Details

sample91.0ms

Algorithm

intervals

Results

51.0ms	152×	body	1280	valid
17.0ms	20×	body	2560	valid
8.0ms	41×	body	640	valid
3.0ms	24×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	6×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize8.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (cos (+ x eps)) (cos x))
1.8b	(cos (+ x eps))

rewrite11.0ms

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:

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

series71.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (cos (+ x eps)) (cos x))
22.0ms	(cos (+ x eps))

simplify114.0ms

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

prune90.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.8b

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))
2.3b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite22.0ms

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:

4.0ms	(+ (* (sin x) (sin eps)) (cos x))
3.0ms	(* (cos x) (cos eps))
4.0ms	(* (sin x) (sin eps))
9.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ (* (sin x) (sin eps)) (cos x))
45.0ms	(* (cos x) (cos eps))
45.0ms	(* (sin x) (sin eps))
133.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (35.0ms)

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

prune243.0ms

Filtered

77 candidates to 53 candidates (68.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(* (cos x) (cos x))
0.3b	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
3.5b	(- (* (cos x) (cos eps)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

52×	`pow1`
20×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-sqr` `pow-prod-up` `sin-mult`
4×	`swap-sqr`
3×	`pow-plus` `*-commutative`
2×	`pow2` `cos-mult` `unswap-sqr`
1×	`frac-times` `sub-neg` `sqr-cos` `flip3--` `diff-log` `div-sub` `associate-r/` `associate-l/` `frac-sub` `flip--` `associate--r-`

Counts

4 → 97

Calls

4 calls:

4.0ms	(* (sin x) (sin eps))
4.0ms	(* (cos x) (cos x))
14.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
32.0ms	(- (* (cos x) (cos eps)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

series412.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin x) (sin eps))
16.0ms	(* (cos x) (cos x))
55.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
293.0ms	(- (* (cos x) (cos eps)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

simplify53.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	397	967
1	1718	824
2	5001	771

prune303.0ms

Filtered

109 candidates to 60 candidates (55.0%)

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.6b

localize17.0ms

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))
2.3b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
2.3b	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

rewrite65.0ms

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:

30.0ms	(exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))))
4.0ms	(* (sin x) (sin eps))
9.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
21.0ms	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))))
43.0ms	(* (sin x) (sin eps))
132.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
127.0ms	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

simplify123.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

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

prune221.0ms

Filtered

81 candidates to 55 candidates (67.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.6b

regimes194.0ms

Accuracy

84.2% (1.6b remaining)

Error of 16.1b against oracle of 14.4b and baseline of 24.9b

bsearch127.0ms

Steps

Iters	Range		Point
10	2.5376598660456323e-18	0.0004320794088804456	9.389133638635202e-07
9	-8.316448984380752e-05	-4.3283440329487994e-10	-1.5330496627903165e-07

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	38
1	40	38

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	4449×	body	1280	valid
620.0ms	693×	body	2560	valid
384.0ms	1793×	body	640	valid
95.0ms	679×	body	320	valid
31.0ms	309×	body	160	valid
4.0ms	77×	body	80	valid