Details

sample211.0ms

Algorithm

intervals

Results

97.0ms	49×	body	2560	valid
64.0ms	92×	body	1280	valid
26.0ms	62×	body	640	valid
9.0ms	33×	body	320	valid
3.0ms	11×	body	160	valid
1.0ms	9×	body	80	valid

simplify17.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite64.0ms

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:

54.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series103.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (- 1.0 (cos x)) (sin x))
36.0ms	(- 1.0 (cos x))

simplify877.0ms

Counts: 58 → 58

prune257.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 98

Calls

4 calls:

47.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
7.0ms	(exp (log (- 1.0 (cos x))))
5.0ms	(log (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series246.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
30.0ms	(exp (log (- 1.0 (cos x))))
128.0ms	(log (- 1.0 (cos x)))
36.0ms	(- 1.0 (cos x))

simplify917.0ms

Counts: 110 → 110

prune381.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`difference-cubes` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

63.0ms	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
4.0ms	(pow (cos x) 3)
15.0ms	(+ (cos x) 1.0)
47.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series257.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
53.0ms	(pow (cos x) 3)
11.0ms	(+ (cos x) 1.0)
58.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.1s

Counts: 101 → 101

prune469.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (cos x) 1.0)
0.4b	(+ (cos x) 1.0)
0.8b	(* (sqrt (+ (cos x) 1.0)) (sqrt (+ (cos x) 1.0)))
0.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
26×	`sqrt-prod`
19×	`pow1`
16×	`difference-of-squares`
12×	`add-cube-cbrt` `unpow-prod-down` `sqrt-div` `cube-prod`
11×	`swap-sqr`
10×	`add-log-exp`
8×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out` `sqr-pow`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-up` `distribute-lft-out--`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`+-commutative` `associate-r/` `associate-l/` `sum-log`
1×	`difference-cubes` `pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 120

Calls

4 calls:

13.0ms	(+ (cos x) 1.0)
14.0ms	(+ (cos x) 1.0)
102.0ms	(* (sqrt (+ (cos x) 1.0)) (sqrt (+ (cos x) 1.0)))
48.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series125.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (cos x) 1.0)
17.0ms	(+ (cos x) 1.0)
19.0ms	(* (sqrt (+ (cos x) 1.0)) (sqrt (+ (cos x) 1.0)))
73.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify788.0ms

Counts: 132 → 132

prune530.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

regimes161.0ms

Accuracy

98.8% (0.4b remaining)

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

bsearch174.0ms

Steps

Iters	Range		Point
8	0.00022617661863457038	0.0815671925612537	0.02301026064809699
11	-31.62993370098301	-4.221128360075206e-33	-0.021757331919882755

simplify821.0ms

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.4s	1576×	body	2560	valid
3.2s	2816×	body	1280	valid
974.0ms	1854×	body	640	valid
388.0ms	932×	body	320	valid
192.0ms	465×	body	160	valid
88.0ms	353×	body	80	valid
28.0ms	4×	body	5120	valid