Details

sample540.0ms

Algorithm

intervals

Results

119.0ms	50×	body	2560	valid
78.0ms	85×	body	1280	valid
20.0ms	60×	body	640	valid
6.0ms	26×	body	320	valid
3.0ms	22×	body	160	valid
1.0ms	13×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5
done	19	5

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite53.0ms

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

Counts

3 → 110

Calls

3 calls:

25.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series175.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify55.0ms

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	472	1059
1	1737	854
2	5001	854
done	5001	854

prune239.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
17.1b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

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

series128.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(fma 27/2800 (pow x 4) 1/2)
45.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify145.0ms

Counts

26 → 26

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	51	133
1	162	117
2	626	117
3	3552	117
4	5001	117
done	5001	117

prune68.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin x) 3)
1.9b	(- (pow x 3) (pow (sin x) 3))
1.9b	(- x (tan x))
20.7b	(/ (- (pow x 3) (pow (sin x) 3)) (* (fma x x (fma (sin x) (sin x) (* x (sin x)))) (- x (tan x))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-sqr-sqrt`
153×	`prod-diff`
123×	`*-un-lft-identity`
114×	`unpow-prod-down` `cube-prod`
91×	`add-cube-cbrt`
50×	`sqr-pow`
49×	`difference-of-squares`
26×	`cube-mult` `unpow3`
25×	`times-frac` `associate-/l*`
16×	`distribute-lft-out--`
15×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-*r/` `div-exp` `associate-/r/` `associate-/l/`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `rem-cube-cbrt`

Counts

4 → 317

Calls

4 calls:

4.0ms	(pow (sin x) 3)
34.0ms	(- (pow x 3) (pow (sin x) 3))
6.0ms	(- x (tan x))
87.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (fma x x (fma (sin x) (sin x) (* x (sin x)))) (- x (tan x))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (sin x) 3)
102.0ms	(- (pow x 3) (pow (sin x) 3))
50.0ms	(- x (tan x))
296.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (fma x x (fma (sin x) (sin x) (* x (sin x)))) (- x (tan x))))

simplify143.0ms

Counts

329 → 329

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	863	4164
1	3682	3059
2	5001	3050
done	5001	3050

prune492.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (pow x 3) (pow (sin x) 3))
1.9b	(- (* x x) (* (tan x) (tan x)))
16.0b	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))
20.7b	(/ (- (pow x 3) (pow (sin x) 3)) (* (fma x x (fma (sin x) (sin x) (* x (sin x)))) (/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

163×	`add-sqr-sqrt`
145×	`prod-diff`
131×	`*-un-lft-identity`
111×	`unpow-prod-down` `cube-prod`
91×	`add-cube-cbrt`
54×	`difference-of-squares`
49×	`sqr-pow`
41×	`times-frac`
29×	`associate-/l*`
25×	`cube-mult` `unpow3`
15×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
13×	`fma-neg`
8×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `associate-/r*` `distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
3×	`difference-cubes` `associate-/r/`
2×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`
1×	`flip3-+` `associate-*r/` `flip-+`

Counts

4 → 325

Calls

4 calls:

31.0ms	(- (pow x 3) (pow (sin x) 3))
8.0ms	(- (* x x) (* (tan x) (tan x)))
27.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))
92.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (fma x x (fma (sin x) (sin x) (* x (sin x)))) (/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))))

series679.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (pow x 3) (pow (sin x) 3))
85.0ms	(- (* x x) (* (tan x) (tan x)))
146.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))
348.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (fma x x (fma (sin x) (sin x) (* x (sin x)))) (/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))))

simplify66.0ms

Counts

337 → 337

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1045	5092
1	5002	3952
done	5002	3952

prune617.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch69.0ms

Steps

Iters	Range		Point
9	9.85435867085541e-08	110.15968793260775	0.02674499741262323
8	-0.1517943218839364	-1.6640733670284383e-05	-0.027801200389932522

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	25	10
done	25	10

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.5s	1600×	body	2560	valid
1.9s	2816×	body	1280	valid
631.0ms	1873×	body	640	valid
195.0ms	892×	body	320	valid
72.0ms	465×	body	160	valid
40.0ms	354×	body	80	valid