Details

Time bar (total: 44.8s)

sample1.4s

Algorithm
intervals
Results
956.0ms104×body1280valid
205.0ms43×body2560valid
111.0ms61×body640valid
18.0ms21×body320valid
11.0ms17×body160valid
3.0ms10×body80valid

simplify42.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
41.0ms
(/ (- x (sin x)) (- x (tan x)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize50.0ms

Local error

Found 3 expressions with local error:

1.2b
(- x (sin x))
1.1b
(- 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
Counts
3 → 83
Calls
3 calls:
Slowest
33.0ms
(/ (- x (sin x)) (- x (tan x)))
13.0ms
(- x (sin x))
8.0ms
(- x (tan x))

series328.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
141.0ms
(/ (- x (sin x)) (- x (tan x)))
100.0ms
(- x (tan x))
86.0ms
(- x (sin x))

simplify3.1s

Counts
82 → 92
Calls
82 calls:
Slowest
440.0ms
(- (+ 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)))))
351.0ms
(- (+ 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)))))
324.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
218.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
205.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune873.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

15.3b
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
0.2b
(* (* x x) 9/40)
0.2b
(* (* x x) (* x x))
0.1b
(* (* (* x x) (* x x)) 27/2800)

rewrite264.0ms

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
138.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
87.0ms
(* (* (* x x) (* x x)) 27/2800)
22.0ms
(* (* x x) (* x x))
14.0ms
(* (* x x) 9/40)

series177.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
56.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
42.0ms
(* (* (* x x) (* x x)) 27/2800)
40.0ms
(* (* x x) 9/40)
39.0ms
(* (* x x) (* x x))

simplify6.6s

Counts
111 → 140
Calls
111 calls:
Slowest
538.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
477.0ms
(* (* (* (* (* 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)))
400.0ms
(* (* (* (* (* 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))

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

15.3b
(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
0.2b
(* (* x x) 9/40)
0.2b
(* (* x x) (* x x))
0.1b
(* (* (* x x) (* x x)) 27/2800)

rewrite120.0ms

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--
Counts
4 → 126
Calls
4 calls:
Slowest
64.0ms
(* (* (* x x) (* x x)) 27/2800)
24.0ms
(* (* x x) (* x x))
15.0ms
(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
14.0ms
(* (* x x) 9/40)

series331.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
57.0ms
(* (* x x) (* x x))
54.0ms
(* (* (* x x) (* x x)) 27/2800)
52.0ms
(* (* x x) 9/40)

simplify6.0s

Counts
110 → 138
Calls
110 calls:
Slowest
468.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
452.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
440.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
393.0ms
(* (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* (* x x) (* x x))) (* (* 27/2800 27/2800) 27/2800))
368.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

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
57.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
19.0ms
(/ (sin x) (- x (tan x)))
4.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series482.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
268.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
81.0ms
(- x (tan x))
76.0ms
(/ (sin x) (- x (tan x)))
57.0ms
(- x (tan x))

simplify4.1s

Counts
95 → 110
Calls
95 calls:
Slowest
439.0ms
(- (+ 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)))))
397.0ms
(- (+ 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)))))
273.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
238.0ms
(- (* x (- x (tan x))) (* (- x (tan x)) (sin x)))
230.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune945.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch151.0ms

end0.0ms

sample17.5s

Algorithm
intervals
Results
8.5s1640×body2560valid
5.1s2729×body1280valid
2.2s1904×body640valid
1.0s852×body320valid
307.0ms489×body160valid
145.0ms386×body80valid