Details

sample57.0ms

Algorithm

intervals

Results

25.0ms	52×	body	2560	valid
11.0ms	37×	body	1280	valid
7.0ms	48×	body	640	valid
2.0ms	25×	body	320	valid
2.0ms	78×	body	80	valid
1.0ms	16×	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: 30.1b

localize6.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1.0 (cos x))
15.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite26.0ms

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:

6.0ms	(- 1.0 (cos x))
19.0ms	(/ (- 1.0 (cos x)) (* x x))

series58.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(- 1.0 (cos x))
42.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify62.0ms

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

prune106.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.1b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))

rewrite105.0ms

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:

15.0ms	(/ (sqrt (- 1.0 (cos x))) x)
64.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))

series158.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (sqrt (- 1.0 (cos x))) x)
43.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
16.0ms	(- 1.0 (cos x))
17.0ms	(- 1.0 (cos x))

simplify89.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (71.0ms)

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

prune379.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.1b	(- 1.0 (cos x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 147

Calls

3 calls:

20.0ms	(/ (/ (- 1.0 (cos x)) x) x)
19.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series97.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (/ (- 1.0 (cos x)) x) x)
42.0ms	(/ (- 1.0 (cos x)) x)
17.0ms	(- 1.0 (cos x))

simplify55.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	531	1270
1	1899	1197
2	5001	1186

prune267.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (log (exp (- 1.0 (cos x))))) x) (/ (sqrt (- 1.0 (cos x))) x))
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))
2.2b	(log (exp (- 1.0 (cos x))))

rewrite133.0ms

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:

96.0ms	(* (/ (sqrt (log (exp (- 1.0 (cos x))))) x) (/ (sqrt (- 1.0 (cos x))) x))
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))
19.0ms	(log (exp (- 1.0 (cos x))))

series92.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (/ (sqrt (log (exp (- 1.0 (cos x))))) x) (/ (sqrt (- 1.0 (cos x))) x))
16.0ms	(- 1.0 (cos x))
16.0ms	(- 1.0 (cos x))
17.0ms	(log (exp (- 1.0 (cos x))))

simplify60.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (47.0ms)

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

prune337.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes57.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 30.1b

bsearch65.0ms

Steps

Iters	Range		Point
8	0.00015704816827310668	9.114942375872904	0.03119086400759214
9	-0.2945747773639613	-3.489101517161873e-08	-0.034379388822557394

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	29
1	45	29
2	45	29

end0.0ms

sample1.6s

Algorithm

intervals

Results

740.0ms	1577×	body	2560	valid
287.0ms	1259×	body	1280	valid
202.0ms	1462×	body	640	valid
91.0ms	908×	body	320	valid
72.0ms	2355×	body	80	valid
31.0ms	439×	body	160	valid