Details

Time bar (total: 47.9s)

sample538.0ms

Algorithm
intervals
Results
227.0ms94×body1280valid
181.0ms50×body2560valid
54.0ms56×body640valid
18.0ms28×body320valid
9.0ms21×body160valid
1.0ms7×body80valid

simplify30.0ms

Calls
1 calls:
Slowest
30.0ms
(/ (- x (sin x)) (- x (tan x)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize37.0ms

Local error

Found 3 expressions with local error:

2.5b
(- x (sin x))
2.5b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt *-un-lft-identity
29×add-cube-cbrt
25×times-frac
18×prod-diff
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
6×fma-neg
5×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×flip3-- flip--
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
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
25.0ms
(/ (- x (sin x)) (- x (tan x)))
19.0ms
(- x (sin x))
11.0ms
(- x (tan x))

series298.0ms

Calls
3 calls:
Slowest
124.0ms
(/ (- x (sin x)) (- x (tan x)))
98.0ms
(- x (tan x))
76.0ms
(- x (sin x))

simplify6.0s

Calls
122 calls:
Slowest
547.0ms
(- (+ 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)))))
472.0ms
(- (+ 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)))))
368.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
359.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
191.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
114×pow1
89×add-sqr-sqrt
45×swap-sqr
41×unswap-sqr
36×pow-prod-up
29×associate-*l*
27×*-un-lft-identity associate-*r*
23×pow-prod-down add-cube-cbrt
22×pow-sqr
18×pow-plus
17×*-commutative
15×add-cbrt-cube add-exp-log
13×pow2
8×prod-exp cbrt-unprod
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
Calls
3 calls:
Slowest
72.0ms
(* (* x x) (* x x))
1.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)

series257.0ms

Calls
3 calls:
Slowest
113.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)
84.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
60.0ms
(* (* x x) (* x x))

simplify4.1s

Calls
187 calls:
Slowest
717.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
315.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
310.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
280.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
209.0ms
(* (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))))

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

15.6b
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.1b
(* (* x x) (* x x))
0.1b
(fma -27/2800 (* (* x x) (* x x)) -1/2)
0.0b
(log (exp (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
116×pow1
92×add-sqr-sqrt
45×swap-sqr
41×unswap-sqr
36×pow-prod-up
30×*-un-lft-identity
29×associate-*l*
27×associate-*r*
26×add-cube-cbrt
23×pow-prod-down
22×pow-sqr
18×pow-plus
17×add-exp-log *-commutative
16×add-cbrt-cube
13×pow2
8×prod-exp cbrt-unprod
4×expm1-log1p-u log-prod log-pow insert-posit16 log1p-expm1-u add-log-exp
3×exp-prod fma-udef
2×rem-log-exp
1×exp-sum
Calls
4 calls:
Slowest
43.0ms
(* (* x x) (* x x))
2.0ms
(log (exp (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))
0.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)

series284.0ms

Calls
4 calls:
Slowest
143.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)
51.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
48.0ms
(log (exp (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))
41.0ms
(* (* x x) (* x x))

simplify5.9s

Calls
199 calls:
Slowest
415.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
367.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
324.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
280.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
249.0ms
(sqrt (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)))

prune1.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

2.5b
(- x (sin x))
2.5b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))
0.0b
(log1p (/ (- x (sin x)) (- x (tan x))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt *-un-lft-identity
30×add-cube-cbrt
25×times-frac
18×prod-diff
14×distribute-lft-out-- difference-of-squares
8×add-log-exp
6×add-cbrt-cube fma-neg add-exp-log
5×expm1-log1p-u associate-/r* associate-/l*
4×pow1 flip3-- insert-posit16 log1p-expm1-u flip--
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv log1p-udef clear-num frac-2neg div-sub div-exp log1p-expm1 div-inv
Calls
4 calls:
Slowest
45.0ms
(/ (- x (sin x)) (- x (tan x)))
6.0ms
(- x (sin x))
5.0ms
(- x (tan x))
1.0ms
(log1p (/ (- x (sin x)) (- x (tan x))))

series383.0ms

Calls
4 calls:
Slowest
151.0ms
(log1p (/ (- x (sin x)) (- x (tan x))))
107.0ms
(/ (- x (sin x)) (- x (tan x)))
76.0ms
(- x (tan x))
48.0ms
(- x (sin x))

simplify6.9s

Calls
126 calls:
Slowest
464.0ms
(- (+ 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)))))
436.0ms
(- (+ 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
(- (+ (log 2) (+ (* 3/8 (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2)))) (* 1/2 (/ (sin x) (* (cos x) x))))) (+ (* 1/8 (/ (pow (sin x) 2) (pow x 2))) (+ (* 1/2 (/ (sin x) x)) (* 1/4 (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))))
395.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
392.0ms
(- (+ (log 2) (+ (* 3/8 (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2)))) (* 1/2 (/ (sin x) (* (cos x) x))))) (+ (* 1/8 (/ (pow (sin x) 2) (pow x 2))) (+ (* 1/2 (/ (sin x) x)) (* 1/4 (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))))

prune1.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes90.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.3b

bsearch146.0ms

end0.0ms

sample16.8s

Algorithm
intervals
Results
7.0s1534×body2560valid
5.8s2789×body1280valid
2.3s1884×body640valid
775.0ms933×body320valid
461.0ms360×body80valid
237.0ms500×body160valid