Details

sample93.0ms

Algorithm

intervals

Results

49.0ms	142×	body	1280	valid
15.0ms	64×	body	640	valid
14.0ms	16×	body	2560	valid
4.0ms	25×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	1×	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: 39.1b

localize9.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
4.4b	(cos (+ x eps))

rewrite35.0ms

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:

23.0ms	(- (cos (+ x eps)) (cos x))
11.0ms	(cos (+ x eps))

series59.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

simplify112.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

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

prune94.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.7b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite78.0ms

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:

12.0ms	(* (cos x) (cos eps))
14.0ms	(+ (* (sin x) (sin eps)) (cos x))
17.0ms	(* (sin x) (sin eps))
32.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos x) (cos eps))
45.0ms	(+ (* (sin x) (sin eps)) (cos x))
46.0ms	(* (sin x) (sin eps))
115.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (36.0ms)

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

prune256.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
2.7b	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
25.2b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
3×	`pow-unpow` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `diff-log` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cos-mult` `frac-sub` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `flip3-+` `pow1/3` `sum-log` `*-commutative` `flip--` `rem-cbrt-cube` `flip-+` `associate--r+` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

14.0ms	(* (sin x) (sin eps))
10.0ms	(pow (* (sin x) (sin eps)) 3)
46.0ms	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
5.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series265.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin x) (sin eps))
63.0ms	(pow (* (sin x) (sin eps)) 3)
115.0ms	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
46.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	374	686
1	1626	613
2	5002	599

prune305.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 13.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
0.6b	(log (exp (* (cos x) (cos eps))))
7.3b	(- (log (exp (* (cos x) (cos eps)))) (+ (* (sin x) (sin eps)) (cos x)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `log-prod` `add-cbrt-cube`
4×	`log-pow`
3×	`associate-r` `associate-l` `associate--l+`
2×	`diff-log` `sum-log` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `sin-mult` `associate--r+` `difference-of-squares` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

14.0ms	(+ (* (sin x) (sin eps)) (cos x))
17.0ms	(* (sin x) (sin eps))
5.0ms	(log (exp (* (cos x) (cos eps))))
30.0ms	(- (log (exp (* (cos x) (cos eps)))) (+ (* (sin x) (sin eps)) (cos x)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (* (sin x) (sin eps)) (cos x))
40.0ms	(* (sin x) (sin eps))
40.0ms	(log (exp (* (cos x) (cos eps))))
116.0ms	(- (log (exp (* (cos x) (cos eps)))) (+ (* (sin x) (sin eps)) (cos x)))

simplify91.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	279	634
1	917	588
2	3215	580
3	5002	580

prune220.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 13.5b

regimes258.0ms

Accuracy

80.6% (2.0b remaining)

Error of 16.2b against oracle of 14.1b and baseline of 24.6b

bsearch113.0ms

Steps

Iters	Range		Point
7	1.6623184518082866e-06	8.950540206577903e-05	4.563413776044954e-06
8	-2.1657566707461104e-28	-6.488020188375565e-32	-2.1193854390859995e-28

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	46
1	46	46

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	4420×	body	1280	valid
558.0ms	635×	body	2560	valid
427.0ms	1848×	body	640	valid
124.0ms	730×	body	320	valid
30.0ms	288×	body	160	valid
4.0ms	79×	body	80	valid