Details

Time bar (total: 24.9s)

sample518.0ms

Algorithm
intervals
Results
295.0ms95×body2560valid
145.0ms83×body1280valid
36.0ms41×body640valid
14.0ms22×body320valid
12.0ms256×pre80true
4.0ms13×body160valid
0.0ms2×body80valid

simplify29.0ms

Calls
1 calls:
Slowest
29.0ms
(- (/ 1 x) (/ 1 (tan x)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.7b

localize20.0ms

Local error

Found 2 expressions with local error:

4.2b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
20×prod-diff
17×*-un-lft-identity
15×add-sqr-sqrt div-inv
13×add-cube-cbrt
5×tan-quot associate-/r/
4×fma-neg distribute-lft-out-- add-log-exp
3×pow1 associate-/r* add-exp-log
2×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
1×rec-exp clear-num sub-neg frac-2neg flip3-- diff-log frac-sub pow-flip flip-- inv-pow difference-of-squares
Calls
2 calls:
Slowest
11.0ms
(- (/ 1 x) (/ 1 (tan x)))
2.0ms
(/ 1 (tan x))

series102.0ms

Calls
2 calls:
Slowest
71.0ms
(- (/ 1 x) (/ 1 (tan x)))
31.0ms
(/ 1 (tan x))

simplify2.9s

Calls
62 calls:
Slowest
281.0ms
(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))
115.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
106.0ms
(fma 1 (/ 1 x) (- (* (cos x) (/ 1 (sin x)))))
106.0ms
(fma 1 (/ 1 x) (- (* (cos x) (/ 1 (sin x)))))
105.0ms
(fma (sqrt (/ 1 x)) (sqrt (/ 1 x)) (- (* (cos x) (/ 1 (sin x)))))

prune447.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (fma 1/45 (* x x) 1/3) x)
0.0b
(fma 1/45 (* x x) 1/3)
0.0b
(fma 2/945 (pow x 5) (* (fma 1/45 (* x x) 1/3) x))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×expm1-log1p-u pow1 add-cbrt-cube associate-*l* add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×*-commutative
Calls
3 calls:
Slowest
3.0ms
(* (fma 1/45 (* x x) 1/3) x)
0.0ms
(fma 1/45 (* x x) 1/3)
0.0ms
(fma 2/945 (pow x 5) (* (fma 1/45 (* x x) 1/3) x))

series95.0ms

Calls
3 calls:
Slowest
41.0ms
(* (fma 1/45 (* x x) 1/3) x)
30.0ms
(fma 2/945 (pow x 5) (* (fma 1/45 (* x x) 1/3) x))
24.0ms
(fma 1/45 (* x x) 1/3)

simplify687.0ms

Calls
11 calls:
Slowest
122.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
115.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
113.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
69.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
55.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune443.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (sqrt (fma 1/45 (* x x) 1/3)) (sqrt (fma 1/45 (* x x) 1/3))) x)
0.0b
(* (sqrt (fma 1/45 (* x x) 1/3)) (sqrt (fma 1/45 (* x x) 1/3)))
0.0b
(fma 1/45 (* x x) 1/3)
0.0b
(fma 1/45 (* x x) 1/3)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-*l*
6×add-cbrt-cube associate-*r* add-exp-log sqrt-prod
4×expm1-log1p-u pow1/2 insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down *-commutative pow-prod-up fma-udef
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp cbrt-unprod
Calls
4 calls:
Slowest
17.0ms
(* (* (sqrt (fma 1/45 (* x x) 1/3)) (sqrt (fma 1/45 (* x x) 1/3))) x)
9.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) (sqrt (fma 1/45 (* x x) 1/3)))
0.0ms
(fma 1/45 (* x x) 1/3)
0.0ms
(fma 1/45 (* x x) 1/3)

series145.0ms

Calls
4 calls:
Slowest
60.0ms
(* (* (sqrt (fma 1/45 (* x x) 1/3)) (sqrt (fma 1/45 (* x x) 1/3))) x)
37.0ms
(fma 1/45 (* x x) 1/3)
26.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) (sqrt (fma 1/45 (* x x) 1/3)))
22.0ms
(fma 1/45 (* x x) 1/3)

simplify1.3s

Calls
35 calls:
Slowest
193.0ms
(* (* (* (sqrt (fma 1/45 (* x x) 1/3)) (sqrt (fma 1/45 (* x x) 1/3))) (sqrt (fma 1/45 (* x x) 1/3))) (* (* (sqrt (fma 1/45 (* x x) 1/3)) (sqrt (fma 1/45 (* x x) 1/3))) (sqrt (fma 1/45 (* x x) 1/3))))
137.0ms
(* (fma 1/45 (* x x) 1/3) (fma 1/45 (* x x) 1/3))
115.0ms
(* (fma 1/45 (* x x) 1/3) (fma 1/45 (* x x) 1/3))
56.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
53.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune858.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (exp (fma 1/45 (* x x) 1/3))) x)
0.0b
(log (exp (fma 1/45 (* x x) 1/3)))
0.0b
(fma 1/45 (* x x) 1/3)
0.0b
(exp (fma 1/45 (* x x) 1/3))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt exp-prod *-un-lft-identity add-cube-cbrt
8×log-pow
7×associate-*l*
6×pow1
5×add-log-exp
4×expm1-log1p-u log-prod add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×fma-udef
2×exp-sum
1×rem-log-exp *-commutative rem-exp-log
Calls
4 calls:
Slowest
10.0ms
(* (log (exp (fma 1/45 (* x x) 1/3))) x)
4.0ms
(log (exp (fma 1/45 (* x x) 1/3)))
3.0ms
(exp (fma 1/45 (* x x) 1/3))
0.0ms
(fma 1/45 (* x x) 1/3)

series121.0ms

Calls
4 calls:
Slowest
49.0ms
(* (log (exp (fma 1/45 (* x x) 1/3))) x)
31.0ms
(log (exp (fma 1/45 (* x x) 1/3)))
21.0ms
(fma 1/45 (* x x) 1/3)
19.0ms
(exp (fma 1/45 (* x x) 1/3))

simplify1.2s

Calls
29 calls:
Slowest
245.0ms
(+ (* 1/45 (* (pow x 2) (exp 1/3))) (+ (exp 1/3) (* 1/4050 (* (pow x 4) (exp 1/3)))))
76.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
75.0ms
(log (* (cbrt (exp (fma 1/45 (* x x) 1/3))) (cbrt (exp (fma 1/45 (* x x) 1/3)))))
75.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
73.0ms
(log (sqrt (exp (fma 1/45 (* x x) 1/3))))

prune772.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

regimes35.0ms

Accuracy

0% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample15.1s

Algorithm
intervals
Results
9.4s3218×body2560valid
3.6s2529×body1280valid
980.0ms1235×body640valid
412.0ms8000×pre80true
352.0ms632×body320valid
153.0ms330×body160valid
37.0ms56×body80valid