Details

sample500.0ms

Algorithm

intervals

Results

179.0ms	54×	body	2560	valid
134.0ms	83×	body	1280	valid
48.0ms	58×	body	640	valid
16.0ms	33×	body	320	valid
5.0ms	14×	body	160	valid
3.0ms	14×	body	80	valid

simplify66.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.2b	(- x (tan x))
1.2b	(- x (sin x))

rewrite61.0ms

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:

33.0ms	(/ (- x (sin x)) (- x (tan x)))
9.0ms	(- x (tan x))
15.0ms	(- x (sin x))

series313.0ms

Counts

3 → 9

Calls

3 calls:

142.0ms	(/ (- x (sin x)) (- x (tan x)))
93.0ms	(- x (tan x))
77.0ms	(- x (sin x))

simplify1.3s

Counts

122 → 122

Iterations

Iter	Nodes
done	2007
3	2007
2	1279
1	504
0	212

prune548.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) (* x x))
0.3b	(fma 27/2800 (* (* x x) (* x x)) 1/2)
14.8b	(fma 9/40 (* x x) (- (fma 27/2800 (* (* x x) (* x x)) 1/2)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

114×	`pow1`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
15×	`add-cbrt-cube` `add-exp-log`
13×	`pow2`
8×	`prod-exp` `cbrt-unprod`
3×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

3 → 88

Calls

3 calls:

53.0ms	(* (* x x) (* x x))
0.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)
1.0ms	(fma 9/40 (* x x) (- (fma 27/2800 (* (* x x) (* x x)) 1/2)))

series300.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* (* x x) (* x x))
163.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)
79.0ms	(fma 9/40 (* x x) (- (fma 27/2800 (* (* x x) (* x x)) 1/2)))

simplify1.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	2153
3	2153
2	665
1	202
0	79

prune254.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.8b	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
1.2b	(- x (sin x))
29.4b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-prod` `associate-/r*` `fma-neg`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `pow1/3` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 95

Calls

4 calls:

1.0ms	(cbrt x)
19.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
6.0ms	(- x (sin x))
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.7s

Counts

4 → 12

Calls

4 calls:

334.0ms	(cbrt x)
832.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
47.0ms	(- x (sin x))
488.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify1.3s

Counts

107 → 107

Iterations

Iter	Nodes
done	2002
3	2002
2	939
1	366
0	172

prune488.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
0.2b	(/ (sin x) (cos x))
1.2b	(- x (/ (sin x) (cos x)))
1.2b	(- x (sin x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
73×	`times-frac`
67×	`add-cube-cbrt`
48×	`prod-diff`
22×	`difference-of-squares`
15×	`distribute-lft-out--`
9×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp`
6×	`fma-neg`
5×	`div-inv`
4×	`expm1-log1p-u` `pow1` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `associate-/r/` `associate-/l/`
1×	`quot-tan` `div-sub`

Counts

4 → 181

Calls

4 calls:

52.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
8.0ms	(/ (sin x) (cos x))
10.0ms	(- x (/ (sin x) (cos x)))
6.0ms	(- x (sin x))

series309.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
35.0ms	(/ (sin x) (cos x))
100.0ms	(- x (/ (sin x) (cos x)))
42.0ms	(- x (sin x))

simplify1.4s

Counts

193 → 193

Iterations

Iter	Nodes
done	2001
2	2001
1	815
0	329

prune996.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes139.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch212.0ms

Steps

Iters	Range		Point
10	0.001953933407705698	32640636.358721357	0.02961693412874807
9	-5.107543836967609	-2.6017364714010764e-05	-0.02778090518414558

simplify8.0ms

Iterations

Iter	Nodes
done	24
1	24
0	21

end0.0ms

sample17.3s

Algorithm

intervals

Results

7.9s	1622×	body	2560	valid
5.5s	2646×	body	1280	valid
2.2s	1916×	body	640	valid
794.0ms	984×	body	320	valid
617.0ms	447×	body	160	valid
97.0ms	385×	body	80	valid