Details

Time bar (total: 41.6s)

sample1.0s

Algorithm
intervals
Results
437.0ms57×body2560valid
363.0ms93×body1280valid
74.0ms56×body640valid
28.0ms34×body320valid
5.0ms9×body160valid
2.0ms7×body80valid

simplify34.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
33.0ms
(/ (- x (sin x)) (- x (tan x)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize45.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

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)))
7.0ms
(- x (tan x))
5.0ms
(- x (sin x))

series238.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
110.0ms
(- x (tan x))
91.0ms
(/ (- x (sin x)) (- x (tan x)))
37.0ms
(- x (sin x))

simplify3.3s

Counts
82 → 92
Calls
82 calls:
Slowest
461.0ms
(- (+ 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)))))
450.0ms
(- (+ 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)))))
379.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
257.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
162.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune836.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

16.8b
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
0.1b
(* (* x x) 9/40)
0.1b
(* (* x x) (* x x))
0.1b
(* (* (* x x) (* x x)) 27/2800)

rewrite286.0ms

Algorithm
rewrite-expression-head
Rules
138×pow1
39×add-cbrt-cube pow-prod-down add-exp-log
36×pow-prod-up
24×prod-exp cbrt-unprod
22×pow-sqr
18×pow-plus
13×pow2
9×add-log-exp
8×add-sqr-sqrt
7×associate-*r*
6×*-un-lft-identity add-cube-cbrt
4×insert-posit16
3×associate-*l* *-commutative unswap-sqr
2×diff-log
1×sum-log sub-neg flip3-- swap-sqr flip-- associate--r+
Counts
4 → 128
Calls
4 calls:
Slowest
153.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
85.0ms
(* (* (* x x) (* x x)) 27/2800)
22.0ms
(* (* x x) (* x x))
21.0ms
(* (* x x) 9/40)

series220.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
68.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
60.0ms
(* (* (* x x) (* x x)) 27/2800)
56.0ms
(* (* x x) (* x x))
36.0ms
(* (* x x) 9/40)

simplify6.9s

Counts
111 → 140
Calls
111 calls:
Slowest
900.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
423.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
418.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
369.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
369.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))

prune982.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.6b
(- x (tan x))
0.6b
(- x (tan x))
0.1b
(/ (sin x) (- x (tan x)))

rewrite74.0ms

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
43.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
16.0ms
(/ (sin x) (- x (tan x)))
9.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series437.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
237.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
75.0ms
(/ (sin x) (- x (tan x)))
69.0ms
(- x (tan x))
56.0ms
(- x (tan x))

simplify4.1s

Counts
95 → 110
Calls
95 calls:
Slowest
417.0ms
(- (+ 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)))))
389.0ms
(- (+ 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)))))
274.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
241.0ms
(- (/ x (- (pow x 3) (pow (tan x) 3))) (/ (sin x) (- (pow x 3) (pow (tan x) 3))))
238.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune965.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(- x (tan x))
0.6b
(- x (tan x))
0.6b
(- x (tan x))
0.3b
(- (/ x (sqrt (- x (tan x)))) (/ (sin x) (sqrt (- x (tan x)))))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
50×*-un-lft-identity
36×times-frac
22×sqrt-prod
20×distribute-lft-out--
14×difference-of-squares
12×add-log-exp
8×add-cube-cbrt
6×flip3-- flip--
4×pow1 sub-neg add-cbrt-cube sqrt-div diff-log add-exp-log associate-/r/ insert-posit16
3×distribute-rgt-out--
2×div-inv
1×frac-sub sub-div
Counts
4 → 85
Calls
4 calls:
Slowest
93.0ms
(- (/ x (sqrt (- x (tan x)))) (/ (sin x) (sqrt (- x (tan x)))))
8.0ms
(- x (tan x))
7.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series458.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
228.0ms
(- (/ x (sqrt (- x (tan x)))) (/ (sin x) (sqrt (- x (tan x)))))
93.0ms
(- x (tan x))
71.0ms
(- x (tan x))
66.0ms
(- x (tan x))

simplify2.5s

Counts
78 → 97
Calls
78 calls:
Slowest
279.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
261.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
231.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
220.0ms
(- (/ x (sqrt (- (pow x 3) (pow (tan x) 3)))) (/ (sin x) (sqrt (- (pow x 3) (pow (tan x) 3)))))
137.0ms
(- (/ x (sqrt (- (* x x) (* (tan x) (tan x))))) (/ (sin x) (sqrt (- (* x x) (* (tan x) (tan x))))))

prune1.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes67.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.0b

bsearch149.0ms

end0.0ms

sample17.5s

Algorithm
intervals
Results
7.8s1677×body2560valid
5.6s2724×body1280valid
2.9s1845×body640valid
771.0ms932×body320valid
228.0ms450×body160valid
98.0ms372×body80valid