Details

sample217.0ms

Algorithm

intervals

Results

110.0ms	60×	body	2560	valid
61.0ms	89×	body	1280	valid
21.0ms	58×	body	640	valid
7.0ms	30×	body	320	valid
3.0ms	1×	body	5120	valid
2.0ms	10×	body	80	valid
1.0ms	8×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 1.0 (cos x))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

68.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series82.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- 1.0 (cos x)) (sin x))
35.0ms	(- 1.0 (cos x))

simplify101.0ms

Counts: 58 → 58

prune206.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.0b	(+ (* 1/240 (pow x 5)) (* 1/2 x))
0.0b	(* 1/240 (pow x 5))
0.1b	(* 1/24 (pow x 3))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3`

Counts

4 → 80

Calls

4 calls:

27.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
11.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
32.0ms	(* 1/240 (pow x 5))
27.0ms	(* 1/24 (pow x 3))

series433.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
221.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
69.0ms	(* 1/240 (pow x 5))
55.0ms	(* 1/24 (pow x 3))

simplify53.0ms

Counts: 92 → 92

prune288.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.0b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.5b	(- 1.0 (cos x))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
25.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
11.0ms	(- 1.0 (cos x))

series216.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (- 1.0 (cos x)) (sin x))
71.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
46.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
38.0ms	(- 1.0 (cos x))

simplify58.0ms

Counts: 124 → 124

prune447.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
0.4b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
48×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
15×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 139

Calls

4 calls:

107.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
4.0ms	(pow (cos x) 3)
7.0ms	(+ (cos x) 1.0)
39.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series436.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
47.0ms	(pow (cos x) 3)
20.0ms	(+ (cos x) 1.0)
97.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify103.0ms

Counts: 151 → 151

prune599.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes272.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 32.3b

bsearch174.0ms

Steps

Iters	Range		Point
9	8.845201659255268e-06	4.45864614599283	0.02122713234710593
10	-119.54622503529531	-1.822584514918214e-10	-0.023280958375624945

simplify71.0ms

end0.0ms

sample8.9s

Algorithm

intervals

Results

4.0s	1574×	body	2560	valid
3.1s	2747×	body	1280	valid
921.0ms	1896×	body	640	valid
330.0ms	926×	body	320	valid
97.0ms	480×	body	160	valid
45.0ms	373×	body	80	valid
17.0ms	4×	body	5120	valid