Details

sample86.0ms

Algorithm

intervals

Results

46.0ms	141×	body	1280	valid
15.0ms	18×	body	2560	valid
11.0ms	53×	body	640	valid
4.0ms	28×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	3×	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: 40.1b

localize15.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (cos (+ x eps)) (cos x))
2.7b	(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:

6.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series64.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify80.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (71.0ms)

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

prune122.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.3b	(* (sin x) (sin eps))
3.8b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite27.0ms

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))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms	(* (sin x) (sin eps))
10.0ms	(- (- (* (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)))
49.0ms	(* (sin x) (sin eps))
127.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify49.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (41.0ms)

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

prune314.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (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))
3.8b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite25.0ms

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:

5.0ms	(* (sin x) (sin eps))
9.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
9.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
1.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series387.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin x) (sin eps))
100.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
101.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
141.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify90.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (82.0ms)

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

prune409.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
0.2b	(fma (sin x) (sin eps) (cos x))
3.8b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))
3.8b	(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `log-pow` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
2×	`exp-sum`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 52

Calls

4 calls:

2.0ms	(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
1.0ms	(fma (sin x) (sin eps) (cos x))
1.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))
3.0ms	(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))

series475.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
57.0ms	(fma (sin x) (sin eps) (cos x))
138.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))
143.0ms	(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	137	627
1	357	554
2	1340	554
3	5002	551

prune230.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.7b

regimes232.0ms

Accuracy

86.6% (1.3b remaining)

Error of 15.6b against oracle of 14.3b and baseline of 24.3b

bsearch155.0ms

Steps

Iters	Range		Point
9	6.076487468149909e-10	0.8818080259852756	1.1618945885559161e-07
8	-1.1644421995593973e-08	-1.289801985686209e-11	-8.54115634291998e-10

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	67
1	49	67

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4498×	body	1280	valid
535.0ms	601×	body	2560	valid
380.0ms	1840×	body	640	valid
95.0ms	680×	body	320	valid
28.0ms	286×	body	160	valid
5.0ms	95×	body	80	valid