Details

sample468.0ms

Algorithm

intervals

Results

244.0ms	56×	body	2560	valid
96.0ms	78×	body	1280	valid
33.0ms	59×	body	640	valid
17.0ms	38×	body	320	valid
4.0ms	15×	body	160	valid
2.0ms	10×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
3	19
2	17
1	13
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.8b	(- x (tan x))
1.8b	(- x (sin x))

rewrite119.0ms

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` `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 → 110

Calls

3 calls:

84.0ms	(/ (- x (sin x)) (- x (tan x)))
10.0ms	(- x (tan x))
17.0ms	(- x (sin x))

series294.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(/ (- x (sin x)) (- x (tan x)))
88.0ms	(- x (tan x))
71.0ms	(- x (sin x))

simplify1.3s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	2273
1	502
0	209

prune491.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 9/40 (* x x) -1/2)
0.3b	(* (pow x 4) 27/2800)
13.1b	(- (fma 9/40 (* x x) -1/2) (* (pow x 4) 27/2800))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma 9/40 (* x x) -1/2)
17.0ms	(* (pow x 4) 27/2800)
10.0ms	(- (fma 9/40 (* x x) -1/2) (* (pow x 4) 27/2800))

series204.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(fma 9/40 (* x x) -1/2)
76.0ms	(* (pow x 4) 27/2800)
64.0ms	(- (fma 9/40 (* x x) -1/2) (* (pow x 4) 27/2800))

simplify835.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
2	900
1	215
0	98

prune316.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (/ (- x (sin x)) (- x (tan x))))
0.0b	(/ (- x (sin x)) (- x (tan x)))
1.8b	(- x (tan x))
1.8b	(- x (sin x))

rewrite59.0ms

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

Counts

4 → 121

Calls

4 calls:

0.0ms	(log1p (/ (- x (sin x)) (- x (tan x))))
35.0ms	(/ (- x (sin x)) (- x (tan x)))
14.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series403.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(log1p (/ (- x (sin x)) (- x (tan x))))
111.0ms	(/ (- x (sin x)) (- x (tan x)))
76.0ms	(- x (tan x))
45.0ms	(- x (sin x))

simplify1.6s

Counts

133 → 133

Iterations

Iter	Nodes
done	5001
2	2587
1	578
0	241

prune687.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.4b	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x)))
15.1b	(/ (sin x) (* x x))
15.1b	(/ (sin x) (* x x))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
202×	`add-sqr-sqrt`
195×	`*-un-lft-identity`
193×	`add-cube-cbrt`
129×	`prod-diff`
43×	`fma-neg`
18×	`div-inv`
15×	`add-exp-log`
14×	`add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`pow-unpow` `unpow-prod-down` `difference-of-squares`
2×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `fma-udef` `flip--` `associate--r+` `distribute-lft-out--` `unpow2` `sqr-pow`

Counts

4 → 257

Calls

4 calls:

3.0ms	(pow (cos x) 2)
70.0ms	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x)))
19.0ms	(/ (sin x) (* x x))
17.0ms	(/ (sin x) (* x x))

series393.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (cos x) 2)
251.0ms	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x)))
53.0ms	(/ (sin x) (* x x))
60.0ms	(/ (sin x) (* x x))

simplify2.2s

Counts

269 → 269

Iterations

Iter	Nodes
done	5000
2	4225
1	927
0	375

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes84.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.3b

bsearch120.0ms

Steps

Iters	Range		Point
10	5.09324609688744e-06	47495130.80298876	2.491803263157965
10	-1138.2876542095912	-1.6260248627107784e-07	-0.02976690073964273

simplify4.0ms

Iterations

Iter	Nodes
done	40
1	40
0	36

end0.0ms

sample13.8s

Algorithm

intervals

Results

5.7s	1586×	body	2560	valid
4.5s	2745×	body	1280	valid
2.4s	1906×	body	640	valid
446.0ms	956×	body	320	valid
213.0ms	328×	body	80	valid
145.0ms	479×	body	160	valid