4 calls:
23.0ms
(sqrt (+ 1 (exp (* -2 x))))
35.0ms
(/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x)))))
11.0ms
(/ 2 (sqrt (+ 1 (exp (* -2 x)))))
221.0ms
(- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)

series254.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(sqrt (+ 1 (exp (* -2 x))))
34.0ms
(/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x)))))
74.0ms
(/ 2 (sqrt (+ 1 (exp (* -2 x)))))
91.0ms
(- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)

simplify1.4s

Counts
1145 → 1145
Iterations
IterNodes
done2004
11634
0711

prune2.7s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (exp (* -2 x)) 1)
0.0b
(/ 2 (+ (exp (* -2 x)) 1))
2.7b
(- (/ 2 (+ (exp (* -2 x)) 1)) 1)

rewrite533.0ms

Algorithm
rewrite-expression-head
Rules
101×*-un-lft-identity
74×add-sqr-sqrt
63×times-frac add-cube-cbrt
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
8×add-exp-log
7×add-log-exp
6×flip3-+ flip-+
5×add-cbrt-cube div-inv
4×associate-/r* difference-of-squares
3×expm1-log1p-u pow1 fma-def insert-posit16 log1p-expm1-u associate-/l*
2×expm1-def difference-of-sqr-1 div-exp
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-- diff-log flip-- distribute-lft-out--
Counts
3 → 150
Calls
3 calls:
381.0ms
(+ (exp (* -2 x)) 1)
27.0ms
(/ 2 (+ (exp (* -2 x)) 1))
119.0ms
(- (/ 2 (+ (exp (* -2 x)) 1)) 1)

series160.0ms

Counts
3 → 9
Calls
3 calls:
15.0ms
(+ (exp (* -2 x)) 1)
39.0ms
(/ 2 (+ (exp (* -2 x)) 1))
106.0ms
(- (/ 2 (+ (exp (* -2 x)) 1)) 1)

simplify863.0ms

Counts
159 → 159
Iterations
IterNodes
done2005
2962
1418
0180

prune414.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes188.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.8b

bsearch3.0ms

simplify9.0ms

Iterations
IterNodes
done31
131
023

end0.0ms

sample2.3s

Algorithm
intervals
Results
936.0ms1757×body1280valid
477.0ms1239×body640valid
388.0ms4031×body80valid
220.0ms645×body320valid
81.0ms328×body160valid