Details

sample562.0ms

Algorithm

intervals

Results

229.0ms	52×	body	2560	valid
142.0ms	98×	body	1280	valid
55.0ms	53×	body	640	valid
15.0ms	26×	body	320	valid
6.0ms	15×	body	160	valid
3.0ms	12×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	19
3	19
2	17
1	13
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize46.0ms

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))

rewrite39.0ms

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:

22.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series257.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(/ (- x (sin x)) (- x (tan x)))
77.0ms	(- x (tan x))
82.0ms	(- x (sin x))

simplify1.5s

Counts

122 → 122

Iterations

Iter	Nodes
3	4396
2	1293
1	504
0	212

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 9/40 (* 27/2800 (* x x)))
0.1b	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
0.4b	(* 27/2800 (* x x))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `prod-diff` `add-cube-cbrt`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp`
4×	`associate-r` `associate-l`
3×	`expm1-log1p-u` `sub-neg` `fma-neg` `insert-posit16` `log1p-expm1-u`
2×	`flip3--` `associate-r/` `-commutative` `flip--` `unswap-sqr`
1×	`diff-log`

Counts

3 → 77

Calls

3 calls:

11.0ms	(- 9/40 (* 27/2800 (* x x)))
44.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
26.0ms	(* 27/2800 (* x x))

series359.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(- 9/40 (* 27/2800 (* x x)))
201.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
53.0ms	(* 27/2800 (* x x))

simplify2.4s

Counts

86 → 86

Iterations

Iter	Nodes
3	3175
2	1030
1	343
0	113

prune711.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
42×	`add-cube-cbrt`
32×	`log-pow`
31×	`exp-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`log-prod`
2×	`sub-neg` `diff-log` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp`

Counts

4 → 160

Calls

4 calls:

25.0ms	(/ (- x (sin x)) (- x (tan x)))
24.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
9.0ms	(- x (tan x))
13.0ms	(- x (sin x))

series356.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- x (sin x)) (- x (tan x)))
113.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
101.0ms	(- x (tan x))
52.0ms	(- x (sin x))

simplify1.7s

Counts

172 → 172

Iterations

Iter	Nodes
3	4586
2	1373
1	576
0	277

prune1.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (* (cos x) (cos x)))
0.3b	(* (cos x) (cos x))
0.5b	(- (/ (sin x) (* x (cos x))) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
31.3b	(fma (/ (/ (sin x) x) x) (/ (sin x) (* (cos x) (cos x))) (- (/ (sin x) (* x (cos x))) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
21×	`prod-diff`
15×	`times-frac`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`fma-neg`
6×	`add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`swap-sqr` `associate-r` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cos-mult` `cbrt-unprod` `fma-udef`
1×	`pow2` `sqr-cos` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `pow-plus` `flip3--` `diff-log` `pow-prod-down` `associate-/r/` `pow-sqr` `-commutative` `pow-prod-up` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

13.0ms	(/ (sin x) (* (cos x) (cos x)))
10.0ms	(* (cos x) (cos x))
53.0ms	(- (/ (sin x) (* x (cos x))) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
1.0ms	(fma (/ (/ (sin x) x) x) (/ (sin x) (* (cos x) (cos x))) (- (/ (sin x) (* x (cos x))) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))

series864.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (sin x) (* (cos x) (cos x)))
31.0ms	(* (cos x) (cos x))
254.0ms	(- (/ (sin x) (* x (cos x))) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
520.0ms	(fma (/ (/ (sin x) x) x) (/ (sin x) (* (cos x) (cos x))) (- (/ (sin x) (* x (cos x))) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))

simplify3.0s

Counts

124 → 124

Iterations

Iter	Nodes
3	7197
2	1479
1	471
0	206

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes70.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch137.0ms

Steps

Iters	Range		Point
10	3.724243043503383e-05	335086.0623706297	2.433269626118002
9	-1352.1675980196485	-0.00125944232679287	-0.02581010450665607

simplify8.0ms

Iterations

Iter	Nodes
2	41
1	41
0	35

end0.0ms

sample16.7s

Algorithm

intervals

Results

7.6s	1622×	body	2560	valid
4.9s	2697×	body	1280	valid
2.7s	1901×	body	640	valid
941.0ms	948×	body	320	valid
223.0ms	479×	body	160	valid
90.0ms	353×	body	80	valid