Details

sample46.0ms

Algorithm

intervals

Results

18.0ms	40×	body	2560	valid
9.0ms	40×	body	1280	valid
6.0ms	40×	body	640	valid
3.0ms	30×	body	320	valid
3.0ms	89×	body	80	valid
1.0ms	17×	body	160	valid

simplify7.0ms

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: 29.3b

localize10.0ms

Local error

Found 2 expressions with local error:

2.6b	(- 1.0 (cos x))
12.3b	(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

4.0ms	(- 1.0 (cos x))
7.0ms	(/ (- 1.0 (cos x)) (* x x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
44.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify67.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune104.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
2.6b	(- 1.0 (cos x))
2.6b	(- 1.0 (cos x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-sqr-sqrt`
156×	`times-frac`
143×	`*-un-lft-identity`
104×	`sqrt-prod`
89×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 206

Calls

4 calls:

6.0ms	(/ (sqrt (- 1.0 (cos x))) x)
25.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series182.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (sqrt (- 1.0 (cos x))) x)
43.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
24.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify96.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	667	2403
1	3340	2087
2	5001	1922

prune394.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sqrt (log (exp (- 1.0 (cos x))))) x) (/ (sqrt (- 1.0 (cos x))) x))
2.6b	(- 1.0 (cos x))
2.6b	(- 1.0 (cos x))
2.8b	(log (exp (- 1.0 (cos x))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-sqr-sqrt`
72×	`times-frac`
61×	`*-un-lft-identity`
48×	`sqrt-prod`
43×	`add-cube-cbrt`
40×	`associate-l`
28×	`associate-r`
24×	`log-pow`
20×	`exp-prod`
16×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
8×	`add-log-exp`
5×	`log-prod`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
3×	`sub-neg`
2×	`flip3--` `diff-log` `exp-sum` `flip--` `div-inv`
1×	`frac-times` `log-div` `exp-diff` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 145

Calls

4 calls:

30.0ms	(* (/ (sqrt (log (exp (- 1.0 (cos x))))) x) (/ (sqrt (- 1.0 (cos x))) x))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
8.0ms	(log (exp (- 1.0 (cos x))))

series105.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (/ (sqrt (log (exp (- 1.0 (cos x))))) x) (/ (sqrt (- 1.0 (cos x))) x))
19.0ms	(- 1.0 (cos x))
23.0ms	(- 1.0 (cos x))
20.0ms	(log (exp (- 1.0 (cos x))))

simplify64.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	610	1629
1	2502	1227
2	5001	1130

prune368.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ 1.0 (cos x))
2.6b	(- 1.0 (cos x))
2.6b	(- (* 1.0 1.0) (* (cos x) (cos x)))
2.8b	(log (exp (- 1.0 (cos x))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-log-exp`
6×	`add-cube-cbrt` `log-pow`
5×	`pow1` `log-prod` `exp-prod`
4×	`add-exp-log` `add-cbrt-cube`
3×	`sub-neg` `difference-of-squares`
2×	`flip3--` `diff-log` `exp-sum` `flip--` `distribute-lft-out--`
1×	`+-commutative` `log-div` `sqr-cos` `flip3-+` `exp-diff` `rem-log-exp` `sum-log` `flip-+` `distribute-lft-out` `associate--r+`

Counts

4 → 60

Calls

4 calls:

3.0ms	(+ 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
4.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))
5.0ms	(log (exp (- 1.0 (cos x))))

series84.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
37.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))
19.0ms	(log (exp (- 1.0 (cos x))))

simplify66.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	247	350
1	813	312
2	2259	312
3	5001	312

prune229.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes55.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.7b

bsearch82.0ms

Steps

Iters	Range		Point
10	9.558161037350472e-13	0.8818080259852756	0.034074837610598666
5	-0.041603525395973645	-0.015510049556855336	-0.03305941206486147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	48
1	63	48

end0.0ms

sample1.5s

Algorithm

intervals

Results

721.0ms	1582×	body	2560	valid
286.0ms	1255×	body	1280	valid
198.0ms	1427×	body	640	valid
99.0ms	942×	body	320	valid
68.0ms	2280×	body	80	valid
52.0ms	514×	body	160	valid