Details

Time bar (total: 1.2m)

sample708.0ms

Algorithm
intervals
Results
265.0ms59×body2560valid
220.0ms74×body1280valid
62.0ms64×body640valid
46.0ms33×body320valid
7.0ms15×body160valid
2.0ms11×body80valid

simplify92.0ms

Calls
1 calls:
Slowest
91.0ms
(/ (- x (sin x)) (- x (tan x)))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize33.0ms

Local error

Found 3 expressions with local error:

0.7b
(- x (sin x))
0.6b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite59.0ms

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
Calls
3 calls:
Slowest
33.0ms
(/ (- x (sin x)) (- x (tan x)))
13.0ms
(- x (sin x))
8.0ms
(- x (tan x))

series328.0ms

Calls
3 calls:
Slowest
146.0ms
(/ (- x (sin x)) (- x (tan x)))
108.0ms
(- x (tan x))
69.0ms
(- x (sin x))

simplify3.5s

Calls
82 calls:
Slowest
501.0ms
(- (+ 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)))))
424.0ms
(/ (- (sqrt x) (sqrt (sin x))) (- (sqrt x) (sqrt (tan x))))
316.0ms
(- (+ 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)))))
261.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
225.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune851.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (/ (/ (sin x) (cos x)) x) (/ (sin x) x))
0.7b
(+ (* (/ (sin x) x) (/ (/ (sin x) (cos x)) x)) -1)
0.2b
(* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x))
0.1b
(/ (sin x) (cos x))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
306×times-frac
211×add-sqr-sqrt
162×*-un-lft-identity
154×add-cube-cbrt
43×swap-sqr associate-*r* associate-*l*
42×add-cbrt-cube add-exp-log
19×cbrt-undiv div-exp div-inv
11×pow1
9×prod-exp cbrt-unprod unswap-sqr
8×add-log-exp
6×difference-of-squares
4×insert-posit16 distribute-lft-out--
3×associate-/r* associate-/l*
1×pow2 frac-times +-commutative quot-tan clear-num sum-log sub-neg frac-2neg flip3-+ pow-plus flip3-- distribute-rgt-out-- diff-log pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up frac-sub flip-+ flip-- sub-div
Calls
4 calls:
Slowest
54.0ms
(* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x))
31.0ms
(- (/ (/ (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))

series448.0ms

Calls
4 calls:
Slowest
160.0ms
(+ (* (/ (sin x) x) (/ (/ (sin x) (cos x)) x)) -1)
149.0ms
(- (/ (/ (sin x) (cos x)) x) (/ (sin x) x))
108.0ms
(* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x))
31.0ms
(/ (sin x) (cos x))

simplify31.1s

Calls
279 calls:
Slowest
785.0ms
(* (/ (/ 1 (sqrt (cos x))) (* (cbrt x) (cbrt x))) (/ (/ 1 (sqrt (cos x))) (* (cbrt x) (cbrt x))))
707.0ms
(* (/ (/ 1 (* (cbrt (cos x)) (cbrt (cos x)))) (sqrt x)) (/ (/ 1 (* (cbrt (cos x)) (cbrt (cos x)))) (sqrt x)))
679.0ms
(* (/ (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))) (sqrt x)) (/ (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))) (sqrt x)))
609.0ms
(* (/ (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt (cos x))) (* (cbrt x) (cbrt x))) (/ (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt (cos x))) (* (cbrt x) (cbrt x))))
528.0ms
(* (/ (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* x x) x)) (/ (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (* (* x x) x)))

prune2.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

15.6b
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
0.1b
(* (* x x) (* x x))
0.1b
(* (* x x) 9/40)
0.1b
(* (* (* x x) (* x x)) 27/2800)

rewrite319.0ms

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+
Calls
4 calls:
Slowest
162.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
91.0ms
(* (* (* x x) (* x x)) 27/2800)
34.0ms
(* (* x x) (* x x))
29.0ms
(* (* x x) 9/40)

series238.0ms

Calls
4 calls:
Slowest
82.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
65.0ms
(* (* (* x x) (* x x)) 27/2800)
62.0ms
(* (* x x) (* x x))
28.0ms
(* (* x x) 9/40)

simplify6.8s

Calls
111 calls:
Slowest
556.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
550.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
463.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
410.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
396.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))

prune995.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

15.6b
(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
0.1b
(* (* x x) (* x x))
0.1b
(* (* x x) 9/40)
0.1b
(* (* (* x x) (* x x)) 27/2800)

rewrite174.0ms

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
8×add-sqr-sqrt
7×associate-*r*
6×*-un-lft-identity add-cube-cbrt add-log-exp
4×insert-posit16
3×associate-*l* *-commutative unswap-sqr
1×sub-neg flip3-- diff-log swap-sqr flip--
Calls
4 calls:
Slowest
83.0ms
(* (* (* x x) (* x x)) 27/2800)
32.0ms
(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
32.0ms
(* (* x x) (* x x))
23.0ms
(* (* x x) 9/40)

series324.0ms

Calls
4 calls:
Slowest
188.0ms
(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
52.0ms
(* (* x x) (* x x))
45.0ms
(* (* (* x x) (* x x)) 27/2800)
38.0ms
(* (* x x) 9/40)

simplify6.2s

Calls
110 calls:
Slowest
533.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
465.0ms
(* (* (* (* (* 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))
409.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
391.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.7b

bsearch153.0ms

end0.0ms

sample17.5s

Algorithm
intervals
Results
8.1s1706×body2560valid
4.9s2597×body1280valid
2.3s1982×body640valid
1.3s943×body320valid
666.0ms435×body160valid
86.0ms337×body80valid