Details

sample66.0ms

Algorithm

intervals

Results

32.0ms	60×	body	2560	valid
10.0ms	33×	body	1280	valid
8.0ms	40×	body	640	valid
4.0ms	80×	body	80	valid
3.0ms	22×	body	320	valid
2.0ms	21×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize6.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
16.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 58

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
10.0ms	(/ (- 1.0 (cos x)) (* x x))

series66.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
49.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	279	446
1	1006	326
2	5001	317

prune127.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ 1.0 (cos x))
0.4b	(pow (cos x) 3)
1.3b	(- (pow 1.0 3) (pow (cos x) 3))
16.7b	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (* x x))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

309×	`add-sqr-sqrt`
229×	`times-frac`
213×	`*-un-lft-identity`
162×	`unpow-prod-down` `cube-prod`
144×	`prod-diff`
141×	`add-cube-cbrt`
112×	`difference-of-squares`
82×	`sqr-pow`
79×	`associate-/l*`
35×	`distribute-lft-out--`
26×	`cube-mult` `unpow3`
17×	`add-exp-log` `add-cbrt-cube`
12×	`fma-neg`
8×	`add-log-exp`
7×	`difference-cubes`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `div-inv`
2×	`div-sub` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `pow-exp` `clear-num` `associate-/r*` `sum-log` `flip--` `flip-+` `associate-/l/` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 415

Calls

4 calls:

3.0ms	(+ 1.0 (cos x))
2.0ms	(pow (cos x) 3)
22.0ms	(- (pow 1.0 3) (pow (cos x) 3))
61.0ms	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (* x x))

series237.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ 1.0 (cos x))
27.0ms	(pow (cos x) 3)
51.0ms	(- (pow 1.0 3) (pow (cos x) 3))
149.0ms	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (* x x))

simplify182.0ms

Algorithm

egg-herbie

Counts

427 → 427

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1211	6148
1	4958	5139
2	5001	5139

prune694.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ 1.0 (cos x))
0.4b	(+ 1.0 (cos x))
0.4b	(+ 1.0 (cos x))
1.5b	(- 1.0 (cos x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`add-log-exp`
9×	`fma-def` `prod-diff`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`+-commutative` `flip3-+` `fma-neg` `sum-log` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 79

Calls

4 calls:

3.0ms	(+ 1.0 (cos x))
3.0ms	(+ 1.0 (cos x))
7.0ms	(+ 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series48.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ 1.0 (cos x))
10.0ms	(+ 1.0 (cos x))
10.0ms	(+ 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify113.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	191	445
1	624	333
2	3273	324
3	5002	321

prune292.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ 1.0 (cos x))
0.4b	(+ 1.0 (cos x))
0.4b	(+ 1.0 (cos x))
1.5b	(- (* 1.0 1.0) (* (cos x) (cos x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`add-log-exp`
9×	`fma-def`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`
1×	`sub-neg` `sqr-cos` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `associate--r+` `difference-of-squares`

Counts

4 → 69

Calls

4 calls:

3.0ms	(+ 1.0 (cos x))
3.0ms	(+ 1.0 (cos x))
3.0ms	(+ 1.0 (cos x))
7.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ 1.0 (cos x))
9.0ms	(+ 1.0 (cos x))
9.0ms	(+ 1.0 (cos x))
32.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	188	353
1	638	308
2	2124	304
3	5001	298

prune284.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes74.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 30.9b

bsearch83.0ms

Steps

Iters	Range		Point
8	0.007618006570916684	21.02059315853866	0.033083936116779844
11	-7.192008941699975e+16	-0.00038629318802677867	-0.02946646932882836

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	29
1	38	29

end0.0ms

sample2.0s

Algorithm

intervals

Results

880.0ms	1617×	body	2560	valid
371.0ms	1223×	body	1280	valid
300.0ms	1502×	body	640	valid
139.0ms	902×	body	320	valid
110.0ms	2243×	body	80	valid
52.0ms	513×	body	160	valid