Details

Time bar (total: 50.0s)

sample556.0ms

Algorithm
intervals
Results
252.0ms98×body1280valid
146.0ms38×body2560valid
63.0ms60×body640valid
26.0ms38×body320valid
4.0ms14×body80valid
3.0ms8×body160valid

simplify29.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
28.0ms
(/ (- x (sin x)) (- x (tan x)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize19.0ms

Local error

Found 3 expressions with local error:

1.1b
(- x (tan x))
1.1b
(- x (sin x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite47.0ms

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
33.0ms
(/ (- x (sin x)) (- x (tan x)))
6.0ms
(- x (tan x))
6.0ms
(- x (sin x))

series264.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
117.0ms
(/ (- x (sin x)) (- x (tan x)))
98.0ms
(- x (tan x))
48.0ms
(- x (sin x))

simplify3.1s

Counts
82 → 92
Calls
82 calls:
Slowest
429.0ms
(- (+ 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)))))
392.0ms
(- (+ 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)))))
291.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
195.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
173.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune847.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

1.1b
(- x (tan x))
1.1b
(- x (tan x))
1.1b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.1b
(/ (sin x) (- x (tan x)))

rewrite87.0ms

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
61.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
13.0ms
(/ (sin x) (- x (tan x)))
6.0ms
(- x (tan x))
5.0ms
(- x (tan x))

series478.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
244.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
96.0ms
(- x (tan x))
75.0ms
(/ (sin x) (- x (tan x)))
63.0ms
(- x (tan x))

simplify4.8s

Counts
95 → 110
Calls
95 calls:
Slowest
917.0ms
(- (+ 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
(- (+ 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)))))
291.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
257.0ms
(- (/ x (- (pow x 3) (pow (tan x) 3))) (/ (sin x) (- (pow x 3) (pow (tan x) 3))))
256.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune961.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (/ (/ (sin x) (cos x)) x) (/ (sin x) x))
1.1b
(+ (* (/ (sin x) x) (/ (/ (sin x) (cos x)) x)) -1)
0.1b
(/ (/ (sin x) (cos x)) x)
0.1b
(/ (/ (sin x) (cos x)) x)

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
111×add-sqr-sqrt
98×*-un-lft-identity
90×add-cube-cbrt
26×associate-/l*
14×add-cbrt-cube add-exp-log
12×div-inv
8×add-log-exp
6×cbrt-undiv associate-/r* div-exp difference-of-squares
4×pow1 insert-posit16 distribute-lft-out--
2×clear-num frac-2neg associate-/l/
1×+-commutative sum-log sub-neg flip3-+ flip3-- distribute-rgt-out-- diff-log frac-sub flip-+ flip-- sub-div
Counts
4 → 180
Calls
4 calls:
Slowest
38.0ms
(- (/ (/ (sin x) (cos x)) x) (/ (sin x) x))
21.0ms
(/ (/ (sin x) (cos x)) x)
19.0ms
(+ (* (/ (sin x) x) (/ (/ (sin x) (cos x)) x)) -1)
14.0ms
(/ (/ (sin x) (cos x)) x)

series433.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
183.0ms
(- (/ (/ (sin x) (cos x)) x) (/ (sin x) x))
138.0ms
(+ (* (/ (sin x) x) (/ (/ (sin x) (cos x)) x)) -1)
59.0ms
(/ (/ (sin x) (cos x)) x)
53.0ms
(/ (/ (sin x) (cos x)) x)

simplify10.5s

Counts
232 → 192
Calls
232 calls:
Slowest
757.0ms
(/ (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (* (* x x) x))
681.0ms
(/ (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (* (* x x) x))
444.0ms
(* (exp (* (/ (sin x) x) (/ (/ (sin x) (cos x)) x))) (exp -1))
422.0ms
(/ (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* x x) x))
393.0ms
(* -1 (/ (- (sin x) (/ (sin x) (cos x))) x))

prune2.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

17.3b
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
0.2b
(* (* x x) 9/40)
0.1b
(* (* (* x x) (* x x)) 27/2800)
0.1b
(* (* x x) (* x x))

rewrite338.0ms

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))
110.0ms
(* (* (* x x) (* x x)) 27/2800)
49.0ms
(* (* x x) (* x x))
24.0ms
(* (* x x) 9/40)

series193.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
56.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
50.0ms
(* (* (* x x) (* x x)) 27/2800)
44.0ms
(* (* x x) (* x x))
42.0ms
(* (* x x) 9/40)

simplify6.4s

Counts
111 → 140
Calls
111 calls:
Slowest
464.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
449.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
438.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
384.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
361.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.5b

bsearch186.0ms

end0.0ms

sample17.1s

Algorithm
intervals
Results
7.3s1644×body2560valid
6.3s2753×body1280valid
2.0s1788×body640valid
919.0ms1006×body320valid
222.0ms464×body160valid
88.0ms345×body80valid