Details

sample209.0ms

Algorithm

intervals

Results

113.0ms	146×	body	1280	valid
43.0ms	29×	body	2560	valid
33.0ms	54×	body	640	valid
8.0ms	18×	body	320	valid
2.0ms	6×	body	160	valid
0.0ms	3×	body	80	valid

simplify8.0ms

Calls

1 calls:

Slowest

8.0ms

(- (cos (+ x eps)) (cos x))

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize15.0ms

Local error

Found 2 expressions with local error:

3.4b	(cos (+ x eps))
0.9b	(- (cos (+ x eps)) (cos x))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Calls

2 calls:

Slowest

6.0ms	(- (cos (+ x eps)) (cos x))
2.0ms	(cos (+ x eps))

series77.0ms

Calls

2 calls:

Slowest

59.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify1.4s

Calls

33 calls:

Slowest

327.0ms	(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
218.0ms	(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
84.0ms	(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
79.0ms	(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
57.0ms	(/ (exp (cos (+ x eps))) (exp (cos x)))

prune511.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 4 expressions with local error:

3.2b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))
0.0b	(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod` `flip-+`

Calls

4 calls:

Slowest

18.0ms	(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
10.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
3.0ms	(sin (/ (+ x (+ eps x)) 2))
2.0ms	(+ x (+ eps x))

series336.0ms

Calls

4 calls:

Slowest

130.0ms	(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
115.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
50.0ms	(sin (/ (+ x (+ eps x)) 2))
40.0ms	(+ x (+ eps x))

simplify1.3s

Calls

22 calls:

Slowest

331.0ms	(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
196.0ms	(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
122.0ms	(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
118.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
68.0ms	(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune783.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

6.2b	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
6.2b	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
6.2b	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
3.2b	(sin (/ (+ x (+ eps x)) 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-*r/` `sin-mult`

Calls

4 calls:

Slowest

8.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
8.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
8.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
3.0ms	(sin (/ (+ x (+ eps x)) 2))

series611.0ms

Calls

4 calls:

Slowest

211.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
191.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
174.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
35.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify2.1s

Calls

18 calls:

Slowest

411.0ms	(- (+ (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4))))) (* 1/3 (* x (* (cbrt -2) (exp (* 1/3 (- (log 2) (log eps)))))))) (+ (* 1/9 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (- (log 16) (* 4 (log eps)))))))) (* 1/6 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4)))))))))
406.0ms	(- (+ (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4))))) (* 1/3 (* x (* (cbrt -2) (exp (* 1/3 (- (log 2) (log eps)))))))) (+ (* 1/9 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (- (log 16) (* 4 (log eps)))))))) (* 1/6 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4)))))))))
366.0ms	(- (+ (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4))))) (* 1/3 (* x (* (cbrt -2) (exp (* 1/3 (- (log 2) (log eps)))))))) (+ (* 1/9 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (- (log 16) (* 4 (log eps)))))))) (* 1/6 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4)))))))))
142.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
104.0ms	(cbrt (* -2 (- (cos (- (/ (+ x (+ eps x)) 2) (/ eps 2))) (cos (+ (/ (+ x (+ eps x)) 2) (/ eps 2))))))

prune952.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

6.2b	(cbrt (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
6.2b	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
6.2b	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
3.2b	(sin (/ (+ x (+ eps x)) 2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-mult`
2×	`associate-*r/`

Calls

4 calls:

Slowest

4.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
4.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
4.0ms	(cbrt (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
3.0ms	(sin (/ (+ x (+ eps x)) 2))

series701.0ms

Calls

4 calls:

Slowest

261.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
198.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
196.0ms	(cbrt (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
46.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify2.3s

Calls

18 calls:

Slowest

499.0ms	(- (+ (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4))))) (* 1/3 (* x (* (cbrt -2) (exp (* 1/3 (- (log 2) (log eps)))))))) (+ (* 1/9 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (- (log 16) (* 4 (log eps)))))))) (* 1/6 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4)))))))))
445.0ms	(- (+ (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4))))) (* 1/3 (* x (* (cbrt -2) (exp (* 1/3 (- (log 2) (log eps)))))))) (+ (* 1/9 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (- (log 16) (* 4 (log eps)))))))) (* 1/6 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4)))))))))
277.0ms	(- (+ (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4)))) (* 1/3 (* x (exp (* 1/3 (- (log 2) (log eps))))))) (* 13/162 (* (pow x 2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4)))))))
165.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
131.0ms	(cbrt (* -2 (- (cos (- (/ (+ x (+ eps x)) 2) (/ eps 2))) (cos (+ (/ (+ x (+ eps x)) 2) (/ eps 2))))))

prune970.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 0.5b

regimes444.0ms

Accuracy

97.6% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.2b

bsearch205.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

5.0s	4384×	body	1280	valid
1.5s	1878×	body	640	valid
1.2s	653×	body	2560	valid
255.0ms	693×	body	320	valid
73.0ms	301×	body	160	valid
12.0ms	91×	body	80	valid