Details

sample222.0ms

Algorithm

intervals

Results

105.0ms	1368×	body	80	nan
33.0ms	398×	body	80	valid
4.0ms	9×	body	640	valid
3.0ms	10×	body	320	valid
1.0ms	7×	body	160	valid

simplify39.0ms

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

prune3.0ms

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: 2.4b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.2b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.8b	(log (- 1.0 z))

rewrite50.0ms

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:

9.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
11.0ms	(* y (- (log z) t))
16.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms	(log (- 1.0 z))

series447.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
73.0ms	(* y (- (log z) t))
190.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
42.0ms	(log (- 1.0 z))

simplify95.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (77.0ms)

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

prune567.0ms

Filtered

194 candidates to 126 candidates (64.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	188	6	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	189	6	195

Merged error: 0.1b

Counts

195 → 6

localize28.0ms

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))))
0.1b	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
0.2b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

108×	`prod-diff`
96×	`*-un-lft-identity`
93×	`add-sqr-sqrt`
75×	`add-cube-cbrt`
74×	`associate-+r+`
71×	`distribute-rgt-in` `distribute-lft-in`
52×	`associate--l+`
34×	`associate-+l+`
33×	`pow1`
25×	`log-pow`
18×	`log-prod`
14×	`distribute-lft-out--`
10×	`associate-r/` `associate-r*`
9×	`add-log-exp`
8×	`sub-neg` `add-cbrt-cube`
7×	`add-exp-log` `difference-of-squares`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`exp-prod`
2×	`exp-sum` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `flip-+`

Counts

4 → 221

Calls

4 calls:

18.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
20.0ms	(* x (exp (+ (* y (- (log z) t)) (* 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)))

series688.0ms

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))))
224.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
69.0ms	(* y (- (log z) t))
233.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify131.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	1066	3859
1	4196	3046
2	5001	3040

prune854.0ms

Filtered

233 candidates to 147 candidates (63.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	231	2	233
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	233	6	239

Merged error: 0.1b

Counts

239 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
11×	`associate-l`
10×	`pow1`
9×	`add-cube-cbrt`
8×	`add-cbrt-cube`
7×	`add-exp-log` `associate-r`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--`
3×	`exp-prod` `fma-udef`
2×	`exp-sum` `pow-prod-down` `associate-l/` `prod-exp` `log-pow` `-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
1×	`flip3--` `flip--` `rem-exp-log` `difference-of-squares`

Counts

4 → 72

Calls

4 calls:

8.0ms	(* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)
2.0ms	(exp (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))
5.0ms	(* x (exp (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
1.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

series716.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)
176.0ms	(exp (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))
221.0ms	(* x (exp (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
234.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

simplify45.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	320	1189
1	1155	1039
2	5001	1033

prune330.0ms

Filtered

84 candidates to 62 candidates (73.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	84	6	90

Merged error: 0.1b

Counts

90 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow E (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.2b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.8b	(log (- 1.0 z))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 188

Calls

4 calls:

6.0ms	(pow E (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
9.0ms	(* y (- (log z) t))
17.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
7.0ms	(log (- 1.0 z))

series454.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(pow E (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
69.0ms	(* y (- (log z) t))
188.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
47.0ms	(log (- 1.0 z))

simplify105.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	961	2008
1	3884	1597
2	5001	1582

prune559.0ms

Filtered

200 candidates to 130 candidates (65.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	198	2	200
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	200	6	206

Merged error: 0.1b

Counts

206 → 6

regimes372.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	27	14

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.9s	40324×	body	80	nan
1.0s	12433×	body	80	valid
155.0ms	361×	body	640	valid
111.0ms	405×	body	320	valid
50.0ms	61×	body	1280	valid
47.0ms	276×	body	160	valid