Details

Time bar (total: 31.3s)

sample594.0ms

Algorithm
intervals
Results
226.0ms59×body2560valid
192.0ms74×body1280valid
54.0ms64×body640valid
36.0ms15×body160valid
24.0ms33×body320valid
3.0ms11×body80valid

simplify26.0ms

Calls
1 calls:
Slowest
25.0ms
(/ (- x (sin x)) (- x (tan x)))

prune312.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize35.0ms

Local error

Found 3 expressions with local error:

0.7b
(- x (sin x))
0.6b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite14.0ms

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
7.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (sin x))
1.0ms
(- x (tan x))

series198.0ms

Calls
3 calls:
Slowest
84.0ms
(/ (- x (sin x)) (- x (tan x)))
66.0ms
(- x (tan x))
48.0ms
(- x (sin x))

simplify2.2s

Calls
39 calls:
Slowest
346.0ms
(- (+ 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)))))
341.0ms
(- (+ 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)))))
317.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
236.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
165.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune703.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.7b
(- x (sin x))
0.6b
(- x (tan x))
0.0b
(/ 1 (/ (- x (tan x)) (- x (sin x))))
0.0b
(/ (- x (tan x)) (- x (sin x)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×associate-/r* times-frac
9×add-exp-log
6×add-cbrt-cube
5×pow1 flip3-- associate-/r/ flip--
4×insert-posit16 add-log-exp
3×div-inv associate-/l*
2×rec-exp clear-num sub-neg frac-2neg div-exp associate-/l/
1×cbrt-undiv div-sub pow-flip inv-pow
Calls
4 calls:
Slowest
4.0ms
(/ (- x (tan x)) (- x (sin x)))
2.0ms
(/ 1 (/ (- x (tan x)) (- x (sin x))))
1.0ms
(- x (sin x))
1.0ms
(- x (tan x))

series382.0ms

Calls
4 calls:
Slowest
146.0ms
(/ 1 (/ (- x (tan x)) (- x (sin x))))
103.0ms
(/ (- x (tan x)) (- x (sin x)))
98.0ms
(- x (tan x))
34.0ms
(- x (sin x))

simplify3.0s

Calls
59 calls:
Slowest
316.0ms
(- (+ 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)))))
309.0ms
(/ (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))) (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))))
294.0ms
(- (+ (/ (pow (sin x) 2) (pow x 2)) (+ (/ (sin x) x) 1)) (+ (/ (sin x) (* (cos x) x)) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
283.0ms
(- (+ (/ (pow (sin x) 2) (pow x 2)) (+ (/ (sin x) x) 1)) (+ (/ (sin x) (* (cos x) x)) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
276.0ms
(- (+ 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)))))

prune887.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.7b
(- 1 (/ (sin x) x))
0.2b
(* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x))
0.1b
(/ (sin x) (cos x))
0.1b
(/ (sin x) (cos x))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
10×add-cbrt-cube add-exp-log
9×pow1
6×associate-/r* associate-/l*
4×associate-*r* associate-*l* insert-posit16 div-inv add-log-exp
2×cbrt-undiv quot-tan clear-num frac-2neg div-exp
1×pow2 frac-times sub-neg pow-plus flip3-- pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod flip--
Calls
4 calls:
Slowest
20.0ms
(* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x))
4.0ms
(/ (sin x) (cos x))
4.0ms
(/ (sin x) (cos x))
3.0ms
(- 1 (/ (sin x) x))

series203.0ms

Calls
4 calls:
Slowest
77.0ms
(* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x))
53.0ms
(- 1 (/ (sin x) x))
40.0ms
(/ (sin x) (cos x))
32.0ms
(/ (sin x) (cos x))

simplify2.8s

Calls
78 calls:
Slowest
441.0ms
(/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2)))
366.0ms
(/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2)))
230.0ms
(* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x))
175.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
168.0ms
(+ (log (/ (/ (sin x) (cos x)) x)) (log (/ (/ (sin x) (cos x)) x)))

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (- (- (* -9/10 (* x x)) (* (pow x 4) 513/1400)) 2))
0.1b
(* -9/10 (* x x))
0.1b
(* (pow x 4) 513/1400)
0.0b
(- (* -9/10 (* x x)) (* (pow x 4) 513/1400))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
5×pow1 add-exp-log
4×add-cbrt-cube insert-posit16
3×associate-/r* associate-*l*
2×flip3-- associate-/r/ *-commutative flip--
1×rec-exp clear-num sub-neg frac-2neg diff-log associate-*r* div-inv pow-flip inv-pow
Calls
4 calls:
Slowest
11.0ms
(/ 1 (- (- (* -9/10 (* x x)) (* (pow x 4) 513/1400)) 2))
4.0ms
(- (* -9/10 (* x x)) (* (pow x 4) 513/1400))
3.0ms
(* (pow x 4) 513/1400)
1.0ms
(* -9/10 (* x x))

series309.0ms

Calls
4 calls:
Slowest
155.0ms
(- (* -9/10 (* x x)) (* (pow x 4) 513/1400))
62.0ms
(/ 1 (- (- (* -9/10 (* x x)) (* (pow x 4) 513/1400)) 2))
52.0ms
(* (pow x 4) 513/1400)
40.0ms
(* -9/10 (* x x))

simplify1.5s

Calls
21 calls:
Slowest
211.0ms
(- (* 196000/29241 (/ 1 (pow x 6))) (+ (* 1400/513 (/ 1 (pow x 4))) (* 7840000/5000211 (/ 1 (pow x 8)))))
162.0ms
(- (* 196000/29241 (/ 1 (pow x 6))) (+ (* 1400/513 (/ 1 (pow x 4))) (* 7840000/5000211 (/ 1 (pow x 8)))))
150.0ms
(+ (* (- (* -9/10 (* x x)) (* (pow x 4) 513/1400)) (- (* -9/10 (* x x)) (* (pow x 4) 513/1400))) (+ (* 2 2) (* (- (* -9/10 (* x x)) (* (pow x 4) 513/1400)) 2)))
133.0ms
(/ (exp (* -9/10 (* x x))) (exp (* (pow x 4) 513/1400)))
126.0ms
(- (- (* -9/10 (* x x)) (* (pow x 4) 513/1400)) 2)

prune537.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.3b

bsearch168.0ms

end0.0ms

sample16.1s

Algorithm
intervals
Results
7.2s1706×body2560valid
5.1s2597×body1280valid
2.1s1982×body640valid
1.1s943×body320valid
228.0ms435×body160valid
112.0ms337×body80valid