Details

sample72.0ms

Algorithm

intervals

Results

21.0ms	58×	body	1280	valid
17.0ms	59×	body	640	valid
5.0ms	95×	body	80	valid
5.0ms	29×	body	320	valid
5.0ms	90×	body	80	overflowed
2.0ms	16×	body	160	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5061	12

prune11.0ms

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: 39.6b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
5.7b	(- (pow (exp x) 2.0) 1.0)
5.7b	(- (exp x) 1.0)

rewrite48.0ms

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:

13.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
12.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
7.0ms	(- (pow (exp x) 2.0) 1.0)
7.0ms	(- (exp x) 1.0)

series45.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
17.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
5.0ms	(- (pow (exp x) 2.0) 1.0)
12.0ms	(- (exp x) 1.0)

simplify70.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4962	2789
1	4962	2789

prune320.0ms

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: 0.2b

Counts

160 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ x (sqrt 2)) x) 3/16)
0.2b	(* (/ x (sqrt 2)) x)
0.4b	(/ x (sqrt 2))
0.4b	(/ x (sqrt 2))

rewrite33.0ms

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:

9.0ms	(* (* (/ x (sqrt 2)) x) 3/16)
9.0ms	(* (/ x (sqrt 2)) x)
5.0ms	(/ x (sqrt 2))
5.0ms	(/ x (sqrt 2))

series27.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (* (/ x (sqrt 2)) x) 3/16)
7.0ms	(* (/ x (sqrt 2)) x)
6.0ms	(/ x (sqrt 2))
7.0ms	(/ x (sqrt 2))

simplify46.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4935	1163
1	4935	1163

prune270.0ms

Filtered

98 candidates to 153 candidates (-56.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.2b

Counts

155 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ x (sqrt 2))
0.4b	(/ x (sqrt 2))
3.1b	(exp (log (* x (* (/ x (sqrt 2)) 3/16))))
27.8b	(log (* x (* (/ x (sqrt 2)) 3/16)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`sqrt-prod`
18×	`add-exp-log`
16×	`pow1`
12×	`associate-/r*`
8×	`add-cbrt-cube`
6×	`exp-prod` `pow-prod-down` `log-pow` `associate-/l*`
5×	`prod-exp`
4×	`rem-log-exp` `add-log-exp`
3×	`div-exp`
2×	`cbrt-undiv` `log-div` `log-prod` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `div-inv`
1×	`exp-diff` `exp-sum` `rem-exp-log`

Counts

4 → 110

Calls

4 calls:

5.0ms	(/ x (sqrt 2))
5.0ms	(/ x (sqrt 2))
8.0ms	(exp (log (* x (* (/ x (sqrt 2)) 3/16))))
8.0ms	(log (* x (* (/ x (sqrt 2)) 3/16)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ x (sqrt 2))
6.0ms	(/ x (sqrt 2))
8.0ms	(exp (log (* x (* (/ x (sqrt 2)) 3/16))))
22.0ms	(log (* x (* (/ x (sqrt 2)) 3/16)))

simplify40.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5171	948

prune253.0ms

Filtered

78 candidates to 122 candidates (-56.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	121	3	124

Merged error: 0.2b

Counts

124 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
0.2b	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))))
5.7b	(- (pow (exp x) 2.0) 1.0)
5.7b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite97.0ms

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:

11.0ms	(/ (- (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))))
8.0ms	(- (pow (exp x) 2.0) 1.0)
6.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

series25.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
5.0ms	(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))

simplify116.0ms

Algorithm

egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5073	11152

prune845.0ms

Filtered

204 candidates to 356 candidates (-74.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	355	1	356
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	355	4	359

Merged error: 0.2b

Counts

359 → 4

regimes48.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.0b

bsearch20.0ms

Steps

Iters	Range		Point
9	-0.0001616040529746431	-1.1951251334293225e-11	-9.388060895583263e-06

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	48
1	37	48

end0.0ms

sample1.7s

Algorithm

intervals

Results

726.0ms	2297×	body	1280	valid
349.0ms	1663×	body	640	valid
128.0ms	2864×	body	80	valid
114.0ms	802×	body	320	valid
105.0ms	2519×	body	80	overflowed
40.0ms	423×	body	160	valid

Details

sample72.0ms

simplify29.0ms

prune11.0ms

localize21.0ms

rewrite48.0ms

series45.0ms

simplify70.0ms

prune320.0ms

localize12.0ms

rewrite33.0ms

series27.0ms

simplify46.0ms

prune270.0ms

localize15.0ms

rewrite30.0ms

series41.0ms

simplify40.0ms

prune253.0ms

localize14.0ms

rewrite97.0ms

series25.0ms

simplify116.0ms

prune845.0ms

regimes48.0ms

bsearch20.0ms

simplify1.0ms

end0.0ms

sample1.7s

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