Details

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 53.90625%

Results

31.0ms	83×	body	1280	valid
14.0ms	58×	body	640	valid
4.0ms	29×	body	320	valid
3.0ms	78×	body	80	valid
3.0ms	81×	body	80	overflowed
1.0ms	10×	body	160	valid

simplify409.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2626	7
7	5001	7

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 44.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.7b	(- (exp x) 1.0)
3.9b	(- (exp (* 2.0 x)) 1.0)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
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 → 123

Calls

4 calls:

10.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
19.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)
6.0ms	(- (exp (* 2.0 x)) 1.0)

series34.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
8.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
2.0ms	(- (exp x) 1.0)
11.0ms	(- (exp (* 2.0 x)) 1.0)

simplify120.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4265	1301
3	5002	1293

prune245.0ms

Filtered

92 candidates to 135 candidates (-46.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	3	136

Merged error: 0.0b

Counts

136 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ 1.0 (* 0.5 x)))
9.2b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sqrt-prod`
2×	`flip3-+` `sqrt-div` `associate-*r/` `flip-+` `add-log-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 37

Calls

2 calls:

5.0ms	(* x (+ 1.0 (* 0.5 x)))
8.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series12.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(* x (+ 1.0 (* 0.5 x)))
6.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	279	280
1	1132	268
2	5002	256

prune66.0ms

Filtered

30 candidates to 43 candidates (-43.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	43	3	46

Merged error: 0.0b

Counts

46 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
0.1b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.2b	(/ (pow x 2) (sqrt 2.0))
0.5b	(/ x (sqrt 2.0))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
108×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
67×	`sqrt-prod`
52×	`associate-l`
41×	`unpow-prod-down`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`add-log-exp` `unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r`
4×	`associate-*r/` `prod-exp`
3×	`cbrt-undiv` `sum-log` `div-inv`
2×	`distribute-rgt-in` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `flip3-+` `frac-add` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `flip-+` `difference-of-squares`
1×	`+-commutative` `associate-+r+` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out--`

Counts

4 → 221

Calls

4 calls:

9.0ms	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
24.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
6.0ms	(/ (pow x 2) (sqrt 2.0))
4.0ms	(/ x (sqrt 2.0))

series26.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
7.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
6.0ms	(/ (pow x 2) (sqrt 2.0))
6.0ms	(/ x (sqrt 2.0))

simplify85.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	723	1889
1	3042	1708
2	5001	1694

prune469.0ms

Filtered

143 candidates to 233 candidates (-62.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	233	3	236

Merged error: 0b

Counts

236 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow x 2) (sqrt 2.0))
0.5b	(/ x (sqrt 2.0))
3.8b	(log (exp (/ x (sqrt 2.0))))
9.8b	(+ (* 0.5 (log (exp (/ x (sqrt 2.0))))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
67×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
48×	`sqrt-prod`
23×	`log-pow`
22×	`exp-prod`
21×	`unpow-prod-down`
12×	`associate-/r*`
11×	`add-exp-log` `associate-/l*`
9×	`log-prod` `add-log-exp`
8×	`add-cbrt-cube`
7×	`unpow2` `sqr-pow`
6×	`associate-+l+`
5×	`pow1`
4×	`div-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sum-log` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `clear-num`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `rem-log-exp` `pow-exp` `flip-+`

Counts

4 → 168

Calls

4 calls:

6.0ms	(/ (pow x 2) (sqrt 2.0))
4.0ms	(/ x (sqrt 2.0))
6.0ms	(log (exp (/ x (sqrt 2.0))))
13.0ms	(+ (* 0.5 (log (exp (/ x (sqrt 2.0))))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))

series25.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (pow x 2) (sqrt 2.0))
6.0ms	(/ x (sqrt 2.0))
6.0ms	(log (exp (/ x (sqrt 2.0))))
7.0ms	(+ (* 0.5 (log (exp (/ x (sqrt 2.0))))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	462	1325
1	1659	1141
2	5001	1119

prune374.0ms

Filtered

110 candidates to 180 candidates (-63.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	180	3	183

Merged error: 0b

Counts

183 → 3

regimes42.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.9b

bsearch21.0ms

Steps

Iters	Range		Point
9	-0.8430794056005784	-8.448379255005245e-07	-3.3852818843480064e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	29
1	40	29

end0.0ms

sample3.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 53.90625%

Results

801.0ms	2266×	body	1280	valid
378.0ms	1655×	body	640	valid
125.0ms	2905×	body	80	valid
119.0ms	806×	body	320	valid
105.0ms	2699×	body	80	overflowed
42.0ms	412×	body	160	valid

Details

sample1.8s

simplify409.0ms

prune5.0ms

localize11.0ms

rewrite45.0ms

series34.0ms

simplify120.0ms

prune245.0ms

localize6.0ms

rewrite14.0ms

series12.0ms

simplify36.0ms

prune66.0ms

localize13.0ms

rewrite53.0ms

series26.0ms

simplify85.0ms

prune469.0ms

localize15.0ms

rewrite39.0ms

series25.0ms

simplify49.0ms

prune374.0ms

regimes42.0ms

bsearch21.0ms

simplify2.0ms

end0.0ms

sample3.3s

Profiling