Details

Time bar (total: 54.6s)

sample733.0ms

Algorithm
intervals
Results
328.0ms48×body2560valid
181.0ms80×body1280valid
90.0ms76×body640valid
20.0ms26×body320valid
7.0ms14×body160valid
3.0ms12×body80valid

simplify42.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
42.0ms
(/ (- x (sin x)) (- x (tan x)))

prune44.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize27.0ms

Local error

Found 3 expressions with local error:

1.3b
(- x (sin x))
1.3b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite41.0ms

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
26.0ms
(/ (- x (sin x)) (- x (tan x)))
7.0ms
(- x (sin x))
4.0ms
(- x (tan x))

series287.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
109.0ms
(/ (- x (sin x)) (- x (tan x)))
93.0ms
(- x (tan x))
84.0ms
(- x (sin x))

simplify3.7s

Counts
82 → 92
Calls
82 calls:
Slowest
614.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
426.0ms
(- (+ 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)))))
393.0ms
(- (+ 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)))))
270.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
229.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune785.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 3 expressions with local error:

1.3b
(- x (sin x))
1.3b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite60.0ms

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
37.0ms
(/ (- x (sin x)) (- x (tan x)))
12.0ms
(- x (sin x))
8.0ms
(- x (tan x))

series263.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
114.0ms
(/ (- x (sin x)) (- x (tan x)))
90.0ms
(- x (tan x))
59.0ms
(- x (sin x))

simplify3.2s

Counts
82 → 92
Calls
82 calls:
Slowest
418.0ms
(- (+ 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)))))
387.0ms
(- (+ 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)))))
336.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
272.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
179.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune710.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

1.3b
(- x (sin x))
1.3b
(- x (tan x))
0.0b
(/ 1 (/ (- x (tan x)) (- x (sin x))))
0.0b
(/ (- x (tan x)) (- x (sin x)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
218×times-frac
200×add-sqr-sqrt *-un-lft-identity
92×add-cube-cbrt
54×distribute-lft-out-- difference-of-squares
36×associate-/r*
17×add-exp-log
11×add-cbrt-cube associate-/r/
8×flip3-- div-exp flip-- associate-/l* add-log-exp
6×div-inv
5×pow1
4×cbrt-undiv insert-posit16
2×rec-exp clear-num sub-neg frac-2neg diff-log 1-exp associate-/l/
1×div-sub pow-flip inv-pow
Counts
4 → 232
Calls
4 calls:
Slowest
36.0ms
(/ 1 (/ (- x (tan x)) (- x (sin x))))
22.0ms
(/ (- x (tan x)) (- x (sin x)))
10.0ms
(- x (sin x))
8.0ms
(- x (tan x))

series325.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(/ (- x (tan x)) (- x (sin x)))
114.0ms
(/ 1 (/ (- x (tan x)) (- x (sin x))))
60.0ms
(- x (tan x))
36.0ms
(- x (sin x))

simplify21.9s

Counts
312 → 244
Calls
312 calls:
Slowest
476.0ms
(- (+ 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)))))
431.0ms
(- (+ 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)))))
410.0ms
(/ (* (* 1 1) 1) (* (* (/ (- x (tan x)) (- x (sin x))) (/ (- x (tan x)) (- x (sin x)))) (/ (- x (tan x)) (- x (sin x)))))
396.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- x (tan x))) (cbrt (- x (tan x)))) (* (cbrt (- x (sin x))) (cbrt (- x (sin x))))))
379.0ms
(/ 1 (/ (- x (tan x)) (- (* x x) (* (sin x) (sin x)))))

prune1.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.4b
(* (* x x) 27/2800)
0.1b
(* (* x x) (- (* (* x x) 27/2800) 9/40))
0.0b
(- (* (* x x) 27/2800) 9/40)

rewrite161.0ms

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
105.0ms
(* (* x x) (- (* (* x x) 27/2800) 9/40))
29.0ms
(* (* x x) 27/2800)
26.0ms
(- (* (* x x) 27/2800) 9/40)

series271.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
143.0ms
(* (* x x) (- (* (* x x) 27/2800) 9/40))
88.0ms
(- (* (* x x) 27/2800) 9/40)
40.0ms
(* (* x x) 27/2800)

simplify2.3s

Counts
37 → 68
Calls
37 calls:
Slowest
351.0ms
(+ (* (* (* x x) 27/2800) (* (* x x) 27/2800)) (+ (* 9/40 9/40) (* (* (* x x) 27/2800) 9/40)))
284.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* 27/2800 27/2800) 27/2800))
250.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* 27/2800 27/2800) 27/2800))
247.0ms
(/ (exp (* (* x x) 27/2800)) (exp 9/40))
132.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (- (* (* x x) 27/2800) 9/40) (- (* (* x x) 27/2800) 9/40)) (- (* (* x x) 27/2800) 9/40)))

prune393.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes86.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.2b

bsearch95.0ms

end0.0ms

sample17.1s

Algorithm
intervals
Results
7.5s1614×body2560valid
6.0s2710×body1280valid
2.2s1895×body640valid
727.0ms938×body320valid
254.0ms475×body160valid
123.0ms368×body80valid