Details

sample203.0ms

Algorithm

intervals

Results

121.0ms	146×	body	1280	valid
42.0ms	29×	body	2560	valid
24.0ms	54×	body	640	valid
6.0ms	18×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	3×	body	80	valid

simplify8.0ms

Calls

1 calls:

Slowest

8.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite45.0ms

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

23.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series90.0ms

Calls

2 calls:

Slowest

65.0ms	(- (cos (+ x eps)) (cos x))
25.0ms	(cos (+ x eps))

simplify2.2s

Calls

33 calls:

Slowest

241.0ms	(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
236.0ms	(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
197.0ms	(fma (* (cbrt (cos (+ x eps))) (cbrt (cos (+ x eps)))) (cbrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
192.0ms	(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
184.0ms	(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune424.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize33.0ms

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))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`add-log-exp`
8×	`add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `fma-def` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Calls

4 calls:

Slowest

55.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
43.0ms	(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
24.0ms	(sin (/ (+ x (+ eps x)) 2))
11.0ms	(+ x (+ eps x))

series273.0ms

Calls

4 calls:

Slowest

130.0ms	(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
83.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
34.0ms	(sin (/ (+ x (+ eps x)) 2))
25.0ms	(+ x (+ eps x))

simplify3.3s

Calls

38 calls:

Slowest

611.0ms	(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
554.0ms	(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
385.0ms	(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
340.0ms	(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
270.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune975.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.5b

localize37.0ms

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))

rewrite187.0ms

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

78.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
40.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
37.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
32.0ms	(sin (/ (+ x (+ eps x)) 2))

series600.0ms

Calls

4 calls:

Slowest

200.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
187.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
183.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
30.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify5.5s

Calls

18 calls:

Slowest

661.0ms	(* (cbrt -2) (pow (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))) 1/3))
588.0ms	(* (cbrt -2) (pow (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))) 1/3))
573.0ms	(* (cbrt -2) (pow (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))) 1/3))
559.0ms	(* (cbrt -2) (pow (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))) 1/3))
557.0ms	(* (cbrt -2) (pow (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))) 1/3))

prune921.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.5b

localize56.0ms

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))

rewrite166.0ms

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

69.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
64.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
20.0ms	(sin (/ (+ x (+ eps x)) 2))
12.0ms	(cbrt (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

series681.0ms

Calls

4 calls:

Slowest

237.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
206.0ms	(cbrt (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
206.0ms	(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
30.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify4.5s

Calls

18 calls:

Slowest

612.0ms	(* (cbrt -2) (pow (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))) 1/3))
552.0ms	(* (cbrt -2) (pow (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))) 1/3))
521.0ms	(* (cbrt -2) (pow (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))) 1/3))
499.0ms	(* (cbrt -2) (pow (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))) 1/3))
434.0ms	(- (+ (* (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)))))))))

prune1.3s

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 0.5b

regimes430.0ms

Accuracy

97.6% (0.4b remaining)

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

bsearch258.0ms

end0.0ms

sample8.0s

Algorithm

intervals

Results

4.9s	4384×	body	1280	valid
1.3s	653×	body	2560	valid
1.2s	1878×	body	640	valid
373.0ms	693×	body	320	valid
82.0ms	301×	body	160	valid
11.0ms	91×	body	80	valid