Details

sample95.0ms

Algorithm

intervals

Results

49.0ms	158×	body	1280	valid
22.0ms	26×	body	2560	valid
10.0ms	47×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	4×	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: 36.6b

localize15.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.1b	(cos (+ x eps))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

15.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series63.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

simplify113.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164

prune83.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
1.9b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
3×	`cos-mult`
2×	`flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip--` `sin-mult` `associate--r+`

Counts

4 → 65

Calls

4 calls:

13.0ms	(+ (* (sin x) (sin eps)) (cos x))
11.0ms	(* (cos x) (cos eps))
12.0ms	(* (sin x) (sin eps))
32.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ (* (sin x) (sin eps)) (cos x))
36.0ms	(* (cos x) (cos eps))
40.0ms	(* (sin x) (sin eps))
120.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	576
2	5002	567

prune251.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))))
0.2b	(* (sin x) (sin eps))
1.9b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
1.9b	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-log-exp`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`log-prod`
4×	`diff-log` `exp-sum` `log-pow`
3×	`sub-neg` `associate-r` `associate-l` `rem-exp-log`
2×	`exp-diff` `sum-log` `cos-mult` `frac-sub`
1×	`log-div` `flip3--` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `sin-mult` `associate--r+` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

77.0ms	(exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))))
12.0ms	(* (sin x) (sin eps))
30.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
52.0ms	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))))
41.0ms	(* (sin x) (sin eps))
122.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
116.0ms	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

simplify133.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	309	860
1	1092	782
2	4878	771
3	5001	771

prune271.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 13.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.4b	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
0.5b	(pow (* (cos x) (cos eps)) 3)
1.8b	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
20×	`add-exp-log` `add-cbrt-cube`
18×	`add-sqr-sqrt` `pow-prod-down`
10×	`*-un-lft-identity`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `difference-of-squares` `sqr-pow`
7×	`cube-div` `cos-mult`
6×	`unpow-prod-down` `pow-unpow` `cube-prod` `add-log-exp`
4×	`pow-sqr` `pow-prod-up`
3×	`pow-pow` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `flip3-+` `pow-plus` `unpow3` `frac-sub` `flip-+`
1×	`difference-cubes` `pow2` `frac-times` `sub-neg` `flip3--` `diff-log` `associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-l/` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 109

Calls

4 calls:

43.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
15.0ms	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
8.0ms	(pow (* (cos x) (cos eps)) 3)
57.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

series550.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
68.0ms	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
57.0ms	(pow (* (cos x) (cos eps)) 3)
376.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

simplify95.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	538	1143
1	2688	1064
2	5001	1060

prune353.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 13.8b

regimes296.0ms

Accuracy

83.2% (1.7b remaining)

Error of 15.9b against oracle of 14.2b and baseline of 24.3b

bsearch133.0ms

Steps

Iters	Range		Point
11	4.083453529187016e-23	0.5429513389937057	9.805431973736002e-10
7	-1.5317450828987306e-09	-4.0039902443278174e-11	-1.3208939428373893e-09

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	28
1	36	28

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4474×	body	1280	valid
528.0ms	627×	body	2560	valid
385.0ms	1866×	body	640	valid
93.0ms	636×	body	320	valid
29.0ms	305×	body	160	valid
10.0ms	92×	body	80	valid