Details

sample99.0ms

Algorithm

intervals

Results

50.0ms	150×	body	1280	valid
24.0ms	28×	body	2560	valid
12.0ms	51×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	2×	body	80	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: 41.6b

localize15.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
2.3b	(cos (+ x eps))

rewrite14.0ms

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:

8.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series64.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify83.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (74.0ms)

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

prune125.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.7b

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))
2.6b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite38.0ms

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)))
4.0ms	(* (sin x) (sin eps))
23.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series299.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos x) (cos eps))
84.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms	(* (sin x) (sin eps))
131.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify55.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	381	989
1	1342	838
2	5002	822

prune332.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 17.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
0.4b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.4b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.6b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-+l+` `fma-def`
4×	`pow1` `expm1-log1p-u` `flip3-+` `times-frac` `associate-/r*` `sum-log` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `diff-log` `associate-*r/` `div-exp` `prod-diff` `associate-/r/` `associate-/l/`
1×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 83

Calls

4 calls:

38.0ms	(/ (* (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
15.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
15.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series476.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (* (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
100.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
98.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
136.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify52.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	288	1375
1	1440	1074
2	5001	1067

prune426.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 17.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))) (+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (fma (sin x) (+ (- (sin eps)) (sin eps)) (cos x)))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
0.4b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.4b	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (fma (sin x) (+ (- (sin eps)) (sin eps)) (cos x)))
2.6b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
11×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`fma-def`
4×	`pow1` `expm1-log1p-u` `associate-+l+` `flip3-+` `times-frac` `associate-/r*` `flip-+` `log1p-expm1-u` `distribute-lft-out`
3×	`sum-log` `fma-udef`
2×	`cbrt-undiv` `+-commutative` `associate-*r/` `div-exp` `associate-/r/` `associate-/l/`
1×	`associate-+l-` `sub-neg` `associate-+r+` `frac-2neg` `diff-log` `prod-diff` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 80

Calls

4 calls:

23.0ms	(/ (* (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))) (+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (fma (sin x) (+ (- (sin eps)) (sin eps)) (cos x)))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
15.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
3.0ms	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (fma (sin x) (+ (- (sin eps)) (sin eps)) (cos x)))
0.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series760.0ms

Counts

4 → 12

Calls

4 calls:

417.0ms	(/ (* (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))) (+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (fma (sin x) (+ (- (sin eps)) (sin eps)) (cos x)))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
98.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
110.0ms	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (fma (sin x) (+ (- (sin eps)) (sin eps)) (cos x)))
136.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify54.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	372	2040
1	1760	1749
2	5001	1724

prune466.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 17.5b

regimes221.0ms

Accuracy

86.9% (1.3b remaining)

Error of 15.7b against oracle of 14.3b and baseline of 24.4b

bsearch101.0ms

Steps

Iters	Range		Point
11	9.428505616792786e-16	4321407464.299789	2.63597490420144e-08
3	-1.4160683835321931e-14	-1.1208393596952507e-14	-1.3976165695423843e-14

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	29
1	36	29

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4384×	body	1280	valid
581.0ms	668×	body	2560	valid
401.0ms	1880×	body	640	valid
97.0ms	680×	body	320	valid
30.0ms	300×	body	160	valid
5.0ms	88×	body	80	valid