Details

Time bar (total: 48.8s)

sample1.0s

Algorithm
intervals
Results
245.0ms55×body2560valid
195.0ms96×body1280valid
169.0ms22×body320valid
65.0ms56×body640valid
8.0ms15×body160valid
3.0ms12×body80valid

simplify27.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
26.0ms
(/ (- x (sin x)) (- x (tan x)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize18.0ms

Local error

Found 3 expressions with local error:

1.4b
(- x (tan x))
1.2b
(- x (sin x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt *-un-lft-identity
25×times-frac
15×add-cube-cbrt
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
5×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×flip3-- flip--
3×pow1 insert-posit16
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Counts
3 → 83
Calls
3 calls:
Slowest
17.0ms
(/ (- x (sin x)) (- x (tan x)))
6.0ms
(- x (tan x))
5.0ms
(- x (sin x))

series205.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
91.0ms
(/ (- x (sin x)) (- x (tan x)))
70.0ms
(- x (tan x))
44.0ms
(- x (sin x))

simplify5.6s

Counts
125 → 92
Calls
125 calls:
Slowest
467.0ms
(- (+ 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)))))
382.0ms
(- (+ 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)))))
381.0ms
(* (* (- x (sin x)) (- x (sin x))) (- x (sin x)))
321.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
284.0ms
(* (* (- x (tan x)) (- x (tan x))) (- x (tan x)))

prune859.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (* x x) 27/2800)
0.1b
(* (* x x) (- 9/40 (* (* x x) 27/2800)))
0.0b
(- 9/40 (* (* x x) 27/2800))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-cbrt-cube add-exp-log
7×add-sqr-sqrt
6×associate-*r* pow-prod-down prod-exp cbrt-unprod
5×*-un-lft-identity add-cube-cbrt add-log-exp
3×sub-neg insert-posit16
2×distribute-rgt-in distribute-lft-in flip3-- associate-*l* associate-*r/ *-commutative flip-- unswap-sqr
1×diff-log
Counts
3 → 59
Calls
3 calls:
Slowest
30.0ms
(* (* x x) (- 9/40 (* (* x x) 27/2800)))
17.0ms
(* (* x x) 27/2800)
8.0ms
(- 9/40 (* (* x x) 27/2800))

series282.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
183.0ms
(* (* x x) (- 9/40 (* (* x x) 27/2800)))
69.0ms
(- 9/40 (* (* x x) 27/2800))
29.0ms
(* (* x x) 27/2800)

simplify7.8s

Counts
74 → 68
Calls
74 calls:
Slowest
565.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* 27/2800 27/2800) 27/2800))
428.0ms
(- (pow 9/40 3) (pow (* (* x x) 27/2800) 3))
369.0ms
(- (* 9/40 9/40) (* (* (* x x) 27/2800) (* (* x x) 27/2800)))
340.0ms
(* (* x x) (- (* 9/40 9/40) (* (* (* x x) 27/2800) (* (* x x) 27/2800))))
329.0ms
(exp (- 9/40 (* (* x x) 27/2800)))

prune554.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b
(- x (tan x))
1.4b
(- x (tan x))
0.8b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.1b
(/ (sin x) (- x (tan x)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
44×add-sqr-sqrt
33×times-frac
18×distribute-lft-out--
16×add-cube-cbrt
12×difference-of-squares
10×add-log-exp
6×flip3-- add-cbrt-cube add-exp-log associate-/r/ flip--
5×associate-/r*
4×pow1 insert-posit16
3×sub-neg distribute-rgt-out-- diff-log div-inv associate-/l*
1×cbrt-undiv clear-num frac-2neg div-exp frac-sub sub-div
Counts
4 → 98
Calls
4 calls:
Slowest
67.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
12.0ms
(/ (sin x) (- x (tan x)))
5.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series551.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
301.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
97.0ms
(- x (tan x))
84.0ms
(/ (sin x) (- x (tan x)))
70.0ms
(- x (tan x))

simplify7.9s

Counts
139 → 110
Calls
139 calls:
Slowest
471.0ms
(- (+ 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)))))
461.0ms
(* (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))) (/ (sin x) (- x (tan x))))
430.0ms
(+ (* (/ x (- x (tan x))) (/ x (- x (tan x)))) (+ (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))) (* (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))))
389.0ms
(* (* (- x (tan x)) (- x (tan x))) (- x (tan x)))
379.0ms
(- (+ 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)))))

prune943.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

1.4b
(- x (tan x))
1.4b
(- x (tan x))
1.4b
(- x (tan x))
1.2b
(- x (sin x))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-log-exp
4×pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt insert-posit16 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 60
Calls
4 calls:
Slowest
9.0ms
(- x (sin x))
9.0ms
(- x (tan x))
8.0ms
(- x (tan x))
8.0ms
(- x (tan x))

series302.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(- x (tan x))
92.0ms
(- x (tan x))
68.0ms
(- x (tan x))
43.0ms
(- x (sin x))

simplify3.8s

Counts
84 → 72
Calls
84 calls:
Slowest
390.0ms
(* (* (- x (tan x)) (- x (tan x))) (- x (tan x)))
348.0ms
(* (* (- x (sin x)) (- x (sin x))) (- x (sin x)))
337.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
315.0ms
(* (* (- x (tan x)) (- x (tan x))) (- x (tan x)))
279.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune778.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes95.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch197.0ms

end0.0ms

sample17.5s

Algorithm
intervals
Results
6.7s2818×body1280valid
6.7s1619×body2560valid
2.6s1814×body640valid
857.0ms912×body320valid
298.0ms498×body160valid
90.0ms339×body80valid