Details

sample204.0ms

Algorithm

intervals

Results

87.0ms	47×	body	2560	valid
65.0ms	92×	body	1280	valid
24.0ms	65×	body	640	valid
8.0ms	28×	body	320	valid
3.0ms	15×	body	160	valid
3.0ms	1×	body	5120	valid
1.0ms	8×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	16
3	16
2	14
1	11
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.0b	(- 1.0 (cos x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 68

Calls

2 calls:

42.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series86.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (- 1.0 (cos x)) (sin x))
27.0ms	(- 1.0 (cos x))

simplify837.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
2	1211
1	309
0	134

prune423.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.0b	(- 1.0 (cos x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 68

Calls

2 calls:

29.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(- 1.0 (cos x))

series68.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- 1.0 (cos x)) (sin x))
22.0ms	(- 1.0 (cos x))

simplify892.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
2	1211
1	309
0	134

prune320.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.5b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.0b	(- 1.0 (cos x))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
40×	`add-cube-cbrt`
38×	`exp-prod`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `associate-/r*` `fma-neg` `div-sub` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `rem-exp-log`

Counts

4 → 132

Calls

4 calls:

30.0ms	(/ (- 1.0 (cos x)) (sin x))
38.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
38.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
11.0ms	(- 1.0 (cos x))

series258.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (- 1.0 (cos x)) (sin x))
87.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
68.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
35.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1390
1	392
0	195

prune655.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.5b	(log (exp (/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (* (cos x) (+ (cos x) 1.0))) (sin x)))))
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

144×	`prod-diff`
134×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
102×	`unpow-prod-down` `cube-prod`
86×	`add-cube-cbrt`
42×	`sqr-pow`
32×	`difference-of-squares`
30×	`log-pow`
29×	`exp-prod`
26×	`cube-mult` `unpow3`
25×	`times-frac`
12×	`fma-neg`
10×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`pow1`
5×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `log-prod` `fma-def`
2×	`difference-cubes`
1×	`pow-to-exp` `+-commutative` `log-div` `sum-log` `sub-neg` `pow-pow` `flip3-+` `flip3--` `exp-diff` `diff-log` `div-sub` `rem-log-exp` `pow-exp` `flip-+` `div-inv` `flip--` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 278

Calls

4 calls:

4.0ms	(pow (cos x) 3)
11.0ms	(+ (cos x) 1.0)
114.0ms	(log (exp (/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (* (cos x) (+ (cos x) 1.0))) (sin x)))))
48.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series408.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(pow (cos x) 3)
19.0ms	(+ (cos x) 1.0)
284.0ms	(log (exp (/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (* (cos x) (+ (cos x) 1.0))) (sin x)))))
57.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.6s

Counts

290 → 290

Iterations

Iter	Nodes
done	5000
2	3679
1	792
0	345

prune975.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.1b

regimes428.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 30.7b

bsearch103.0ms

Steps

Iters	Range		Point
9	7.294142785006675e-07	13.800596953327334	0.018056437645311372
7	-0.10952899301968014	-0.00181011214377754	-0.022988205514711212

simplify7.0ms

Iterations

Iter	Nodes
done	32
2	32
1	31
0	24

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.5s	1672×	body	2560	valid
2.7s	2688×	body	1280	valid
1.1s	1889×	body	640	valid
444.0ms	351×	body	80	valid
308.0ms	898×	body	320	valid
100.0ms	499×	body	160	valid
19.0ms	3×	body	5120	valid