Details

Time bar (total: 24.0s)

sample143.0ms

Algorithm
intervals
Results
74.0ms115×body1280valid
25.0ms70×body640valid
18.0ms283×body80valid
8.0ms35×body320valid
3.0ms16×body160valid

simplify88.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
88.0ms
(/ (- (exp x) (exp (- x))) 2)

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.8b

localize26.0ms

Local error

Found 1 expressions with local error:

4.8b
(- (exp x) (exp (- x)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
9×prod-diff
8×add-cube-cbrt
3×fma-neg add-log-exp
1×expm1-log1p-u pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log insert-posit16 log1p-expm1-u flip-- distribute-lft-out-- difference-of-squares
Counts
1 → 29
Calls
1 calls:
Slowest
16.0ms
(- (exp x) (exp (- x)))

series60.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
60.0ms
(- (exp x) (exp (- x)))

simplify2.4s

Counts
27 → 32
Calls
27 calls:
Slowest
304.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
228.0ms
(fma 1 (exp x) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
216.0ms
(fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
214.0ms
(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
147.0ms
(fma (- (cbrt (exp (- x)))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))) (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x))))))

prune243.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (fma 1/3 (* x x) 2))
0.0b
(fma 1/3 (* x x) 2)
0.0b
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×fma-udef
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
1×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
3 → 45
Calls
3 calls:
Slowest
5.0ms
(* x (fma 1/3 (* x x) 2))
0.0ms
(fma 1/3 (* x x) 2)
0.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

series269.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
122.0ms
(* x (fma 1/3 (* x x) 2))
89.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
58.0ms
(fma 1/3 (* x x) 2)

simplify2.5s

Counts
21 → 54
Calls
21 calls:
Slowest
764.0ms
(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
327.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
324.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
297.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
199.0ms
(+ (* 2 x) (* 1/3 (pow x 3)))

prune558.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 1/3 (* x x))
0.1b
(* x (* 1/3 (* x x)))
0.0b
(fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2)))
0.0b
(+ (* x (* 1/3 (* x x))) (* x 2))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-cbrt-cube add-exp-log
9×pow-prod-down prod-exp cbrt-unprod
7×add-sqr-sqrt
6×*-un-lft-identity associate-*l* add-cube-cbrt add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×associate-*r* *-commutative
1×+-commutative sum-log fma-def flip3-+ flip-+ fma-udef distribute-lft-out unswap-sqr
Counts
4 → 73
Calls
4 calls:
Slowest
46.0ms
(+ (* x (* 1/3 (* x x))) (* x 2))
36.0ms
(* x (* 1/3 (* x x)))
29.0ms
(* 1/3 (* x x))
0.0ms
(fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
161.0ms
(+ (* x (* 1/3 (* x x))) (* x 2))
81.0ms
(fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2)))
49.0ms
(* x (* 1/3 (* x x)))
31.0ms
(* 1/3 (* x x))

simplify4.1s

Counts
36 → 85
Calls
36 calls:
Slowest
555.0ms
(* (* (* x x) x) (* (* (* 1/3 (* x x)) (* 1/3 (* x x))) (* 1/3 (* x x))))
542.0ms
(* (* (* x x) x) (* (* (* 1/3 1/3) 1/3) (* (* (* x x) (* x x)) (* x x))))
437.0ms
(* (* (* x x) x) (* (* (* 1/3 1/3) 1/3) (* (* (* x x) x) (* (* x x) x))))
350.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
335.0ms
(* (exp (* x (* 1/3 (* x x)))) (exp (* x 2)))

prune836.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 1/3 (* x x))
0.1b
(* x (* 1/3 (* x x)))
0.0b
(expm1 (log1p (fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2)))))
0.0b
(log1p (fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-cbrt-cube add-exp-log
9×pow-prod-down prod-exp cbrt-unprod
7×add-sqr-sqrt
6×*-un-lft-identity associate-*l* add-cube-cbrt
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
2×associate-*r* *-commutative
1×log1p-udef expm1-log1p log1p-expm1 expm1-udef unswap-sqr
Counts
4 → 70
Calls
4 calls:
Slowest
33.0ms
(* x (* 1/3 (* x x)))
13.0ms
(* 1/3 (* x x))
0.0ms
(log1p (fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2))))
0.0ms
(expm1 (log1p (fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2)))))

series458.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
229.0ms
(expm1 (log1p (fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2)))))
143.0ms
(log1p (fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2))))
56.0ms
(* x (* 1/3 (* x x)))
30.0ms
(* 1/3 (* x x))

simplify5.3s

Counts
35 → 82
Calls
35 calls:
Slowest
590.0ms
(* (* (* x x) x) (* (* (* 1/3 (* x x)) (* 1/3 (* x x))) (* 1/3 (* x x))))
556.0ms
(* (* (* 1/3 1/3) 1/3) (* (* (* x x) x) (* (* x x) x)))
515.0ms
(* (* (* x x) x) (* (* (* 1/3 1/3) 1/3) (* (* (* x x) (* x x)) (* x x))))
453.0ms
(fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2)))
396.0ms
(- (+ (* 20 (/ (exp (- (log -1/60) (* 5 (log (/ -1 x))))) (pow x 2))) (+ (* 120 (/ (exp (- (log -1/60) (* 5 (log (/ -1 x))))) (pow x 4))) (exp (- (log -1/60) (* 5 (log (/ -1 x))))))) 1)

prune999.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

60.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.7b

bsearch81.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.3s3365×body1280valid
1.6s2516×body640valid
692.0ms8128×body80valid
347.0ms1230×body320valid
96.0ms596×body160valid