Details

sample94.0ms

Algorithm

intervals

Results

55.0ms	150×	body	1280	valid
13.0ms	64×	body	640	valid
11.0ms	13×	body	2560	valid
2.0ms	17×	body	320	valid
1.0ms	12×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.3b

localize9.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (cos (+ x eps)) (cos x))
3.7b	(cos (+ x eps))

rewrite27.0ms

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:

16.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series68.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

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

prune121.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.2b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite112.0ms

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:

10.0ms	(* (cos x) (cos eps))
20.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
13.0ms	(* (sin x) (sin eps))
67.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series292.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos x) (cos eps))
77.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
48.0ms	(* (sin x) (sin eps))
126.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify48.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	381	988
1	1342	837
2	5002	822

prune318.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.5b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.5b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.3b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite102.0ms

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:

14.0ms	(* (sin x) (sin eps))
42.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
44.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin x) (sin eps))
96.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
96.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
136.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify87.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (77.0ms)

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

prune385.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 12.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
2.2b	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
27.3b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
20×	`prod-diff`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`cbrt-prod`
13×	`associate--l+`
9×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cube-mult` `unpow-prod-down` `pow-unpow` `fma-neg` `diff-log` `unpow3` `cube-prod` `associate-r` `associate-l` `sin-mult` `sqr-pow`
2×	`cube-div` `sub-neg` `pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt`
1×	`associate--l-` `pow-to-exp` `cbrt-div` `flip3--` `pow1/3` `*-commutative` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

12.0ms	(* (sin x) (sin eps))
10.0ms	(pow (* (sin x) (sin eps)) 3)
103.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
5.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series276.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin x) (sin eps))
61.0ms	(pow (* (sin x) (sin eps)) 3)
124.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
44.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify58.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	433	1278
1	1704	976
2	5002	949

prune352.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 12.3b

regimes187.0ms

Accuracy

87.4% (1.2b remaining)

Error of 15.9b against oracle of 14.7b and baseline of 24.2b

bsearch166.0ms

Steps

Iters	Range		Point
9	2.15302222000921e-20	1.638622225374179e-14	1.6114711274948726e-14
10	-12786724.3536924	-3.489101517161873e-08	-8.194833237230457e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	74
1	65	74
2	65	74

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4550×	body	1280	valid
565.0ms	648×	body	2560	valid
392.0ms	1796×	body	640	valid
97.0ms	659×	body	320	valid
26.0ms	259×	body	160	valid
5.0ms	88×	body	80	valid