Details

sample257.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 47.04159%

Results

186.0ms	64×	body	80	overflowed
29.0ms	77×	body	1280	valid
12.0ms	51×	body	640	valid
6.0ms	35×	body	320	valid
4.0ms	82×	body	80	valid
1.0ms	11×	body	160	valid

simplify410.0ms

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: 43.2b

Counts

2 → 1

localize25.0ms

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))
4.4b	(- (exp x) 1.0)
4.8b	(- (exp (* 2.0 x)) 1.0)

rewrite36.0ms

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:

9.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)
6.0ms	(- (exp (* 2.0 x)) 1.0)

series32.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(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)

simplify128.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (114.0ms)

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

prune241.0ms

Filtered

92 candidates to 135 candidates (-46.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	2	136

Merged error: 0.0b

Counts

136 → 2

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)))))
0.2b	(* (/ (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))

rewrite48.0ms

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)))))
20.0ms	(* (/ (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))

series28.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify84.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 2 (64.0ms)

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

prune476.0ms

Filtered

143 candidates to 233 candidates (-62.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	232	3	235

Merged error: 0b

Counts

235 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ x (sqrt 2.0))
0.7b	(* (sqrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))) (sqrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))))
9.4b	(sqrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
9.4b	(sqrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

48×	`sqrt-div`
43×	`add-sqr-sqrt`
36×	`sqrt-prod`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`associate-*r/`
24×	`flip3-+` `frac-add` `flip-+`
21×	`pow1`
18×	`times-frac`
16×	`frac-times`
10×	`sqrt-pow1` `pow1/2`
8×	`add-exp-log` `swap-sqr` `add-cbrt-cube`
6×	`associate-r` `associate-l` `associate-/r*`
5×	`pow-prod-up`
4×	`associate-*l/` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr` `associate-/l*`
2×	`rem-sqrt-square`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 146

Calls

4 calls:

4.0ms	(/ x (sqrt 2.0))
22.0ms	(* (sqrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))) (sqrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))))
8.0ms	(sqrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
8.0ms	(sqrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))

series35.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ x (sqrt 2.0))
7.0ms	(* (sqrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))) (sqrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))))
10.0ms	(sqrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
13.0ms	(sqrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))

simplify91.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	515	3981
1	2406	3731
2	5001	3668

prune686.0ms

Filtered

95 candidates to 158 candidates (-66.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	158	3	161

Merged error: 0b

Counts

161 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
0.0b	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
4.4b	(- (exp x) 1.0)
4.6b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
14×	`sqrt-prod`
11×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
9×	`flip3--` `associate-r` `flip--`
8×	`frac-times` `add-cube-cbrt` `associate-/l/` `add-log-exp`
7×	`distribute-lft-out--`
6×	`pow1` `flip3-+` `flip-+`
5×	`times-frac` `associate-l` `associate-/r*`
4×	`sub-neg` `associate-r/` `associate-l/`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `diff-log` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

18.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
16.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
4.0ms	(- (exp x) 1.0)
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series35.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
10.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
2.0ms	(- (exp x) 1.0)
5.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	481	1464
1	2403	1163
2	5002	1124

prune273.0ms

Filtered

83 candidates to 117 candidates (-41.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	117	3	120

Merged error: 0b

Counts

120 → 3

regimes42.0ms

Accuracy

98.8% (0.2b remaining)

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

bsearch22.0ms

Steps

Iters	Range		Point
7	-1.4449029625915488e-09	-1.3431212883364233e-11	-1.3229309755636334e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	27
1	38	27

end0.0ms

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 47.04159%

Results

809.0ms	2287×	body	1280	valid
371.0ms	1639×	body	640	valid
129.0ms	864×	body	320	valid
124.0ms	2836×	body	80	valid
101.0ms	2621×	body	80	overflowed
40.0ms	418×	body	160	valid

Details

sample257.0ms

simplify410.0ms

prune5.0ms

localize25.0ms

rewrite36.0ms

series32.0ms

simplify128.0ms

prune241.0ms

localize13.0ms

rewrite48.0ms

series28.0ms

simplify84.0ms

prune476.0ms

localize16.0ms

rewrite48.0ms

series35.0ms

simplify91.0ms

prune686.0ms

localize13.0ms

rewrite47.0ms

series35.0ms

simplify65.0ms

prune273.0ms

regimes42.0ms

bsearch22.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling