Details

sample171.0ms

Algorithm

intervals

Results

71.0ms	1288×	body	80	nan
23.0ms	377×	body	80	valid
6.0ms	15×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	2×	body	1280	valid
1.0ms	6×	body	160	valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	10
1	62	10
2	137	10
3	344	10
4	1155	10
5	5001	10

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 1.9b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.8b	(log (- 1.0 z))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

72×	`prod-diff`
66×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
56×	`add-cube-cbrt`
53×	`distribute-rgt-in` `distribute-lft-in`
38×	`associate-+r+`
34×	`associate-+l+`
27×	`log-prod`
26×	`pow1`
22×	`associate--l+`
20×	`log-pow`
10×	`associate-*r/`
9×	`add-log-exp`
7×	`add-exp-log`
6×	`sub-neg` `flip3--` `associate-r` `add-cbrt-cube` `flip--`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u` `difference-of-squares`
3×	`exp-prod` `associate-l`
2×	`log-div` `sum-log` `rem-exp-log`
1×	`+-commutative` `fma-def` `flip3-+` `rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 182

Calls

4 calls:

8.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
8.0ms	(* y (- (log z) t))
16.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms	(log (- 1.0 z))

series444.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
72.0ms	(* y (- (log z) t))
191.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
47.0ms	(log (- 1.0 z))

simplify93.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	904	1913
1	3501	1501
2	5001	1500

prune550.0ms

Filtered

194 candidates to 126 candidates (64.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	190	4	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	191	4	195

Merged error: 0.0b

Counts

195 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

168×	`prod-diff`
155×	`*-un-lft-identity`
141×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
108×	`distribute-rgt-in` `distribute-lft-in`
92×	`associate--l+`
74×	`associate-+r+`
46×	`pow1`
38×	`log-pow`
34×	`associate-+l+`
31×	`distribute-lft-out--`
24×	`log-prod`
14×	`difference-of-squares`
13×	`associate-r`
12×	`sub-neg` `associate-*r/`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `associate-l` `flip--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`exp-prod`
2×	`pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `exp-sum` `flip-+`

Counts

4 → 300

Calls

4 calls:

19.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
25.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
8.0ms	(* y (- (log z) t))
29.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series583.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
102.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
72.0ms	(* y (- (log z) t))
247.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify151.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	1091	5982
1	4469	4426
2	5001	4420

prune935.0ms

Filtered

312 candidates to 159 candidates (51.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	311	1	312
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	313	3	316

Merged error: 0.0b

Counts

316 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
0.0b	(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.1b	(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

68×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
60×	`prod-diff`
43×	`add-cube-cbrt`
40×	`associate--l+`
37×	`distribute-rgt-in` `distribute-lft-in`
21×	`pow1`
17×	`distribute-lft-out--`
13×	`log-pow`
11×	`associate-r`
8×	`add-cbrt-cube`
7×	`add-exp-log` `difference-of-squares`
6×	`log-prod` `associate-l`
5×	`add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`exp-prod` `fma-udef`
2×	`associate-r/` `exp-sum` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `flip--` `rem-exp-log`

Counts

4 → 145

Calls

4 calls:

5.0ms	(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
2.0ms	(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
27.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
1.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series726.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
166.0ms	(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
100.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
239.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify79.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	570	3486
1	2092	2505
2	5003	2306

prune395.0ms

Filtered

157 candidates to 76 candidates (48.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	157	3	160

Merged error: 0.0b

Counts

160 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

4.8b	(log (- 1.0 z))
13.8b	(cbrt (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
13.8b	(cbrt (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
13.8b	(cbrt (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-*r/`
18×	`cbrt-div`
13×	`flip3--` `flip--`
12×	`frac-add`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`cbrt-prod`
8×	`add-cube-cbrt`
5×	`pow1` `add-exp-log` `log-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`log-div`
1×	`rem-log-exp` `log-pow` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 75

Calls

4 calls:

4.0ms	(log (- 1.0 z))
7.0ms	(cbrt (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
7.0ms	(cbrt (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
7.0ms	(cbrt (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))

series2.0s

Counts

4 → 12

Calls

4 calls:

41.0ms	(log (- 1.0 z))
653.0ms	(cbrt (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
652.0ms	(cbrt (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
640.0ms	(cbrt (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))

simplify67.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	651	1823
1	2379	1751
2	5001	1739

prune545.0ms

Filtered

87 candidates to 83 candidates (95.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	87	3	90

Merged error: 0.0b

Counts

90 → 3

regimes275.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	15
1	29	15

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.3s	41385×	body	80	nan
784.0ms	12476×	body	80	valid
136.0ms	384×	body	640	valid
95.0ms	417×	body	320	valid
50.0ms	70×	body	1280	valid
33.0ms	247×	body	160	valid