Details

sample95.0ms

Algorithm

intervals

Results

51.0ms	141×	body	1280	valid
19.0ms	22×	body	2560	valid
12.0ms	62×	body	640	valid
3.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	80	valid

simplify6.0ms

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: 40.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (cos (+ x eps)) (cos x))
3.4b	(cos (+ x eps))

rewrite12.0ms

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:

7.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series73.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify75.0ms

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

prune123.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.4b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(fma (sin x) (sin eps) (cos x))
1.1b	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `prod-diff` `log1p-expm1-u`
2×	`fma-udef`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `cos-mult` `*-commutative` `flip--` `cbrt-unprod` `associate--r+` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

5.0ms	(* (cos x) (cos eps))
1.0ms	(fma (sin x) (sin eps) (cos x))
5.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

series232.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* (cos x) (cos eps))
51.0ms	(fma (sin x) (sin eps) (cos x))
135.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify115.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	235	486
1	832	409
2	4494	406
3	5001	404

prune218.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.3b

localize14.0ms

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))
1.1b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite29.0ms

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:

4.0ms	(* (cos x) (cos eps))
6.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms	(* (sin x) (sin eps))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series303.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos x) (cos eps))
85.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (sin x) (sin eps))
128.0ms	(- (- (* (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

prune316.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps))))
0.4b	(/ (* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (fma (cos x) (cos eps) (* (sin x) (sin eps))))
2.3b	(- (/ (* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (fma (cos x) (cos eps) (* (sin x) (sin eps)))) (cos x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
23×	`prod-diff`
15×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-*r/`
7×	`fma-neg`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`div-inv` `sin-mult`
4×	`expm1-log1p-u` `cos-mult` `log1p-expm1-u` `associate-/l/`
3×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `prod-exp` `associate-/r*` `flip--` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `sub-div` `unswap-sqr`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 122

Calls

4 calls:

5.0ms	(* (sin x) (sin eps))
8.0ms	(* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps))))
9.0ms	(/ (* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (fma (cos x) (cos eps) (* (sin x) (sin eps))))
13.0ms	(- (/ (* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (fma (cos x) (cos eps) (* (sin x) (sin eps)))) (cos x))

series428.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin x) (sin eps))
169.0ms	(* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps))))
83.0ms	(/ (* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (fma (cos x) (cos eps) (* (sin x) (sin eps))))
127.0ms	(- (/ (* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (fma (cos x) (cos eps) (* (sin x) (sin eps)))) (cos x))

simplify86.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	535	3034
1	2540	2568
2	5001	2219

prune389.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.2b

regimes136.0ms

Accuracy

84.6% (1.5b remaining)

Error of 15.8b against oracle of 14.3b and baseline of 24.2b

bsearch135.0ms

Steps

Iters	Range		Point
11	3.318030725202088e-29	4.9177062248324165e-05	3.284559791012932e-07
11	-358284796.04772377	-9.565599748882727e-17	-1.133154992718873e-10

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	16
1	33	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	4393×	body	1280	valid
546.0ms	632×	body	2560	valid
381.0ms	1898×	body	640	valid
102.0ms	708×	body	320	valid
27.0ms	286×	body	160	valid
4.0ms	83×	body	80	valid