Details

Time bar (total: 24.9s)

sample594.0ms

Algorithm
intervals
Results
207.0ms96×body1280valid
193.0ms48×body2560valid
107.0ms53×body640valid
20.0ms28×body320valid
7.0ms16×body160valid
3.0ms15×body80valid

simplify37.0ms

Calls
1 calls:
Slowest
36.0ms
(/ (- x (sin x)) (- x (tan x)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize36.0ms

Local error

Found 3 expressions with local error:

2.2b
(- x (tan x))
2.2b
(- x (sin x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log
4×flip3-- flip--
3×pow1 associate-/r* insert-posit16 associate-/l* add-log-exp
2×sub-neg associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Calls
3 calls:
Slowest
8.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (tan x))
1.0ms
(- x (sin x))

series251.0ms

Calls
3 calls:
Slowest
107.0ms
(/ (- x (sin x)) (- x (tan x)))
102.0ms
(- x (tan x))
43.0ms
(- x (sin x))

simplify2.1s

Calls
39 calls:
Slowest
380.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
366.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
301.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
233.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
146.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune655.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

14.3b
(- (* (* x x) 9/40) (- (* (pow x 4) 27/2800) -1/2))
0.2b
(* (* x x) 9/40)
0.1b
(* (pow x 4) 27/2800)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
4×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
3×pow1 add-cbrt-cube add-exp-log insert-posit16
2×sub-neg *-commutative associate--r+
1×flip3-- diff-log flip-- associate--r-
Calls
3 calls:
Slowest
15.0ms
(- (* (* x x) 9/40) (- (* (pow x 4) 27/2800) -1/2))
5.0ms
(* (* x x) 9/40)
3.0ms
(* (pow x 4) 27/2800)

series63.0ms

Calls
3 calls:
Slowest
25.0ms
(* (pow x 4) 27/2800)
22.0ms
(- (* (* x x) 9/40) (- (* (pow x 4) 27/2800) -1/2))
17.0ms
(* (* x x) 9/40)

simplify600.0ms

Calls
14 calls:
Slowest
159.0ms
(/ (exp (* (* x x) 9/40)) (exp (- (* (pow x 4) 27/2800) -1/2)))
135.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
104.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
89.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
19.0ms
(* 9/40 (pow x 2))

prune358.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

14.3b
(- (* (* x x) 9/40) (* (pow x 4) 27/2800))
0.2b
(* (* x x) 9/40)
0.1b
(* (pow x 4) 27/2800)
0.0b
(+ (- (* (* x x) 9/40) (* (pow x 4) 27/2800)) -1/2)

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube associate-*l* add-exp-log insert-posit16
2×associate-+l+ sub-neg *-commutative
1×+-commutative flip3-+ flip3-- diff-log associate-+l- flip-+ flip--
Calls
4 calls:
Slowest
18.0ms
(+ (- (* (* x x) 9/40) (* (pow x 4) 27/2800)) -1/2)
14.0ms
(- (* (* x x) 9/40) (* (pow x 4) 27/2800))
5.0ms
(* (* x x) 9/40)
5.0ms
(* (pow x 4) 27/2800)

series123.0ms

Calls
4 calls:
Slowest
62.0ms
(- (* (* x x) 9/40) (* (pow x 4) 27/2800))
21.0ms
(* (* x x) 9/40)
20.0ms
(* (pow x 4) 27/2800)
20.0ms
(+ (- (* (* x x) 9/40) (* (pow x 4) 27/2800)) -1/2)

simplify600.0ms

Calls
18 calls:
Slowest
101.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
92.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
91.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
83.0ms
(/ (exp (* (* x x) 9/40)) (exp (* (pow x 4) 27/2800)))
56.0ms
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

prune529.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

14.3b
(+ (* 9/40 (* x x)) (* -27/2800 (pow x 4)))
2.2b
(log (exp (+ (* 9/40 (* x x)) (* -27/2800 (pow x 4)))))
0.2b
(* 9/40 (* x x))
0.1b
(* -27/2800 (pow x 4))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-log-exp
5×pow1
4×log-prod add-cbrt-cube associate-*r* add-exp-log log-pow insert-posit16
3×exp-prod
2×*-commutative
1×+-commutative sum-log flip3-+ rem-log-exp exp-sum flip-+
Calls
4 calls:
Slowest
7.0ms
(log (exp (+ (* 9/40 (* x x)) (* -27/2800 (pow x 4)))))
4.0ms
(+ (* 9/40 (* x x)) (* -27/2800 (pow x 4)))
1.0ms
(* -27/2800 (pow x 4))
1.0ms
(* 9/40 (* x x))

series141.0ms

Calls
4 calls:
Slowest
69.0ms
(+ (* 9/40 (* x x)) (* -27/2800 (pow x 4)))
47.0ms
(log (exp (+ (* 9/40 (* x x)) (* -27/2800 (pow x 4)))))
15.0ms
(* -27/2800 (pow x 4))
11.0ms
(* 9/40 (* x x))

simplify616.0ms

Calls
24 calls:
Slowest
73.0ms
(log (* (cbrt (exp (+ (* 9/40 (* x x)) (* -27/2800 (pow x 4))))) (cbrt (exp (+ (* 9/40 (* x x)) (* -27/2800 (pow x 4)))))))
60.0ms
(* (exp (* 9/40 (* x x))) (exp (* -27/2800 (pow x 4))))
55.0ms
(log (sqrt (exp (+ (* 9/40 (* x x)) (* -27/2800 (pow x 4))))))
52.0ms
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))
51.0ms
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

prune728.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes37.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch140.0ms

end0.0ms

sample17.1s

Algorithm
intervals
Results
7.4s1605×body2560valid
5.9s2753×body1280valid
2.5s1818×body640valid
760.0ms1000×body320valid
248.0ms432×body160valid
217.0ms392×body80valid