Details

sample628.0ms

Algorithm

intervals

Results

286.0ms	48×	body	2560	valid
177.0ms	80×	body	1280	valid
82.0ms	76×	body	640	valid
19.0ms	26×	body	320	valid
7.0ms	14×	body	160	valid
3.0ms	12×	body	80	valid

simplify27.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

26.0ms

(/ (- x (sin x)) (- x (tan x)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize17.0ms

Local error

Found 3 expressions with local error:

1.3b	(- x (sin x))
1.3b	(- x (tan x))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite48.0ms

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

31.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series234.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

109.0ms	(/ (- x (sin x)) (- x (tan x)))
81.0ms	(- x (tan x))
44.0ms	(- x (sin x))

simplify6.3s

Counts

122 → 122

Calls

122 calls:

Slowest

520.0ms	(- (+ 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)))))
455.0ms	(- (+ 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)))))
410.0ms	(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
316.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
299.0ms	(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune961.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

1.3b	(- x (sin x))
1.3b	(- x (tan x))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite50.0ms

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 (tan x))
7.0ms	(- x (sin x))

series224.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

105.0ms	(/ (- x (sin x)) (- x (tan x)))
72.0ms	(- x (tan x))
46.0ms	(- x (sin x))

simplify7.2s

Counts

122 → 122

Calls

122 calls:

Slowest

922.0ms	(- (+ 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)))))
503.0ms	(- (+ 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)))))
364.0ms	(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
345.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
316.0ms	(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))

prune976.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

1.3b	(- x (sin x))
1.3b	(- x (tan x))
0.0b	(/ (- x (sin x)) (- x (tan x)))
0.0b	(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))

rewrite63.0ms

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×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `pow1` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `expm1-log1p` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv` `expm1-udef`

Counts

4 → 125

Calls

4 calls:

Slowest

42.0ms	(/ (- x (sin x)) (- x (tan x)))
10.0ms	(- x (tan x))
7.0ms	(- x (sin x))
0.0ms	(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

184.0ms	(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))
105.0ms	(/ (- x (sin x)) (- x (tan x)))
97.0ms	(- x (tan x))
62.0ms	(- x (sin x))

simplify7.7s

Counts

126 → 137

Calls

126 calls:

Slowest

487.0ms	(- (+ 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)))))
486.0ms	(- (+ 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)))))
463.0ms	(- (+ 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)))))
445.0ms	(- (+ 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)))))
369.0ms	(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 2 expressions with local error:

0.3b	(fma (* x x) -27/2800 9/40)
0.0b	(fma (* x x) (fma (* x x) -27/2800 9/40) -1/2)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

2 → 22

Calls

2 calls:

Slowest

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

series122.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

62.0ms	(fma (* x x) -27/2800 9/40)
60.0ms	(fma (* x x) (fma (* x x) -27/2800 9/40) -1/2)

simplify1.0s

Counts

6 → 28

Calls

6 calls:

Slowest

309.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
274.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
261.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
74.0ms	(- 9/40 (* 27/2800 (pow x 2)))
44.0ms	(- 9/40 (* 27/2800 (pow x 2)))

prune237.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes97.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.2b

bsearch117.0ms

end0.0ms

sample17.2s

Algorithm

intervals

Results

8.4s	1614×	body	2560	valid
4.9s	2710×	body	1280	valid
2.6s	1895×	body	640	valid
741.0ms	938×	body	320	valid
228.0ms	475×	body	160	valid
96.0ms	368×	body	80	valid