Details

sample189.0ms

Algorithm

intervals

Results

82.0ms	1143×	body	80	nan
30.0ms	388×	body	80	valid
5.0ms	13×	body	640	valid
5.0ms	18×	body	320	valid
3.0ms	3×	body	1280	valid
1.0ms	7×	body	160	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 0.8b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.3b	(log (- 1.0 z))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

84×	`prod-diff`
76×	`add-sqr-sqrt` `*-un-lft-identity`
64×	`add-cube-cbrt`
53×	`distribute-rgt-in` `distribute-lft-in`
38×	`associate-+r+`
34×	`associate-+l+`
31×	`pow1`
30×	`log-prod`
25×	`associate--l+` `log-pow`
10×	`associate-*r/`
7×	`add-exp-log` `sub-neg` `flip3--` `flip--` `distribute-lft-out--` `add-log-exp`
6×	`associate-r` `add-cbrt-cube`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `fma-neg` `frac-add` `log1p-expm1-u`
3×	`associate-l`
2×	`log-div`
1×	`+-commutative` `fma-def` `flip3-+` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 203

Calls

4 calls:

5.0ms	(- (log z) t)
8.0ms	(* y (- (log z) t))
19.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms	(log (- 1.0 z))

series377.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (log z) t)
69.0ms	(* y (- (log z) t))
200.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
43.0ms	(log (- 1.0 z))

simplify96.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	856	1981
1	3296	1486
2	5002	1485

prune585.0ms

Filtered

215 candidates to 131 candidates (60.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	213	2	215
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	214	2	216

Merged error: 0.0b

Counts

216 → 2

localize71.0ms

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	(- (log z) t)
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)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

120×	`prod-diff`
106×	`*-un-lft-identity`
100×	`add-sqr-sqrt`
82×	`add-cube-cbrt`
74×	`associate-+r+`
71×	`distribute-rgt-in` `distribute-lft-in`
55×	`associate--l+`
36×	`pow1`
34×	`associate-+l+`
30×	`log-pow`
21×	`log-prod`
16×	`distribute-lft-out--`
10×	`associate-*r/` `add-log-exp`
9×	`sub-neg`
8×	`difference-of-squares`
6×	`add-exp-log` `flip3--` `associate-r` `add-cbrt-cube` `flip--`
4×	`expm1-log1p-u` `fma-neg` `frac-add` `log1p-expm1-u`
3×	`exp-prod` `associate-l`
2×	`sum-log` `rem-exp-log`
1×	`+-commutative` `fma-def` `flip3-+` `diff-log` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 236

Calls

4 calls:

22.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
5.0ms	(- (log z) t)
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)))

series558.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
63.0ms	(- (log z) t)
75.0ms	(* y (- (log z) t))
248.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify121.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	996	3661
1	3785	2813
2	5001	2807

prune890.0ms

Filtered

248 candidates to 147 candidates (59.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	247	1	248
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	248	2	250

Merged error: 0.0b

Counts

250 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (exp (+ (* y (- (log z) t)) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))) 3))
0.0b	(pow (exp (+ (* y (- (log z) t)) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))) 3)
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `prod-diff`
45×	`add-cube-cbrt`
34×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
20×	`pow1`
14×	`cbrt-prod`
13×	`log-pow`
12×	`log-prod` `associate--l+`
8×	`unpow-prod-down` `cube-prod`
7×	`add-cbrt-cube`
6×	`add-exp-log` `associate-r/` `associate-r*` `add-log-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `pow-pow` `exp-sum` `associate-*l/` `frac-add` `log1p-expm1-u`
3×	`pow-unpow` `exp-prod` `associate-l`
2×	`cube-mult` `unpow3` `distribute-lft-out--` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `fma-def` `flip3-+` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `flip-+` `rem-cube-cbrt` `difference-of-squares` `unswap-sqr`

Counts

4 → 166

Calls

4 calls:

7.0ms	(cbrt (pow (exp (+ (* y (- (log z) t)) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))) 3))
14.0ms	(pow (exp (+ (* y (- (log z) t)) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))) 3)
8.0ms	(* y (- (log z) t))
12.0ms	(+ (* y (- (log z) t)) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

series818.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt (pow (exp (+ (* y (- (log z) t)) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))) 3))
323.0ms	(pow (exp (+ (* y (- (log z) t)) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))) 3)
77.0ms	(* y (- (log z) t))
234.0ms	(+ (* y (- (log z) t)) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

simplify110.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	750	2798
1	3324	2403
2	5001	2395

prune694.0ms

Filtered

178 candidates to 107 candidates (60.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	177	3	180

Merged error: 0.0b

Counts

180 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (exp (* 3 (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))))
0.0b	(exp (* 3 (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
0.2b	(* 3 (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))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity` `fma-udef`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`cbrt-prod`
4×	`expm1-log1p-u` `exp-sum` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l`
1×	`exp-prod` `exp-to-pow` `pow1/3` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

2.0ms	(cbrt (exp (* 3 (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))))
2.0ms	(exp (* 3 (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
4.0ms	(* 3 (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))

series976.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(cbrt (exp (* 3 (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))))
209.0ms	(exp (* 3 (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
268.0ms	(* 3 (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))
230.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

simplify105.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	262	1185
1	915	1034
2	3763	1020
3	5001	1020

prune324.0ms

Filtered

73 candidates to 57 candidates (78.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	73	3	76

Merged error: 0.0b

Counts

76 → 3

regimes172.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	17
1	33	17

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.9s	40752×	body	80	nan
987.0ms	12453×	body	80	valid
165.0ms	393×	body	640	valid
108.0ms	399×	body	320	valid
60.0ms	74×	body	1280	valid
50.0ms	282×	body	160	valid

Details

sample189.0ms

simplify41.0ms

prune3.0ms

localize15.0ms

rewrite46.0ms

series377.0ms

simplify96.0ms

prune585.0ms

localize71.0ms

rewrite78.0ms

series558.0ms

simplify121.0ms

prune890.0ms

localize25.0ms

rewrite49.0ms

series818.0ms

simplify110.0ms

prune694.0ms

localize28.0ms

rewrite9.0ms

series976.0ms

simplify105.0ms

prune324.0ms

regimes172.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.2s

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