Details

sample95.0ms

Algorithm

intervals

Results

51.0ms	156×	body	1280	valid
20.0ms	24×	body	2560	valid
10.0ms	48×	body	640	valid
3.0ms	21×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	2×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.9b

localize9.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
2.2b	(cos (+ x eps))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `cos-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

22.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series70.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

simplify74.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	192	385
1	523	285
2	2519	275
3	5001	220
done	5001	220

prune126.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
3.6b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`prod-diff` `add-log-exp`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `fma-neg` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `associate--l+` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

18.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
10.0ms	(* (cos x) (cos eps))
12.0ms	(* (sin x) (sin eps))
69.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series324.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
47.0ms	(* (cos x) (cos eps))
49.0ms	(* (sin x) (sin eps))
143.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify53.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	381	989
1	1342	838
2	5001	822
done	5001	822

prune324.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.3b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
3.6b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
12×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `associate-+l+` `fma-def` `add-cbrt-cube`
4×	`expm1-log1p-u` `sum-log` `log1p-expm1-u`
3×	`associate-r` `associate-l`
2×	`+-commutative` `associate-+l-` `sub-neg` `flip3-+` `diff-log` `prod-diff` `flip-+` `distribute-lft-out`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `sin-mult` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

12.0ms	(* (sin x) (sin eps))
41.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
43.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series409.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin x) (sin eps))
105.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
105.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
146.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify82.0ms

Counts

87 → 87

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	238	768
1	735	681
2	3112	663
3	5002	661
done	5002	661

prune415.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 16.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
3.4b	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
4.2b	(log (exp (* (sin x) (sin eps))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`prod-diff`
10×	`pow1` `add-log-exp`
8×	`add-exp-log` `associate--l+` `add-cbrt-cube`
6×	`associate-r` `associate-l` `log-pow`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `diff-log`
2×	`sub-neg` `exp-prod` `exp-to-pow` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `flip3--` `rem-log-exp` `cos-mult` `flip--` `sin-mult` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 96

Calls

4 calls:

10.0ms	(* (cos x) (cos eps))
12.0ms	(* (sin x) (sin eps))
78.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
4.0ms	(log (exp (* (sin x) (sin eps))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos x) (cos eps))
47.0ms	(* (sin x) (sin eps))
140.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
48.0ms	(log (exp (* (sin x) (sin eps))))

simplify43.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	358	1094
1	1206	803
2	5001	791
done	5001	791

prune324.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 16.6b

regimes236.0ms

Accuracy

86.8% (1.3b remaining)

Error of 16.4b against oracle of 15.1b and baseline of 24.9b

bsearch126.0ms

Steps

Iters	Range		Point
8	4.5561658934541904e-07	0.004858038437719416	1.2809888646122553e-06
9	-7.855206308743333e-09	-4.1211929036737376e-16	-1.1531548156266982e-10

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	37
1	40	37
done	40	37

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4536×	body	1280	valid
533.0ms	627×	body	2560	valid
370.0ms	1809×	body	640	valid
101.0ms	695×	body	320	valid
25.0ms	254×	body	160	valid
4.0ms	79×	body	80	valid