Details

sample101.0ms

Algorithm

intervals

Results

35.0ms	48×	body	2560	valid
16.0ms	42×	body	1280	valid
15.0ms	52×	body	640	valid
12.0ms	68×	body	80	valid
5.0ms	27×	body	320	valid
3.0ms	19×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize19.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1.0 (cos x))
15.1b	(/ (- 1.0 (cos x)) (* x x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-cbrt-cube` `add-exp-log`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`expm1-log1p-u` `pow1` `cbrt-undiv` `flip3--` `div-exp` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 58

Calls

2 calls:

6.0ms	(- 1.0 (cos x))
26.0ms	(/ (- 1.0 (cos x)) (* x x))

series114.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(- 1.0 (cos x))
82.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify982.0ms

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
2	1734
1	301
0	116

prune375.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.1b	(- 1.0 (cos x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
110×	`add-sqr-sqrt` `*-un-lft-identity`
76×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `fma-neg` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 165

Calls

3 calls:

23.0ms	(/ (/ (- 1.0 (cos x)) x) x)
15.0ms	(/ (- 1.0 (cos x)) x)
7.0ms	(- 1.0 (cos x))

series166.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ (/ (- 1.0 (cos x)) x) x)
67.0ms	(/ (- 1.0 (cos x)) x)
40.0ms	(- 1.0 (cos x))

simplify1.5s

Counts

174 → 174

Iterations

Iter	Nodes
done	5000
2	2993
1	621
0	259

prune727.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.4b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)) x))
0.5b	(+ 1.0 (cos x))
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite186.0ms

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:

4.0ms	(pow (cos x) 3)
124.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)) x))
10.0ms	(+ 1.0 (cos x))
33.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series342.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(pow (cos x) 3)
232.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)) x))
12.0ms	(+ 1.0 (cos x))
54.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.6s

Counts

316 → 316

Iterations

Iter	Nodes
done	5000
2	4529
1	865
0	337

prune993.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (log (exp (- (pow 1.0 3) (pow (cos x) 3)))) (* (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)) x))
0.5b	(+ 1.0 (cos x))
1.9b	(- (pow 1.0 3) (pow (cos x) 3))
2.0b	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite463.0ms

Algorithm

rewrite-expression-head

Rules

288×	`prod-diff`
254×	`add-sqr-sqrt`
200×	`*-un-lft-identity`
195×	`unpow-prod-down` `cube-prod`
158×	`add-cube-cbrt`
149×	`log-prod`
146×	`exp-sum`
81×	`sqr-pow`
78×	`log-pow`
75×	`exp-prod`
64×	`difference-of-squares`
49×	`cube-mult` `unpow3`
29×	`times-frac` `associate-/l*`
20×	`distribute-lft-out--`
12×	`fma-neg`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`pow1`
4×	`expm1-log1p-u` `difference-cubes` `log1p-expm1-u`
3×	`fma-def`
2×	`cbrt-undiv` `log-div` `sub-neg` `exp-diff` `div-exp`
1×	`+-commutative` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `flip3-+` `flip3--` `diff-log` `div-sub` `rem-log-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `flip--` `distribute-lft-out`

Counts

4 → 471

Calls

4 calls:

283.0ms	(/ (log (exp (- (pow 1.0 3) (pow (cos x) 3)))) (* (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)) x))
8.0ms	(+ 1.0 (cos x))
31.0ms	(- (pow 1.0 3) (pow (cos x) 3))
105.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series432.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(/ (log (exp (- (pow 1.0 3) (pow (cos x) 3)))) (* (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)) x))
12.0ms	(+ 1.0 (cos x))
85.0ms	(- (pow 1.0 3) (pow (cos x) 3))
86.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify2.5s

Counts

483 → 483

Iterations

Iter	Nodes
done	5000
2	4220
1	1043
0	559

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes104.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.7b

bsearch92.0ms

Steps

Iters	Range		Point
9	5.1798647897020696e-05	160.65039477392645	0.033302914266201536
8	-0.9341403346610884	-0.003292329160956242	-0.03305631426271166

simplify8.0ms

Iterations

Iter	Nodes
done	39
1	39
0	35

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	1623×	body	2560	valid
672.0ms	923×	body	320	valid
600.0ms	1237×	body	1280	valid
464.0ms	1505×	body	640	valid
176.0ms	2205×	body	80	valid
67.0ms	507×	body	160	valid