Details

sample219.0ms

Algorithm

intervals

Results

109.0ms	57×	body	2560	valid
59.0ms	82×	body	1280	valid
24.0ms	58×	body	640	valid
11.0ms	38×	body	320	valid
3.0ms	13×	body	160	valid
1.0ms	8×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.3b	(- 1.0 (cos x))

rewrite50.0ms

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:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- 1.0 (cos x)) (sin x))
21.0ms	(- 1.0 (cos x))

simplify1.4s

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
2	1211
1	309
0	134

prune369.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)) (sin x)))
0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.2b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite163.0ms

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-cbrt-cube` `add-exp-log`
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×	`pow-to-exp` `+-commutative` `clear-num` `associate-/r*` `sum-log` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 304

Calls

4 calls:

99.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)) (sin x)))
7.0ms	(pow (cos x) 3)
5.0ms	(+ (cos x) 1.0)
32.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series345.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)) (sin x)))
31.0ms	(pow (cos x) 3)
15.0ms	(+ (cos x) 1.0)
68.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify3.3s

Counts

316 → 316

Iterations

Iter	Nodes
done	5000
2	4370
1	874
0	340

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.4b	(+ (cos x) 1.0)
0.6b	(expm1 (* (cos x) (* (cos x) (cos x))))
1.2b	(- (pow 1.0 3) (log1p (expm1 (* (cos x) (* (cos x) (cos x))))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
36×	`prod-diff`
33×	`add-cube-cbrt`
13×	`unpow-prod-down` `cube-prod`
12×	`fma-neg`
11×	`pow1`
9×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`log1p-expm1-u` `sqr-pow`
4×	`expm1-log1p-u` `cube-mult` `unpow3` `difference-of-squares`
3×	`fma-def` `swap-sqr` `associate-r` `associate-l`
2×	`diff-log`
1×	`pow2` `+-commutative` `sqr-cos` `log1p-udef` `expm1-log1p` `sum-log` `sub-neg` `flip3-+` `pow-plus` `flip3--` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `flip--` `distribute-lft-out` `distribute-lft-out--` `expm1-udef` `unswap-sqr`

Counts

4 → 125

Calls

4 calls:

16.0ms	(* (cos x) (cos x))
10.0ms	(+ (cos x) 1.0)
1.0ms	(expm1 (* (cos x) (* (cos x) (cos x))))
25.0ms	(- (pow 1.0 3) (log1p (expm1 (* (cos x) (* (cos x) (cos x))))))

series581.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (cos x) (cos x))
18.0ms	(+ (cos x) 1.0)
129.0ms	(expm1 (* (cos x) (* (cos x) (cos x))))
402.0ms	(- (pow 1.0 3) (log1p (expm1 (* (cos x) (* (cos x) (cos x))))))

simplify2.4s

Counts

137 → 137

Iterations

Iter	Nodes
done	5001
2	2787
1	478
0	196

prune721.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ 1/2 (* 1/2 (cos (+ x x))))
0.4b	(+ (cos x) 1.0)
0.6b	(expm1 (* (cos x) (+ 1/2 (* 1/2 (cos (+ x x))))))
1.2b	(- (pow 1.0 3) (log1p (expm1 (* (cos x) (+ 1/2 (* 1/2 (cos (+ x x))))))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`prod-diff`
34×	`*-un-lft-identity`
30×	`add-cube-cbrt`
13×	`unpow-prod-down` `cube-prod`
12×	`fma-neg`
11×	`add-log-exp`
6×	`fma-def`
5×	`log1p-expm1-u` `sqr-pow`
4×	`expm1-log1p-u` `cube-mult` `pow1` `add-cbrt-cube` `unpow3` `add-exp-log` `difference-of-squares`
2×	`+-commutative` `sum-log` `flip3-+` `diff-log` `flip-+`
1×	`log1p-udef` `expm1-log1p` `sub-neg` `flip3--` `flip--` `distribute-lft-out` `distribute-lft-out--` `expm1-udef`

Counts

4 → 112

Calls

4 calls:

5.0ms	(+ 1/2 (* 1/2 (cos (+ x x))))
5.0ms	(+ (cos x) 1.0)
0.0ms	(expm1 (* (cos x) (+ 1/2 (* 1/2 (cos (+ x x))))))
22.0ms	(- (pow 1.0 3) (log1p (expm1 (* (cos x) (+ 1/2 (* 1/2 (cos (+ x x))))))))

series613.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ 1/2 (* 1/2 (cos (+ x x))))
19.0ms	(+ (cos x) 1.0)
147.0ms	(expm1 (* (cos x) (+ 1/2 (* 1/2 (cos (+ x x))))))
413.0ms	(- (pow 1.0 3) (log1p (expm1 (* (cos x) (+ 1/2 (* 1/2 (cos (+ x x))))))))

simplify2.4s

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	2210
1	495
0	196

prune725.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

regimes165.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 30.7b

bsearch198.0ms

Steps

Iters	Range		Point
11	3.4817375791661903e-26	573579.0075499975	0.018683255234810868
10	-84463.33967257517	-3.2432757514909933e-09	-0.02027792377591883

simplify16.0ms

Iterations

Iter	Nodes
done	58
2	58
1	57
0	47

end0.0ms

sample8.6s

Algorithm

intervals

Results

4.0s	1642×	body	2560	valid
2.6s	2753×	body	1280	valid
1.4s	1876×	body	640	valid
319.0ms	927×	body	320	valid
90.0ms	452×	body	160	valid
40.0ms	345×	body	80	valid
38.0ms	5×	body	5120	valid