Details

Time bar (total: 39.1s)

sample852.0ms

Algorithm
intervals
Results
360.0ms55×body2560valid
189.0ms98×body1280valid
76.0ms28×body320valid
70.0ms54×body640valid
5.0ms9×body160valid
4.0ms12×body80valid

simplify48.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
47.0ms
(/ (- x (sin x)) (- x (tan x)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize32.0ms

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)))

rewrite75.0ms

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
47.0ms
(/ (- x (sin x)) (- x (tan x)))
14.0ms
(- x (tan x))
10.0ms
(- x (sin x))

series269.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
120.0ms
(/ (- x (sin x)) (- x (tan x)))
88.0ms
(- x (tan x))
61.0ms
(- x (sin x))

simplify3.1s

Counts
82 → 92
Calls
82 calls:
Slowest
493.0ms
(- (+ 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)))))
383.0ms
(- (+ 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)))))
330.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
229.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
223.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune806.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

17.1b
(- (* (* 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)

rewrite327.0ms

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
141.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
129.0ms
(* (* (* x x) (* x x)) 27/2800)
39.0ms
(* (* x x) (* x x))
13.0ms
(* (* x x) 9/40)

series220.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
72.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
69.0ms
(* (* (* x x) (* x x)) 27/2800)
43.0ms
(* (* x x) (* x x))
35.0ms
(* (* x x) 9/40)

simplify6.9s

Counts
111 → 140
Calls
111 calls:
Slowest
578.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
525.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
468.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
386.0ms
(* (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* (* x x) (* x x))) (* (* 27/2800 27/2800) 27/2800))
363.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))

prune882.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt *-un-lft-identity
50×times-frac
32×log-pow
31×exp-prod
28×add-cube-cbrt
24×distribute-lft-out-- difference-of-squares
8×add-log-exp
6×add-cbrt-cube add-exp-log
5×pow1 associate-/r* flip3-- flip-- associate-/l*
4×associate-/r/ insert-posit16
3×log-prod
2×sub-neg diff-log div-sub div-inv associate-/l/
1×cbrt-undiv log-div clear-num frac-2neg exp-diff div-exp rem-log-exp
Counts
4 → 128
Calls
4 calls:
Slowest
26.0ms
(log (exp (/ (- x (sin x)) (- x (tan x)))))
22.0ms
(/ (- x (sin x)) (- x (tan x)))
5.0ms
(- x (sin x))
4.0ms
(- x (tan x))

series377.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
130.0ms
(/ (- x (sin x)) (- x (tan x)))
126.0ms
(log (exp (/ (- x (sin x)) (- x (tan x)))))
86.0ms
(- x (tan x))
35.0ms
(- x (sin x))

simplify5.2s

Counts
121 → 140
Calls
121 calls:
Slowest
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)))))
445.0ms
(- (+ 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)))))
406.0ms
(- (+ 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)))))
382.0ms
(- (+ 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)))))
361.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-log-exp
4×pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt insert-posit16 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 60
Calls
4 calls:
Slowest
12.0ms
(- x (tan x))
10.0ms
(- x (sin x))
5.0ms
(- x (sin x))
4.0ms
(- x (tan x))

series266.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
80.0ms
(- x (tan x))
73.0ms
(- x (tan x))
58.0ms
(- x (sin x))
55.0ms
(- x (sin x))

simplify1.2s

Counts
28 → 72
Calls
28 calls:
Slowest
269.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
259.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
225.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
182.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
22.0ms
(/ (exp x) (exp (sin x)))

prune1.0s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes97.0ms

Accuracy

100% (0.0b remaining)

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

bsearch175.0ms

end0.0ms

sample15.8s

Algorithm
intervals
Results
6.2s1624×body2560valid
4.8s2726×body1280valid
3.3s1919×body640valid
975.0ms930×body320valid
245.0ms457×body160valid
81.0ms344×body80valid