Details

sample590.0ms

Algorithm

intervals

Results

243.0ms	59×	body	2560	valid
104.0ms	74×	body	1280	valid
92.0ms	60×	body	640	valid
19.0ms	36×	body	320	valid
5.0ms	13×	body	160	valid
3.0ms	14×	body	80	valid

simplify60.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize83.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.4b	(- x (tan x))
1.4b	(- x (sin x))

rewrite165.0ms

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:

101.0ms	(/ (- x (sin x)) (- x (tan x)))
19.0ms	(- x (tan x))
26.0ms	(- x (sin x))

series349.0ms

Counts

3 → 9

Calls

3 calls:

148.0ms	(/ (- x (sin x)) (- x (tan x)))
123.0ms	(- x (tan x))
77.0ms	(- x (sin x))

simplify8.4s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
3	4764
2	1272
1	503
0	212

prune974.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize98.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (fma (* x x) 9/40 (* (* (* x x) (* x x)) -27/2800)) -1/2)
0.1b	(* (* x x) (* x x))
0.3b	(* (* (* x x) (* x x)) -27/2800)
14.7b	(fma (* x x) 9/40 (* (* (* x x) (* x x)) -27/2800))

rewrite403.0ms

Algorithm

rewrite-expression-head

Rules

133×	`pow1`
36×	`pow-prod-down` `pow-prod-up`
34×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
21×	`prod-exp` `cbrt-unprod`
18×	`pow-plus`
13×	`pow2`
8×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u`
3×	`fma-def`
2×	`associate-l` `*-commutative` `fma-udef` `unswap-sqr`
1×	`+-commutative` `associate-+l+` `sum-log` `flip3-+` `swap-sqr` `flip-+` `distribute-lft-out`

Counts

4 → 127

Calls

4 calls:

12.0ms	(+ (fma (* x x) 9/40 (* (* (* x x) (* x x)) -27/2800)) -1/2)
84.0ms	(* (* x x) (* x x))
289.0ms	(* (* (* x x) (* x x)) -27/2800)
3.0ms	(fma (* x x) 9/40 (* (* (* x x) (* x x)) -27/2800))

series404.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (fma (* x x) 9/40 (* (* (* x x) (* x x)) -27/2800)) -1/2)
76.0ms	(* (* x x) (* x x))
81.0ms	(* (* (* x x) (* x x)) -27/2800)
183.0ms	(fma (* x x) 9/40 (* (* (* x x) (* x x)) -27/2800))

simplify7.0s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
3	3228
2	950
1	366
0	126

prune786.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize222.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (cos x))
0.2b	(/ (sin x) (* (cos x) (cos x)))
0.6b	(- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
1.4b	(+ 1 (- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))

rewrite682.0ms

Algorithm

rewrite-expression-head

Rules

468×	`times-frac`
353×	`add-sqr-sqrt`
349×	`*-un-lft-identity`
342×	`add-cube-cbrt`
258×	`prod-diff`
131×	`associate-+r+`
43×	`fma-neg`
29×	`div-inv`
11×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `swap-sqr` `associate-r` `associate-l` `associate-/l*` `difference-of-squares`
2×	`cbrt-undiv` `sum-log` `sub-neg` `diff-log` `div-exp` `prod-exp` `cos-mult` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`
1×	`pow2` `+-commutative` `sqr-cos` `clear-num` `associate-+r-` `associate-/r` `frac-2neg` `flip3-+` `pow-plus` `flip3--` `pow-prod-down` `associate-/r/` `pow-sqr` `-commutative` `pow-prod-up` `flip-+` `fma-udef` `flip--` `associate--r+` `unswap-sqr`

Counts

4 → 399

Calls

4 calls:

28.0ms	(* (cos x) (cos x))
68.0ms	(/ (sin x) (* (cos x) (cos x)))
215.0ms	(- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
291.0ms	(+ 1 (- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))

series826.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (cos x) (cos x))
114.0ms	(/ (sin x) (* (cos x) (cos x)))
405.0ms	(- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
251.0ms	(+ 1 (- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))

simplify7.6s

Counts

411 → 411

Iterations

Iter	Nodes
done	5003
2	3272
1	1255
0	543

prune6.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize323.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (* (cos x) (cos x)))
0.6b	(- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
1.4b	(+ 1 (log (exp (- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))))
3.5b	(log (exp (- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

669×	`times-frac`
507×	`add-sqr-sqrt`
496×	`*-un-lft-identity`
489×	`add-cube-cbrt`
387×	`prod-diff`
268×	`log-prod`
262×	`exp-sum`
134×	`associate-+r+`
43×	`fma-neg`
41×	`div-inv`
9×	`add-cbrt-cube` `add-exp-log` `log-pow`
7×	`exp-prod` `add-log-exp`
6×	`pow1` `difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `fma-def` `associate-/l*`
2×	`cbrt-undiv` `log-div` `exp-diff` `div-exp` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `clear-num` `associate-+r-` `associate-/r*` `sum-log` `frac-2neg` `flip3-+` `flip3--` `diff-log` `rem-log-exp` `prod-exp` `associate-/r/` `cos-mult` `cbrt-unprod` `flip-+` `fma-udef` `flip--` `associate--r+`

Counts

4 → 525

Calls

4 calls:

49.0ms	(/ (sin x) (* (cos x) (cos x)))
204.0ms	(- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
955.0ms	(+ 1 (log (exp (- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))))
363.0ms	(log (exp (- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (sin x) (* (cos x) (cos x)))
434.0ms	(- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
264.0ms	(+ 1 (log (exp (- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))))
448.0ms	(log (exp (- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))))

simplify7.6s

Counts

537 → 537

Iterations

Iter	Nodes
done	5008
2	3437
1	1483
0	819

prune6.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes159.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.6b

bsearch173.0ms

Steps

Iters	Range		Point
8	1.874259372897972	986.1969312707462	2.4203399319729506
9	-209901990.47645873	-0.28008678268591264	-2.508948866519329

simplify35.0ms

Iterations

Iter	Nodes
done	38
1	38
0	30

end0.0ms

sample14.6s

Algorithm

intervals

Results

6.6s	1543×	body	2560	valid
5.0s	2735×	body	1280	valid
1.8s	1953×	body	640	valid
524.0ms	908×	body	320	valid
373.0ms	499×	body	160	valid
72.0ms	362×	body	80	valid