Details

Time bar (total: 1.6m)

sample890.0ms

Algorithm
intervals
Results
342.0ms96×body1280valid
267.0ms47×body2560valid
72.0ms59×body640valid
40.0ms14×body160valid
25.0ms29×body320valid
7.0ms11×body80valid

simplify162.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
161.0ms
(/ (- x (sin x)) (- x (tan x)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize19.0ms

Local error

Found 3 expressions with local error:

1.0b
(- x (sin x))
1.0b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite38.0ms

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
18.0ms
(/ (- x (sin x)) (- x (tan x)))
11.0ms
(- x (sin x))
5.0ms
(- x (tan x))

series219.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
83.0ms
(/ (- x (sin x)) (- x (tan x)))
70.0ms
(- x (sin x))
65.0ms
(- x (tan x))

simplify3.6s

Counts
82 → 92
Calls
82 calls:
Slowest
588.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
521.0ms
(- (+ 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)))))
380.0ms
(- (+ 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)))))
289.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
215.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune738.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (/ (/ (sin x) (cos x)) x) (/ (sin x) x))
1.0b
(+ (* (/ (sin x) x) (/ (/ (sin x) (cos x)) x)) -1)
0.2b
(/ (sin x) (cos x))
0.2b
(/ (sin x) (cos x))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
33×times-frac
30×*-un-lft-identity
22×add-cube-cbrt
8×add-cbrt-cube add-exp-log add-log-exp
6×associate-/r* associate-/l* difference-of-squares
4×pow1 insert-posit16 div-inv distribute-lft-out--
2×cbrt-undiv quot-tan clear-num frac-2neg div-exp
1×+-commutative sum-log sub-neg flip3-+ flip3-- distribute-rgt-out-- diff-log frac-sub flip-+ flip-- sub-div
Counts
4 → 96
Calls
4 calls:
Slowest
46.0ms
(- (/ (/ (sin x) (cos x)) x) (/ (sin x) x))
17.0ms
(+ (* (/ (sin x) x) (/ (/ (sin x) (cos x)) x)) -1)
15.0ms
(/ (sin x) (cos x))
10.0ms
(/ (sin x) (cos x))

series335.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(- (/ (/ (sin x) (cos x)) x) (/ (sin x) x))
137.0ms
(+ (* (/ (sin x) x) (/ (/ (sin x) (cos x)) x)) -1)
28.0ms
(/ (sin x) (cos x))
20.0ms
(/ (sin x) (cos x))

simplify3.9s

Counts
88 → 108
Calls
88 calls:
Slowest
434.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
371.0ms
(* (exp (* (/ (sin x) x) (/ (/ (sin x) (cos x)) x))) (exp -1))
352.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
340.0ms
(* -1 (/ (- (sin x) (/ (sin x) (cos x))) x))
299.0ms
(- (/ (pow (sin x) 2) (* (cos x) (pow x 2))) 1)

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

20.1b
(- (* (* 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)

rewrite294.0ms

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
149.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
91.0ms
(* (* (* x x) (* x x)) 27/2800)
28.0ms
(* (* x x) (* x x))
23.0ms
(* (* x x) 9/40)

series215.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
88.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
53.0ms
(* (* (* x x) (* x x)) 27/2800)
47.0ms
(* (* x x) (* x x))
27.0ms
(* (* x x) 9/40)

simplify6.7s

Counts
111 → 140
Calls
111 calls:
Slowest
552.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
528.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
432.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
401.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
387.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

36.5b
(/ (- (pow x 3) (pow (sin x) 3)) (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x)))))
1.0b
(- x (tan x))
1.0b
(- (pow x 3) (pow (sin x) 3))
0.4b
(pow (sin x) 3)

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
159×add-sqr-sqrt
89×*-un-lft-identity
81×difference-of-squares
75×times-frac
63×unpow-prod-down cube-prod
41×sqr-pow
37×add-cube-cbrt
26×distribute-lft-out--
25×associate-/l*
8×add-log-exp
7×add-cbrt-cube add-exp-log
5×pow1 difference-cubes
4×insert-posit16
3×pow-unpow associate-/r* flip3-- flip--
2×sub-neg diff-log associate-/r/ associate-/l/
1×cube-mult pow-to-exp cbrt-undiv clear-num pow-pow frac-2neg flip3-+ unpow3 div-sub div-exp pow-exp flip-+ div-inv rem-cube-cbrt
Counts
4 → 195
Calls
4 calls:
Slowest
78.0ms
(/ (- (pow x 3) (pow (sin x) 3)) (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x)))))
11.0ms
(- (pow x 3) (pow (sin x) 3))
4.0ms
(- x (tan x))
3.0ms
(pow (sin x) 3)

series994.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
696.0ms
(/ (- (pow x 3) (pow (sin x) 3)) (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x)))))
161.0ms
(- (pow x 3) (pow (sin x) 3))
101.0ms
(- x (tan x))
36.0ms
(pow (sin x) 3)

simplify54.2s

Counts
254 → 207
Calls
254 calls:
Slowest
715.0ms
(/ (- (sqrt (pow x 3)) (sqrt (pow (sin x) 3))) (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x)))))
479.0ms
(/ (+ (pow (sqrt x) 3) (pow (sqrt (sin x)) 3)) (* (cbrt (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x))))) (cbrt (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x)))))))
476.0ms
(/ (- (pow (sqrt x) 3) (pow (sqrt (sin x)) 3)) (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x)))))
470.0ms
(/ (* (* (- (pow x 3) (pow (sin x) 3)) (- (pow x 3) (pow (sin x) 3))) (- (pow x 3) (pow (sin x) 3))) (* (* (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x)))) (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x))))) (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x))))))
468.0ms
(/ (- (pow (sqrt x) 3) (pow (sqrt (sin x)) 3)) (sqrt (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x))))))

prune2.8s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes129.0ms

Accuracy

100% (0.0b remaining)

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

bsearch191.0ms

end0.0ms

sample16.8s

Algorithm
intervals
Results
6.7s1572×body2560valid
5.5s2694×body1280valid
3.1s1895×body640valid
851.0ms970×body320valid
326.0ms513×body160valid
97.0ms356×body80valid