Details

sample668.0ms

Algorithm

intervals

Results

259.0ms	50×	body	2560	valid
172.0ms	92×	body	1280	valid
74.0ms	64×	body	640	valid
19.0ms	19×	body	320	valid
11.0ms	21×	body	160	valid
3.0ms	10×	body	80	valid

simplify53.0ms

Counts: 1 → 1

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize29.0ms

Local error

Found 3 expressions with local error:

1.4b	(- x (sin x))
1.4b	(- x (tan x))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite60.0ms

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`

Counts

3 → 113

Calls

3 calls:

Slowest

32.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series286.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

132.0ms	(/ (- x (sin x)) (- x (tan x)))
78.0ms	(- x (sin x))
75.0ms	(- x (tan x))

simplify2.1s

Counts: 122 → 122

prune1.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
0.2b	(/ (/ (sin x) x) (cos x))
0.2b	(/ (/ (sin x) x) (cos x))
0.2b	(/ (/ (sin x) x) (cos x))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

1547×	`times-frac`
942×	`add-sqr-sqrt`
927×	`*-un-lft-identity`
921×	`add-cube-cbrt`
559×	`prod-diff`
114×	`div-inv`
43×	`fma-neg`
39×	`associate-/l*`
19×	`add-cbrt-cube` `add-exp-log`
9×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg` `associate-/l/`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 845

Calls

4 calls:

Slowest

74.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
22.0ms	(/ (/ (sin x) x) (cos x))
21.0ms	(/ (/ (sin x) x) (cos x))
21.0ms	(/ (/ (sin x) x) (cos x))

series326.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

153.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
68.0ms	(/ (/ (sin x) x) (cos x))
52.0ms	(/ (/ (sin x) x) (cos x))
52.0ms	(/ (/ (sin x) x) (cos x))

simplify1.4s

Counts: 857 → 857

prune14.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

16.8b	(- (* (* x 9/40) x) (fma 27/2800 (pow x 4) 1/2))
0.2b	(* x 9/40)
0.1b	(* (* x 9/40) x)
0.1b	(fma 27/2800 (pow x 4) 1/2)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`prod-diff`
2×	`*-commutative` `fma-udef`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--` `associate--r+` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

Slowest

33.0ms	(- (* (* x 9/40) x) (fma 27/2800 (pow x 4) 1/2))
25.0ms	(* (* x 9/40) x)
10.0ms	(* x 9/40)
0.0ms	(fma 27/2800 (pow x 4) 1/2)

series298.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

148.0ms	(fma 27/2800 (pow x 4) 1/2)
74.0ms	(- (* (* x 9/40) x) (fma 27/2800 (pow x 4) 1/2))
48.0ms	(* (* x 9/40) x)
28.0ms	(* x 9/40)

simplify948.0ms

Counts: 85 → 85

prune878.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

16.8b	(- (* (* x 9/40) x) (* 27/2800 (pow x 4)))
0.2b	(* x 9/40)
0.1b	(* (* x 9/40) x)
0.1b	(* 27/2800 (pow x 4))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
11×	`pow1`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l` `prod-exp`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `unpow-prod-down` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `pow-exp` `flip--`

Counts

4 → 87

Calls

4 calls:

Slowest

18.0ms	(* (* x 9/40) x)
16.0ms	(- (* (* x 9/40) x) (* 27/2800 (pow x 4)))
11.0ms	(* x 9/40)
8.0ms	(* 27/2800 (pow x 4))

series279.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

172.0ms	(- (* (* x 9/40) x) (* 27/2800 (pow x 4)))
52.0ms	(* 27/2800 (pow x 4))
34.0ms	(* (* x 9/40) x)
20.0ms	(* x 9/40)

simplify1.0s

Counts: 99 → 99

prune777.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes64.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 32.2b

bsearch157.0ms

end0.0ms

sample14.9s

Algorithm

intervals

Results

6.4s	1645×	body	2560	valid
5.1s	2712×	body	1280	valid
2.1s	1884×	body	640	valid
802.0ms	910×	body	320	valid
272.0ms	475×	body	160	valid
84.0ms	374×	body	80	valid