Details

sample115.0ms

Algorithm

intervals

Results

59.0ms	48×	body	2560	valid
16.0ms	42×	body	1280	valid
16.0ms	51×	body	640	valid
6.0ms	28×	body	320	valid
4.0ms	72×	body	80	valid
2.0ms	15×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
4	28
3	26
2	21
1	13
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize14.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1.0 (cos x))
13.9b	(/ (- 1.0 (cos x)) (* x x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

9.0ms	(- 1.0 (cos x))
30.0ms	(/ (- 1.0 (cos x)) (* x x))

series131.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(- 1.0 (cos x))
94.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify593.0ms

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
2	1129
1	232
0	88

prune199.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.0b	(- 1.0 (cos x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 147

Calls

3 calls:

19.0ms	(/ (/ (- 1.0 (cos x)) x) x)
14.0ms	(/ (- 1.0 (cos x)) x)
11.0ms	(- 1.0 (cos x))

series164.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ (/ (- 1.0 (cos x)) x) x)
67.0ms	(/ (- 1.0 (cos x)) x)
25.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

156 → 156

Iterations

Iter	Nodes
done	5001
2	2463
1	549
0	229

prune618.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
0.3b	(cbrt (pow (- 1.0 (cos x)) 3))
0.3b	(pow (- 1.0 (cos x)) 3)
2.0b	(- 1.0 (cos x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

80×	`cbrt-prod`
72×	`add-sqr-sqrt` `*-un-lft-identity`
57×	`times-frac`
46×	`add-cube-cbrt`
30×	`unpow-prod-down` `cube-prod`
19×	`associate-/l*`
13×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `add-cbrt-cube` `unpow3` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`cbrt-div` `flip3--` `flip--`
3×	`pow-unpow` `associate-/r*`
2×	`associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-exp` `pow-exp` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 163

Calls

4 calls:

27.0ms	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
7.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
7.0ms	(pow (- 1.0 (cos x)) 3)
5.0ms	(- 1.0 (cos x))

series218.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
28.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
79.0ms	(pow (- 1.0 (cos x)) 3)
35.0ms	(- 1.0 (cos x))

simplify1.8s

Counts

175 → 175

Iterations

Iter	Nodes
done	5001
2	2439
1	479
0	214

prune597.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.3b	(pow (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (+ (cos x) 1.0) (cos x)) (* 1.0 1.0))) 3)
0.4b	(+ (cos x) 1.0)
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

234×	`add-sqr-sqrt`
168×	`unpow-prod-down` `cube-prod`
150×	`times-frac`
138×	`*-un-lft-identity`
112×	`difference-of-squares`
66×	`add-cube-cbrt`
58×	`sqr-pow`
35×	`distribute-lft-out--`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
7×	`difference-cubes`
6×	`pow1` `pow-unpow`
4×	`associate-/r/`
3×	`flip3-+` `pow-exp` `flip-+` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `div-inv`
1×	`cube-div` `cbrt-undiv` `+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `div-exp` `flip--` `distribute-lft-out`

Counts

4 → 251

Calls

4 calls:

5.0ms	(pow (cos x) 3)
68.0ms	(pow (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (+ (cos x) 1.0) (cos x)) (* 1.0 1.0))) 3)
5.0ms	(+ (cos x) 1.0)
35.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series411.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(pow (cos x) 3)
255.0ms	(pow (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (+ (cos x) 1.0) (cos x)) (* 1.0 1.0))) 3)
16.0ms	(+ (cos x) 1.0)
86.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify795.0ms

Counts

263 → 263

Iterations

Iter	Nodes
done	5001
1	1612
0	347

prune913.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes162.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.3b

bsearch86.0ms

Steps

Iters	Range		Point
9	7.294142785006675e-07	13.800596953327334	0.029870589015516296
7	-0.10952899301968014	-0.00181011214377754	-0.029468940558385545

simplify3.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	1675×	body	2560	valid
1.1s	1222×	body	1280	valid
542.0ms	1493×	body	640	valid
230.0ms	894×	body	320	valid
130.0ms	2213×	body	80	valid
67.0ms	503×	body	160	valid