Details

Time bar (total: 30.4s)

sample760.0ms

Algorithm
intervals
Results
351.0ms45×body2560valid
210.0ms99×body1280valid
85.0ms61×body640valid
30.0ms28×body320valid
7.0ms11×body160valid
4.0ms12×body80valid

simplify43.0ms

Calls
1 calls:
Slowest
43.0ms
(/ (- x (sin x)) (- x (tan x)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize31.0ms

Local error

Found 3 expressions with local error:

2.0b
(- x (tan x))
1.5b
(- x (sin x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log
4×flip3-- flip--
3×pow1 associate-/r* insert-posit16 associate-/l* add-log-exp
2×sub-neg associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Calls
3 calls:
Slowest
7.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (tan x))
1.0ms
(- x (sin x))

series270.0ms

Calls
3 calls:
Slowest
124.0ms
(/ (- x (sin x)) (- x (tan x)))
100.0ms
(- x (tan x))
46.0ms
(- x (sin x))

simplify2.7s

Calls
39 calls:
Slowest
437.0ms
(- (+ 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)))))
430.0ms
(- (+ 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)))))
372.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
277.0ms
(- (+ (* 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)))

prune801.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 3 expressions with local error:

16.3b
(- (* (* x x) 9/40) (- (* (pow x 4) 27/2800) -1/2))
0.3b
(* (pow x 4) 27/2800)
0.1b
(* (* x x) 9/40)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
4×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
3×pow1 add-cbrt-cube add-exp-log insert-posit16
2×sub-neg *-commutative associate--r+
1×flip3-- diff-log flip-- associate--r-
Calls
3 calls:
Slowest
13.0ms
(- (* (* x x) 9/40) (- (* (pow x 4) 27/2800) -1/2))
5.0ms
(* (* x x) 9/40)
5.0ms
(* (pow x 4) 27/2800)

series83.0ms

Calls
3 calls:
Slowest
39.0ms
(- (* (* x x) 9/40) (- (* (pow x 4) 27/2800) -1/2))
25.0ms
(* (pow x 4) 27/2800)
19.0ms
(* (* x x) 9/40)

simplify709.0ms

Calls
14 calls:
Slowest
216.0ms
(/ (exp (* (* x x) 9/40)) (exp (- (* (pow x 4) 27/2800) -1/2)))
141.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
133.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
120.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
15.0ms
(* 9/40 (pow x 2))

prune513.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

16.3b
(- (* (* x x) 9/40) (* (pow x 4) 27/2800))
0.3b
(* (pow x 4) 27/2800)
0.1b
(* (* x x) 9/40)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
4×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
3×pow1 add-cbrt-cube add-exp-log insert-posit16
2×*-commutative
1×sub-neg flip3-- diff-log flip--
Calls
3 calls:
Slowest
11.0ms
(- (* (* x x) 9/40) (* (pow x 4) 27/2800))
5.0ms
(* (* x x) 9/40)
5.0ms
(* (pow x 4) 27/2800)

series125.0ms

Calls
3 calls:
Slowest
77.0ms
(- (* (* x x) 9/40) (* (pow x 4) 27/2800))
26.0ms
(* (pow x 4) 27/2800)
22.0ms
(* (* x x) 9/40)

simplify383.0ms

Calls
12 calls:
Slowest
125.0ms
(/ (exp (* (* x x) 9/40)) (exp (* (pow x 4) 27/2800)))
54.0ms
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))
53.0ms
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))
51.0ms
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))
16.0ms
(* 9/40 (pow x 2))

prune524.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

2.0b
(- x (tan x))
2.0b
(- x (tan x))
2.0b
(- x (tan x))
1.5b
(- x (sin x))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt pow1 sub-neg *-un-lft-identity flip3-- add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 flip-- add-log-exp
Calls
4 calls:
Slowest
1.0ms
(- x (tan x))
1.0ms
(- x (sin x))
1.0ms
(- x (tan x))
1.0ms
(- x (tan x))

series281.0ms

Calls
4 calls:
Slowest
81.0ms
(- x (tan x))
80.0ms
(- x (tan x))
73.0ms
(- x (tan x))
47.0ms
(- x (sin x))

simplify1.2s

Calls
12 calls:
Slowest
285.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
277.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
274.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
169.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
23.0ms
(- x (/ (sin x) (cos x)))

prune802.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes128.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch215.0ms

end0.0ms

sample20.8s

Algorithm
intervals
Results
9.8s1640×body2560valid
6.9s2732×body1280valid
2.6s1876×body640valid
802.0ms942×body320valid
309.0ms456×body160valid
109.0ms354×body80valid