Details

sample154.0ms

Algorithm

intervals

Results

78.0ms	54×	body	2560	valid
41.0ms	90×	body	1280	valid
12.0ms	51×	body	640	valid
8.0ms	2×	body	5120	valid
4.0ms	28×	body	320	valid
2.0ms	21×	body	160	valid
1.0ms	10×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.6b	(- 1.0 (cos x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify81.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune162.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.9b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.6b	(- 1.0 (cos x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series140.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
41.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
40.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify91.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766

prune323.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.5b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 189

Calls

4 calls:

22.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
2.0ms	(pow (cos x) 3)
4.0ms	(+ (cos x) 1.0)
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series225.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
28.0ms	(pow (cos x) 3)
10.0ms	(+ (cos x) 1.0)
52.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify96.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	617	3027
1	2695	2961
2	5001	2954

prune467.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.0b	(log (exp (pow (cos x) 3)))
1.5b	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
14×	`log-pow`
12×	`add-cube-cbrt` `exp-prod`
7×	`pow1` `unpow-prod-down` `cube-prod` `add-log-exp`
6×	`log-prod`
5×	`add-exp-log` `add-cbrt-cube`
4×	`difference-of-squares`
3×	`pow-unpow` `associate--r+` `sqr-pow`
2×	`cube-mult` `unpow3` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `flip3-+` `diff-log` `rem-log-exp` `pow-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 80

Calls

4 calls:

3.0ms	(pow (cos x) 3)
4.0ms	(+ (cos x) 1.0)
4.0ms	(log (exp (pow (cos x) 3)))
16.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series122.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (cos x) 3)
10.0ms	(+ (cos x) 1.0)
36.0ms	(log (exp (pow (cos x) 3)))
49.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

simplify41.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	296	446
1	1109	381
2	5001	373

prune261.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

regimes192.0ms

Accuracy

98.2% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	38
1	48	38

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.1s	1576×	body	2560	valid
1.4s	2771×	body	1280	valid
443.0ms	1890×	body	640	valid
148.0ms	912×	body	320	valid
52.0ms	484×	body	160	valid
23.0ms	362×	body	80	valid
18.0ms	5×	body	5120	valid