Details

sample279.0ms

Algorithm

intervals

Results

212.0ms	86×	body	5120	exit
28.0ms	76×	body	1280	valid
12.0ms	50×	body	640	valid
6.0ms	85×	body	80	valid
5.0ms	32×	body	320	valid
1.0ms	13×	body	160	valid

simplify453.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5061	12

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 42.1b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
0.5b	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
3.8b	(- (pow (exp x) 2.0) 1.0)
3.9b	(- (exp x) 1.0)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
87×	`*-un-lft-identity`
71×	`times-frac`
52×	`difference-of-squares`
41×	`sqrt-prod`
31×	`add-cube-cbrt`
28×	`distribute-lft-out--`
12×	`unpow-prod-down` `sqr-pow`
8×	`add-log-exp`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r*` `flip--`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 147

Calls

4 calls:

11.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
11.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
5.0ms	(- (pow (exp x) 2.0) 1.0)
7.0ms	(- (exp x) 1.0)

series40.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
15.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
4.0ms	(- (pow (exp x) 2.0) 1.0)
10.0ms	(- (exp x) 1.0)

simplify77.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4962	2789
1	4962	2789

prune286.0ms

Filtered

113 candidates to 159 candidates (-40.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	158	2	160

Merged error: 0.5b

Counts

160 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (/ x (sqrt 2)) x) 3/16)
0.1b	(* (/ x (sqrt 2)) x)
0.5b	(/ x (sqrt 2))
0.5b	(/ x (sqrt 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
56×	`times-frac`
49×	`add-cube-cbrt` `*-un-lft-identity`
34×	`sqrt-prod`
23×	`associate-l`
22×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-r` `associate-/l*`
4×	`cbrt-undiv` `div-exp` `pow-prod-down` `add-log-exp`
3×	`associate-*l/` `div-inv` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`

Counts

4 → 141

Calls

4 calls:

7.0ms	(* (* (/ x (sqrt 2)) x) 3/16)
8.0ms	(* (/ x (sqrt 2)) x)
4.0ms	(/ x (sqrt 2))
4.0ms	(/ x (sqrt 2))

series22.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (* (/ x (sqrt 2)) x) 3/16)
6.0ms	(* (/ x (sqrt 2)) x)
5.0ms	(/ x (sqrt 2))
5.0ms	(/ x (sqrt 2))

simplify51.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4935	1163
1	4935	1163

prune248.0ms

Filtered

98 candidates to 153 candidates (-56.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	152	3	155

Merged error: 0.5b

Counts

155 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ x (sqrt 2))) (cbrt (/ x (sqrt 2))))
0.6b	(cbrt (/ x (sqrt 2)))
0.6b	(cbrt (/ x (sqrt 2)))
0.6b	(cbrt (/ x (sqrt 2)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

190×	`cbrt-prod`
163×	`add-sqr-sqrt`
154×	`times-frac`
103×	`add-cube-cbrt` `*-un-lft-identity`
77×	`sqrt-prod`
31×	`swap-sqr`
25×	`associate-r` `associate-l`
16×	`unswap-sqr`
11×	`pow1`
9×	`pow1/3`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 211

Calls

4 calls:

19.0ms	(* (cbrt (/ x (sqrt 2))) (cbrt (/ x (sqrt 2))))
3.0ms	(cbrt (/ x (sqrt 2)))
3.0ms	(cbrt (/ x (sqrt 2)))
3.0ms	(cbrt (/ x (sqrt 2)))

series132.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cbrt (/ x (sqrt 2))) (cbrt (/ x (sqrt 2))))
32.0ms	(cbrt (/ x (sqrt 2)))
28.0ms	(cbrt (/ x (sqrt 2)))
30.0ms	(cbrt (/ x (sqrt 2)))

simplify74.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5162	2741

prune610.0ms

Filtered

140 candidates to 223 candidates (-59.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	223	3	226

Merged error: 0.5b

Counts

226 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
0.5b	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))))
3.8b	(- (pow (exp x) 2.0) 1.0)
3.8b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

465×	`times-frac`
385×	`add-sqr-sqrt`
320×	`*-un-lft-identity`
243×	`sqrt-prod`
241×	`difference-of-squares`
136×	`add-cube-cbrt`
69×	`unpow-prod-down` `sqr-pow`
57×	`distribute-lft-out`
35×	`distribute-lft-out--`
34×	`unpow2`
17×	`associate-/r/`
9×	`div-inv`
8×	`flip3-+` `flip-+` `add-log-exp`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`associate-/r*`
3×	`rem-sqrt-square` `flip3--` `flip--`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 344

Calls

4 calls:

9.0ms	(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
36.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))))
5.0ms	(- (pow (exp x) 2.0) 1.0)
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

series27.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
4.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))))
4.0ms	(- (pow (exp x) 2.0) 1.0)
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

simplify115.0ms

Algorithm

egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5071	11156

prune737.0ms

Filtered

204 candidates to 356 candidates (-74.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	356	0	356
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	356	3	359

Merged error: 0.5b

Counts

359 → 3

regimes44.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.7b

bsearch21.0ms

Steps

Iters	Range		Point
9	-0.00018277710226217338	-1.6134268669450407e-10	-1.6951281397363915e-07

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	56
1	36	56

end0.0ms

sample2.4s

Algorithm

intervals

Results

821.0ms	2267×	body	1280	valid
707.0ms	2610×	body	5120	exit
391.0ms	1686×	body	640	valid
130.0ms	867×	body	320	valid
124.0ms	2811×	body	80	valid
42.0ms	421×	body	160	valid

Details

sample279.0ms

simplify453.0ms

prune10.0ms

localize21.0ms

rewrite42.0ms

series40.0ms

simplify77.0ms

prune286.0ms

localize9.0ms

rewrite28.0ms

series22.0ms

simplify51.0ms

prune248.0ms

localize13.0ms

rewrite44.0ms

series132.0ms

simplify74.0ms

prune610.0ms

localize12.0ms

rewrite82.0ms

series27.0ms

simplify115.0ms

prune737.0ms

regimes44.0ms

bsearch21.0ms

simplify2.0ms

end0.0ms

sample2.4s

Profiling