Details

sample216.0ms

Algorithm

intervals

Results

100.0ms	1403×	body	80	nan
33.0ms	431×	body	80	valid
4.0ms	9×	body	640	valid
3.0ms	12×	body	320	valid
1.0ms	9×	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

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: 2.9b

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))))
0.2b	(* y (- (log z) t))
1.0b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
7.4b	(log (- 1.0 z))

rewrite47.0ms

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))))
8.0ms	(* y (- (log z) t))
17.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms	(log (- 1.0 z))

series438.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
73.0ms	(* y (- (log z) t))
180.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
46.0ms	(log (- 1.0 z))

simplify96.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (78.0ms)

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

prune564.0ms

Filtered

194 candidates to 126 candidates (64.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	189	5	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	190	5	195

Merged error: 0.0b

Counts

195 → 5

localize27.0ms

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

rewrite104.0ms

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:

24.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
23.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
9.0ms	(* 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)))

series577.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(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))
67.0ms	(* y (- (log z) t))
242.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify152.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (97.0ms)

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

prune946.0ms

Filtered

312 candidates to 159 candidates (51.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	308	4	312
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	313	4	317

Merged error: 0.0b

Counts

317 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (exp (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t)))))
0.0b	(exp (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))))
0.2b	(* y (- (log z) t))
0.5b	(fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
25×	`add-cube-cbrt`
24×	`prod-diff`
17×	`distribute-rgt-in` `distribute-lft-in`
15×	`pow1`
10×	`associate-r`
8×	`add-cbrt-cube`
7×	`add-exp-log` `log-pow`
6×	`log-prod` `associate-l` `associate--l+`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`exp-prod` `fma-udef`
2×	`sub-neg` `associate-r/` `exp-sum` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`flip3--` `flip--` `rem-exp-log` `difference-of-squares`

Counts

4 → 104

Calls

4 calls:

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

series647.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* x (exp (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t)))))
149.0ms	(exp (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))))
72.0ms	(* y (- (log z) t))
216.0ms	(fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t)))

simplify63.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	454	1406
1	1718	1103
2	5002	1080

prune385.0ms

Filtered

116 candidates to 68 candidates (58.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	116	4	120

Merged error: 0.0b

Counts

120 → 4

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))
0.6b	(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite37.0ms

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))))
22.0ms	(* 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)))

series920.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
168.0ms	(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
99.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
433.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify83.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (50.0ms)

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

prune377.0ms

Filtered

157 candidates to 76 candidates (48.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	157	4	161

Merged error: 0.0b

Counts

161 → 4

regimes210.0ms

Accuracy

0% (0.3b 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	29	15
1	29	15

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.8s	40501×	body	80	nan
985.0ms	12543×	body	80	valid
153.0ms	370×	body	640	valid
107.0ms	405×	body	320	valid
60.0ms	74×	body	1280	valid
45.0ms	268×	body	160	valid

Details

sample216.0ms

simplify38.0ms

prune3.0ms

localize18.0ms

rewrite47.0ms

series438.0ms

simplify96.0ms

prune564.0ms

localize27.0ms

rewrite104.0ms

series577.0ms

simplify152.0ms

prune946.0ms

localize21.0ms

rewrite19.0ms

series647.0ms

simplify63.0ms

prune385.0ms

localize22.0ms

rewrite37.0ms

series920.0ms

simplify83.0ms

prune377.0ms

regimes210.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.2s

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