Details

sample211.0ms

Algorithm

intervals

Results

90.0ms	88×	body	1280	valid
72.0ms	45×	body	2560	valid
22.0ms	54×	body	640	valid
9.0ms	34×	body	320	valid
4.0ms	21×	body	160	valid
1.0ms	14×	body	80	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.4b	(- 1.0 (cos x))

rewrite42.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

26.0ms	(/ (- 1.0 (cos x)) (sin x))
14.0ms	(- 1.0 (cos x))

series84.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(/ (- 1.0 (cos x)) (sin x))
26.0ms	(- 1.0 (cos x))

simplify2.0s

Counts

74 → 74

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	134	964
1	295	831
2	743	731
3	2333	692
done	5000	683

prune250.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
2.4b	(- 1.0 (cos x))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
112×	`add-sqr-sqrt` `*-un-lft-identity`
78×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
9×	`prod-diff`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 177

Calls

3 calls:

30.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
31.0ms	(/ (sin x) (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

series123.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
51.0ms	(/ (sin x) (- 1.0 (cos x)))
22.0ms	(- 1.0 (cos x))

simplify2.7s

Counts

186 → 186

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	269	3021
1	561	2564
2	1226	2279
3	3472	2188
done	5000	2178

prune409.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
0.4b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
2.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
144×	`prod-diff`
117×	`*-un-lft-identity`
114×	`unpow-prod-down` `cube-prod`
85×	`add-cube-cbrt`
50×	`sqr-pow`
48×	`difference-of-squares`
26×	`cube-mult` `unpow3`
25×	`times-frac` `associate-/l*`
15×	`distribute-lft-out--`
12×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`difference-cubes` `pow-unpow` `fma-def`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 304

Calls

4 calls:

142.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
7.0ms	(pow (cos x) 3)
8.0ms	(+ 1.0 (cos x))
53.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series369.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
42.0ms	(pow (cos x) 3)
15.0ms	(+ 1.0 (cos x))
75.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.9s

Counts

316 → 316

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	342	9345
1	787	5855
2	2429	4730
done	5001	4728

prune719.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3)))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
0.4b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
30.4b	(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
18×	`unpow-prod-down` `cube-prod`
12×	`fma-neg` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
8×	`times-frac` `associate-/l*` `add-log-exp` `sqr-pow`
5×	`pow1` `cube-mult` `unpow3`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `expm1-udef` `associate--r-` `rem-cube-cbrt`

Counts

4 → 146

Calls

4 calls:

85.0ms	(/ (- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3)))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
7.0ms	(pow (cos x) 3)
14.0ms	(+ 1.0 (cos x))
30.0ms	(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

series906.0ms

Counts

4 → 12

Calls

4 calls:

503.0ms	(/ (- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3)))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
52.0ms	(pow (cos x) 3)
28.0ms	(+ 1.0 (cos x))
323.0ms	(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

simplify2.1s

Counts

158 → 158

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	238	4063
1	580	2448
2	2018	2067
done	5001	1885

prune595.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes124.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.3b

bsearch155.0ms

Steps

Iters	Range		Point
10	1.5244367550608482e-07	9556.682540875734	0.02350362276191215
9	-1501.2167507114543	-0.006495210018506858	-0.02325473706087107

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	87
1	54	87
done	54	87

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.9s	1534×	body	2560	valid
2.5s	2826×	body	1280	valid
1.4s	1863×	body	640	valid
350.0ms	956×	body	320	valid
142.0ms	458×	body	160	valid
41.0ms	359×	body	80	valid
20.0ms	4×	body	5120	valid