Details

sample93.0ms

Algorithm

intervals

Results

31.0ms	59×	body	1280	valid
22.0ms	330×	body	80	valid
15.0ms	47×	body	640	valid
4.0ms	22×	body	320	valid
3.0ms	51×	body	80	overflowed
2.0ms	12×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (35.0ms)

Iter	Nodes	Cost
0	46	16
1	122	16
2	347	16
3	1295	16
4	5001	15

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 32.3b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
0.0b	(* (+ 1.0 eps) x)
0.0b	(* (- 1.0 eps) x)
2.6b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
76×	`exp-neg` `frac-times`
57×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
38×	`associate-*r/`
31×	`flip3-+` `flip-+`
29×	`flip3--` `flip--`
19×	`un-div-inv`
18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`add-exp-log` `associate-r`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`distribute-lft-out`
1×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 164

Calls

4 calls:

12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
6.0ms	(* (+ 1.0 eps) x)
7.0ms	(* (- 1.0 eps) x)
17.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
26.0ms	(* (+ 1.0 eps) x)
28.0ms	(* (- 1.0 eps) x)
193.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify161.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1243	3854
1	4819	3583
2	5001	3583

prune381.0ms

Filtered

176 candidates to 88 candidates (50.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	173	3	176
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	174	3	177

Merged error: 0.3b

Counts

177 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 0.6666666666666667 (pow x 3)) 2.0)
0.1b	(* 0.6666666666666667 (pow x 3))
5.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`associate-r`
10×	`add-log-exp`
8×	`add-exp-log`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`pow1` `associate-l` `prod-exp`
2×	`diff-log` `sum-log` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `flip3-+` `unpow3` `pow-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `flip-+`

Counts

3 → 56

Calls

3 calls:

5.0ms	(+ (* 0.6666666666666667 (pow x 3)) 2.0)
10.0ms	(* 0.6666666666666667 (pow x 3))
7.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(+ (* 0.6666666666666667 (pow x 3)) 2.0)
40.0ms	(* 0.6666666666666667 (pow x 3))
38.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify40.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	251	336
1	1024	311
2	5002	307

prune117.0ms

Filtered

65 candidates to 41 candidates (63.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	64	4	68

Merged error: 0.3b

Counts

68 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
9.7b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
9.7b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
9.7b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`pow1/3`
2×	`diff-log`
1×	`sub-neg` `associate--l+` `sum-log`

Counts

4 → 53

Calls

4 calls:

7.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
7.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
6.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

series490.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
151.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
143.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
150.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify137.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	252	983
1	905	918
2	4255	839
3	5003	839

prune227.0ms

Filtered

65 candidates to 59 candidates (90.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	65	4	69

Merged error: 0.3b

Counts

69 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 eps) x)
0.0b	(* (- 1.0 eps) x)
0.0b	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
5.6b	(- (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
12×	`times-frac`
10×	`add-cbrt-cube`
9×	`add-exp-log` `associate-l` `frac-sub`
8×	`pow1`
6×	`associate-r` `associate-*l/` `add-log-exp`
5×	`flip3--` `flip--` `distribute-lft-out`
4×	`exp-neg` `frac-times` `associate-/l*`
3×	`neg-sub0` `exp-diff` `associate-/r*`
2×	`flip3-+` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `un-div-inv` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 97

Calls

4 calls:

6.0ms	(* (+ 1.0 eps) x)
6.0ms	(* (- 1.0 eps) x)
11.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
16.0ms	(- (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (+ 1.0 eps) x)
33.0ms	(* (- 1.0 eps) x)
40.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
248.0ms	(- (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	608	1136
1	2440	1057
2	5001	1052

prune241.0ms

Filtered

109 candidates to 74 candidates (67.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	109	4	113

Merged error: 0.3b

Counts

113 → 4

regimes52.0ms

Accuracy

96.6% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 15.9b

bsearch142.0ms

Steps

Iters	Range		Point
9	1.1080729073972495	125321.6248081686	59.77921894335719

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	22
1	49	22
2	49	22

end0.0ms

sample2.7s

Algorithm

intervals

Results

912.0ms	1716×	body	1280	valid
762.0ms	10324×	body	80	valid
419.0ms	1295×	body	640	valid
139.0ms	1971×	body	80	overflowed
136.0ms	625×	body	320	valid
44.0ms	311×	body	160	valid

Details

sample93.0ms

simplify37.0ms

prune10.0ms

localize17.0ms

rewrite51.0ms

series297.0ms

simplify161.0ms

prune381.0ms

localize10.0ms

rewrite23.0ms

series154.0ms

simplify40.0ms

prune117.0ms

localize18.0ms

rewrite28.0ms

series490.0ms

simplify137.0ms

prune227.0ms

localize22.0ms

rewrite42.0ms

series347.0ms

simplify68.0ms

prune241.0ms

regimes52.0ms

bsearch142.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling