Details

sample107.0ms

Algorithm

intervals

Results

38.0ms	67×	body	1280	valid
23.0ms	309×	body	80	valid
14.0ms	41×	body	640	valid
6.0ms	79×	body	80	overflowed
4.0ms	19×	body	320	valid
2.0ms	15×	body	160	valid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (34.0ms)

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

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 32.6b

Counts

2 → 1

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(* (+ 1.0 eps) x)
3.2b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
72×	`exp-neg` `frac-times`
54×	`neg-sub0` `exp-diff`
40×	`associate-*l/`
36×	`associate-*r/`
29×	`flip3--` `flip--`
28×	`flip3-+` `flip-+`
18×	`un-div-inv`
13×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`associate-l`
7×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r`
5×	`add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 136

Calls

3 calls:

6.0ms	(* (- 1.0 eps) x)
6.0ms	(* (+ 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)))))

series57.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* (- 1.0 eps) x)
4.0ms	(* (+ 1.0 eps) x)
48.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify135.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	1178	3582
1	4531	3328
2	5001	3319

prune241.0ms

Filtered

68 candidates to 145 candidates (-113.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	143	3	146

Merged error: 0.2b

Counts

146 → 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))
6.8b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite19.0ms

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

series15.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ (* 0.6666666666666667 (pow x 3)) 2.0)
4.0ms	(* 0.6666666666666667 (pow x 3))
5.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify38.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (32.0ms)

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

prune103.0ms

Filtered

41 candidates to 65 candidates (-58.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	65	3	68

Merged error: 0.2b

Counts

68 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3)
0.1b	(* 0.6666666666666667 (pow x 3))
1.9b	(cbrt (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3))
6.8b	(- (cbrt (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3)) (* 1.0 (pow x 2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

8.0ms	(pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3)
6.0ms	(* 0.6666666666666667 (pow x 3))
6.0ms	(cbrt (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3))
11.0ms	(- (cbrt (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3)) (* 1.0 (pow x 2)))

series22.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3)
4.0ms	(* 0.6666666666666667 (pow x 3))
7.0ms	(cbrt (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3))
4.0ms	(- (cbrt (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3)) (* 1.0 (pow x 2)))

simplify55.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	363	647
1	1646	575
2	5003	567

prune168.0ms

Filtered

59 candidates to 103 candidates (-74.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	102	4	106

Merged error: 0.2b

Counts

106 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
1.2b	(cbrt (pow (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) 3))
1.9b	(cbrt (cbrt (pow (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) 3)))
6.8b	(- (cbrt (cbrt (pow (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) 3))) (* 1.0 (pow x 2)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

93×	`cbrt-prod`
40×	`unpow-prod-down` `cube-prod`
30×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
9×	`add-exp-log`
8×	`cube-div` `sqr-pow`
7×	`cube-mult` `unpow3`
6×	`cbrt-div` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`flip3-+` `pow1/3` `flip-+`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `*-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 127

Calls

4 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
8.0ms	(cbrt (pow (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) 3))
10.0ms	(cbrt (cbrt (pow (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) 3)))
17.0ms	(- (cbrt (cbrt (pow (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) 3))) (* 1.0 (pow x 2)))

series22.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 0.6666666666666667 (pow x 3))
7.0ms	(cbrt (pow (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) 3))
7.0ms	(cbrt (cbrt (pow (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) 3)))
5.0ms	(- (cbrt (cbrt (pow (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) 3))) (* 1.0 (pow x 2)))

simplify68.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	461	1157
1	1946	980
2	5001	978

prune197.0ms

Filtered

63 candidates to 139 candidates (-120.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	139	4	143

Merged error: 0.2b

Counts

143 → 4

regimes224.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.2b

bsearch104.0ms

Steps

Iters	Range		Point
10	4.023680833981601e-08	150298.86953896628	159.8178291510558

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	27
1	60	27
2	60	27

end0.0ms

sample2.9s

Algorithm

intervals

Results

950.0ms	1743×	body	1280	valid
744.0ms	9796×	body	80	valid
427.0ms	1265×	body	640	valid
145.0ms	636×	body	320	valid
143.0ms	1928×	body	80	overflowed
50.0ms	327×	body	160	valid

Details

sample107.0ms

simplify35.0ms

prune9.0ms

localize17.0ms

rewrite38.0ms

series57.0ms

simplify135.0ms

prune241.0ms

localize10.0ms

rewrite19.0ms

series15.0ms

simplify38.0ms

prune103.0ms

localize13.0ms

rewrite33.0ms

series22.0ms

simplify55.0ms

prune168.0ms

localize15.0ms

rewrite48.0ms

series22.0ms

simplify68.0ms

prune197.0ms

regimes224.0ms

bsearch104.0ms

simplify2.0ms

end0.0ms

sample2.9s

Profiling