Details

sample472.0ms

Algorithm

intervals

Results

178.0ms	97×	body	1280	valid
155.0ms	40×	body	2560	valid
30.0ms	55×	body	640	valid
12.0ms	36×	body	320	valid
5.0ms	21×	body	160	valid
1.0ms	7×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize72.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.3b	(- x (tan x))
1.4b	(- x (sin x))

rewrite82.0ms

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:

49.0ms	(/ (- x (sin x)) (- x (tan x)))
10.0ms	(- x (tan x))
16.0ms	(- x (sin x))

series297.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(/ (- x (sin x)) (- x (tan x)))
119.0ms	(- x (tan x))
49.0ms	(- x (sin x))

simplify1.7s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	2273
1	502
0	209

prune510.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (- x (sin x)) (- x (tan x)))))
0.5b	(expm1 (/ (- x (sin x)) (- x (tan x))))
1.3b	(- x (tan x))
1.4b	(- x (sin x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`prod-diff` `add-cube-cbrt`
8×	`add-log-exp`
6×	`fma-neg`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 78

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (- x (sin x)) (- x (tan x)))))
1.0ms	(expm1 (/ (- x (sin x)) (- x (tan x))))
10.0ms	(- x (tan x))
14.0ms	(- x (sin x))

series545.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(log1p (expm1 (/ (- x (sin x)) (- x (tan x)))))
167.0ms	(expm1 (/ (- x (sin x)) (- x (tan x))))
64.0ms	(- x (tan x))
55.0ms	(- x (sin x))

simplify1.7s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	2067
1	469
0	201

prune479.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite586.0ms

Algorithm

rewrite-expression-head

Rules

255×	`times-frac`
245×	`*-un-lft-identity`
135×	`add-sqr-sqrt`
128×	`add-cube-cbrt`
104×	`prod-diff`
42×	`distribute-rgt-out`
16×	`associate-/l*`
15×	`distribute-lft-out`
14×	`distribute-rgt1-in` `div-inv`
13×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
9×	`add-log-exp`
8×	`fma-neg`
6×	`associate-/r*`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`swap-sqr` `associate-r` `associate-l` `frac-sub`
2×	`clear-num` `frac-2neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`pow2` `sqr-cos` `sum-log` `sub-neg` `flip3-+` `pow-plus` `flip3--` `pow-prod-down` `frac-add` `prod-exp` `associate--l+` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `flip--` `unswap-sqr` `associate-/l/`

Counts

4 → 265

Calls

4 calls:

13.0ms	(/ (sin x) x)
16.0ms	(/ (/ (sin x) x) (cos x))
8.0ms	(* (cos x) (cos x))
522.0ms	(- (+ (/ (/ (sin x) x) (cos x)) (/ (* (/ (sin x) x) (/ (sin x) x)) (* (cos x) (cos x)))) (/ (sin x) x))

series349.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (sin x) x)
52.0ms	(/ (/ (sin x) x) (cos x))
20.0ms	(* (cos x) (cos x))
235.0ms	(- (+ (/ (/ (sin x) x) (cos x)) (/ (* (/ (sin x) x) (/ (sin x) x)) (* (cos x) (cos x)))) (/ (sin x) x))

simplify1.0s

Counts

277 → 277

Iterations

Iter	Nodes
done	5001
1	1129
0	427

prune1.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* x x) (* x x)) (exp -1/2))
0.1b	(* (* x x) (* x x))
0.3b	(fma (* x x) 9/40 1)
22.9b	(log1p (fma (fma (* x x) 9/40 1) (exp -1/2) (fma (* (* (* x x) (* x x)) (exp -1/2)) 351/22400 -1)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

133×	`pow1`
36×	`pow-prod-down` `pow-prod-up`
34×	`add-cbrt-cube`
29×	`add-exp-log`
22×	`pow-sqr`
21×	`prod-exp` `cbrt-unprod`
18×	`pow-plus`
13×	`pow2`
6×	`add-sqr-sqrt`
5×	`expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt`
4×	`associate-r` `log1p-expm1-u` `add-log-exp`
2×	`associate-l` `*-commutative` `unswap-sqr`
1×	`log1p-udef` `swap-sqr` `log1p-expm1` `fma-udef`

Counts

4 → 116

Calls

4 calls:

144.0ms	(* (* (* x x) (* x x)) (exp -1/2))
56.0ms	(* (* x x) (* x x))
0.0ms	(fma (* x x) 9/40 1)
1.0ms	(log1p (fma (fma (* x x) 9/40 1) (exp -1/2) (fma (* (* (* x x) (* x x)) (exp -1/2)) 351/22400 -1)))

series624.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (* (* x x) (* x x)) (exp -1/2))
42.0ms	(* (* x x) (* x x))
66.0ms	(fma (* x x) 9/40 1)
366.0ms	(log1p (fma (fma (* x x) 9/40 1) (exp -1/2) (fma (* (* (* x x) (* x x)) (exp -1/2)) 351/22400 -1)))

simplify2.9s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	2728
1	379
0	132

prune444.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 31.6b

bsearch212.0ms

Steps

Iters	Range		Point
9	0.030359728269424062	9645967.64350026	14.281712868651681
11	-14746478108.679678	-8.433739504313006e-14	-2.6074601408363502

simplify11.0ms

Iterations

Iter	Nodes
done	42
1	42
0	33

end0.0ms

sample13.3s

Algorithm

intervals

Results

5.9s	1573×	body	2560	valid
4.6s	2763×	body	1280	valid
1.8s	1835×	body	640	valid
509.0ms	969×	body	320	valid
197.0ms	483×	body	160	valid
60.0ms	377×	body	80	valid