Details

sample181.0ms

Algorithm

intervals

Results

83.0ms	46×	body	2560	valid
58.0ms	92×	body	1280	valid
20.0ms	63×	body	640	valid
6.0ms	29×	body	320	valid
2.0ms	11×	body	160	valid
1.0ms	15×	body	80	valid

simplify8.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize18.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.1b	(- 1.0 (cos x))

rewrite110.0ms

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:

89.0ms	(/ (- 1.0 (cos x)) (sin x))
16.0ms	(- 1.0 (cos x))

series102.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(/ (- 1.0 (cos x)) (sin x))
38.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

74 → 74

Iterations

Useful iterations: done (2.1s)

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

prune266.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

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)
0.4b	(+ 1.0 (cos x))
0.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite238.0ms

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:

144.0ms	(/ (- (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)
13.0ms	(+ 1.0 (cos x))
41.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series387.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
36.0ms	(pow (cos x) 3)
17.0ms	(+ 1.0 (cos x))
75.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.8s

Counts

316 → 316

Iterations

Useful iterations: done (1.8s)

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

prune828.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (* (* (cos x) (cos x)) (cos x))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
0.3b	(* (cos x) (cos x))
0.4b	(+ 1.0 (cos x))
0.9b	(- (pow 1.0 3) (* (* (cos x) (cos x)) (cos x)))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
12×	`fma-neg` `prod-diff`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`unpow-prod-down` `cube-prod`
4×	`expm1-log1p-u` `times-frac` `log1p-expm1-u` `associate-/l*`
3×	`difference-cubes` `fma-def` `swap-sqr` `associate-r` `associate-l` `pow3`
2×	`cbrt-undiv` `cube-mult` `flip3--` `unpow3` `div-exp` `prod-exp` `flip--` `cbrt-unprod` `associate-/l/` `sqr-pow`
1×	`+-commutative` `pow2` `sub-neg` `sqr-cos` `frac-2neg` `flip3-+` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `pow-sqr` `cos-mult` `-commutative` `pow-prod-up` `flip-+` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 113

Calls

4 calls:

98.0ms	(/ (- (pow 1.0 3) (* (* (cos x) (cos x)) (cos x))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
12.0ms	(* (cos x) (cos x))
15.0ms	(+ 1.0 (cos x))
38.0ms	(- (pow 1.0 3) (* (* (cos x) (cos x)) (cos x)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ (- (pow 1.0 3) (* (* (cos x) (cos x)) (cos x))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
25.0ms	(* (cos x) (cos x))
12.0ms	(+ 1.0 (cos x))
90.0ms	(- (pow 1.0 3) (* (* (cos x) (cos x)) (cos x)))

simplify1.9s

Counts

125 → 125

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	207	2265
1	518	1688
2	1822	1480
done	5000	1473

prune609.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (* (+ 1/2 (* 1/2 (cos (* 2 x)))) (cos x))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
0.4b	(+ 1.0 (cos x))
0.5b	(+ 1/2 (* 1/2 (cos (* 2 x))))
0.9b	(- (pow 1.0 3) (* (+ 1/2 (* 1/2 (cos (* 2 x)))) (cos x)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`fma-neg` `prod-diff`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `fma-def` `cube-prod`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `+-commutative` `cube-mult` `flip3--` `flip3-+` `unpow3` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/` `sqr-pow`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `distribute-lft-out`

Counts

4 → 97

Calls

4 calls:

84.0ms	(/ (- (pow 1.0 3) (* (+ 1/2 (* 1/2 (cos (* 2 x)))) (cos x))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
11.0ms	(+ 1.0 (cos x))
17.0ms	(+ 1/2 (* 1/2 (cos (* 2 x))))
49.0ms	(- (pow 1.0 3) (* (+ 1/2 (* 1/2 (cos (* 2 x)))) (cos x)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

319.0ms	(/ (- (pow 1.0 3) (* (+ 1/2 (* 1/2 (cos (* 2 x)))) (cos x))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
19.0ms	(+ 1.0 (cos x))
52.0ms	(+ 1/2 (* 1/2 (cos (* 2 x))))
138.0ms	(- (pow 1.0 3) (* (+ 1/2 (* 1/2 (cos (* 2 x)))) (cos x)))

simplify1.6s

Counts

109 → 109

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	201	2527
1	556	2274
2	1927	1996
done	5001	1911

prune662.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes238.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 29.9b

bsearch164.0ms

Steps

Iters	Range		Point
9	0.0033303272193615503	311302.39110615524	0.018964280563894167
9	-7.35943201301068	-4.403108084983288e-07	-0.01938722760852505

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	73
1	45	73
done	45	73

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.9s	1590×	body	2560	valid
2.9s	2797×	body	1280	valid
1.0s	1830×	body	640	valid
466.0ms	961×	body	320	valid
149.0ms	477×	body	160	valid
40.0ms	341×	body	80	valid
25.0ms	4×	body	5120	valid