Details

sample580.0ms

Algorithm

intervals

Results

212.0ms	55×	body	2560	valid
168.0ms	84×	body	1280	valid
60.0ms	60×	body	640	valid
16.0ms	22×	body	320	valid
9.0ms	20×	body	160	valid
4.0ms	15×	body	80	valid

simplify26.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize24.0ms

Local error

Found 3 expressions with local error:

1.6b	(- x (sin x))
1.6b	(- x (tan x))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite84.0ms

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

54.0ms	(/ (- x (sin x)) (- x (tan x)))
15.0ms	(- x (sin x))
10.0ms	(- x (tan x))

series238.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

95.0ms	(/ (- x (sin x)) (- x (tan x)))
78.0ms	(- x (tan x))
65.0ms	(- x (sin x))

simplify1.6s

Counts: 122 → 122

prune984.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

1.6b	(- x (tan x))
1.6b	(- x (tan x))
1.3b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.1b	(/ (sin x) (- x (tan x)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 592

Calls

4 calls:

Slowest

79.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
12.0ms	(/ (sin x) (- x (tan x)))
6.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series497.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

258.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
106.0ms	(/ (sin x) (- x (tan x)))
78.0ms	(- x (tan x))
55.0ms	(- x (tan x))

simplify1.6s

Counts: 604 → 604

prune7.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize101.0ms

Local error

Found 4 expressions with local error:

16.0b	(/ (* (sin x) (sin x)) (* (* x x) (* (cos x) (cos x))))
15.9b	(/ (/ (* (sin x) (sin x)) (cos x)) (* x x))
0.3b	(* (cos x) (cos x))
0.3b	(* (sin x) (sin x))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-cbrt-cube` `add-exp-log`
28×	`prod-exp` `cbrt-unprod`
20×	`add-sqr-sqrt` `cbrt-undiv` `div-exp`
18×	`pow1`
16×	`*-un-lft-identity` `add-cube-cbrt`
14×	`times-frac`
8×	`associate-/l*`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`div-sub` `sqr-sin`
2×	`pow2` `clear-num` `associate-/r` `frac-2neg` `pow-plus` `pow-prod-down` `pow-sqr` `cos-mult` `-commutative` `pow-prod-up` `sin-mult` `unswap-sqr` `associate-/l/`
1×	`sqr-cos` `associate-*r/` `associate-/r/`

Counts

4 → 141

Calls

4 calls:

Slowest

41.0ms	(/ (* (sin x) (sin x)) (* (* x x) (* (cos x) (cos x))))
21.0ms	(* (cos x) (cos x))
19.0ms	(/ (/ (* (sin x) (sin x)) (cos x)) (* x x))
15.0ms	(* (sin x) (sin x))

series244.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(/ (/ (* (sin x) (sin x)) (cos x)) (* x x))
94.0ms	(/ (* (sin x) (sin x)) (* (* x x) (* (cos x) (cos x))))
31.0ms	(* (cos x) (cos x))
19.0ms	(* (sin x) (sin x))

simplify1.2s

Counts: 153 → 153

prune1.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

16.6b	(- (* (* x x) 9/40) (fma 27/2800 (* (* x x) (* x x)) 1/2))
0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) 9/40)
0.1b	(fma 27/2800 (* (* x x) (* x x)) 1/2)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

120×	`pow1`
36×	`pow-prod-up`
26×	`pow-prod-down`
22×	`pow-sqr`
21×	`add-cbrt-cube` `add-exp-log`
18×	`pow-plus`
13×	`pow2`
11×	`prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u`
3×	`prod-diff`
2×	`associate-l` `*-commutative` `fma-udef` `unswap-sqr`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `swap-sqr` `flip--` `associate--r+`

Counts

4 → 119

Calls

4 calls:

Slowest

28.0ms	(* (* x x) (* x x))
25.0ms	(- (* (* x x) 9/40) (fma 27/2800 (* (* x x) (* x x)) 1/2))
21.0ms	(* (* x x) 9/40)
0.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)

series303.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

126.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)
78.0ms	(- (* (* x x) 9/40) (fma 27/2800 (* (* x x) (* x x)) 1/2))
61.0ms	(* (* x x) (* x x))
38.0ms	(* (* x x) 9/40)

simplify1.2s

Counts: 131 → 131

prune967.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes57.0ms

Accuracy

100% (0.0b remaining)

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

bsearch117.0ms

end0.0ms

sample16.0s

Algorithm

intervals

Results

7.2s	1637×	body	2560	valid
5.0s	2744×	body	1280	valid
2.7s	1865×	body	640	valid
632.0ms	938×	body	320	valid
263.0ms	465×	body	160	valid
110.0ms	351×	body	80	valid