Details

sample219.0ms

Algorithm

intervals

Results

100.0ms	1368×	body	80	nan
32.0ms	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	30	10
1	58	10
2	129	10
3	318	10
4	1073	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: 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))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

27×	`log-prod`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`associate--l+`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`add-cube-cbrt` `associate-+r+`
10×	`associate-+l+` `associate-*r/`
9×	`add-log-exp`
8×	`pow1`
7×	`add-exp-log`
6×	`sub-neg` `flip3--` `associate-r` `add-cbrt-cube` `flip--`
5×	`distribute-lft-out--`
4×	`frac-add` `difference-of-squares`
3×	`exp-prod` `associate-l`
2×	`log-div` `sum-log` `log-pow` `rem-exp-log`
1×	`+-commutative` `flip3-+` `rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

9.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
10.0ms	(* y (- (log z) t))
12.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series454.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
74.0ms	(* y (- (log z) t))
189.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
44.0ms	(log (- 1.0 z))

simplify71.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	630	971
1	2443	914
2	5001	902

prune381.0ms

Filtered

113 candidates to 84 candidates (74.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	5	114

Merged error: 0.3b

Counts

114 → 5

localize21.0ms

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)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate--l+`
21×	`add-sqr-sqrt`
18×	`log-prod` `*-un-lft-identity`
17×	`distribute-rgt-in` `distribute-lft-in`
15×	`add-cube-cbrt`
14×	`associate-+r+`
10×	`associate-+l+` `associate-r/` `associate-r*`
9×	`pow1` `add-log-exp`
8×	`sub-neg` `add-cbrt-cube`
7×	`add-exp-log`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`frac-add`
3×	`exp-prod`
2×	`exp-sum` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `rem-exp-log` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3-+` `log-pow` `flip-+` `difference-of-squares`

Counts

4 → 104

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))))
24.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
7.0ms	(* y (- (log z) t))
21.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series719.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
238.0ms	(* 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))
243.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify78.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	646	1698
1	2788	1557
2	5001	1544

prune492.0ms

Filtered

116 candidates to 83 candidates (71.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	115	6	121

Merged error: 0.1b

Counts

121 → 6

localize17.0ms

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))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

27×	`log-prod`
25×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`associate--l+`
17×	`distribute-rgt-in` `distribute-lft-in`
15×	`add-cube-cbrt`
14×	`associate-+r+`
10×	`associate-+l+` `associate-*r/`
9×	`pow1`
8×	`add-exp-log`
6×	`sub-neg` `flip3--` `associate-r` `add-cbrt-cube` `flip--` `add-log-exp`
5×	`distribute-lft-out--`
4×	`frac-add` `difference-of-squares`
3×	`unpow-prod-down` `pow-unpow` `associate-l`
2×	`log-div` `pow-exp` `log-pow`
1×	`unpow-prod-up` `+-commutative` `pow-to-exp` `e-exp-1` `pow-pow` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr` `sqr-pow`

Counts

4 → 107

Calls

4 calls:

6.0ms	(pow E (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
7.0ms	(* y (- (log z) t))
17.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms	(log (- 1.0 z))

series453.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(pow E (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
72.0ms	(* y (- (log z) t))
189.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
43.0ms	(log (- 1.0 z))

simplify77.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	688	1067
1	2792	1018
2	5001	1005

prune415.0ms

Filtered

119 candidates to 88 candidates (73.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	119	6	125

Merged error: 0.1b

Counts

125 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

42×	`log-prod`
32×	`associate--l+`
28×	`associate-+r+`
26×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`distribute-rgt-in` `distribute-lft-in`
20×	`associate-+l+`
16×	`associate-*r/`
14×	`add-cube-cbrt`
10×	`flip3--` `flip--`
8×	`sub-neg` `frac-add` `add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--` `difference-of-squares`
4×	`log-div` `add-cbrt-cube`
2×	`+-commutative` `flip3-+` `rem-log-exp` `sum-log` `log-pow` `flip-+`

Counts

4 → 110

Calls

4 calls:

12.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
17.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))
3.0ms	(log (- 1.0 z))

series484.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
197.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
50.0ms	(log (- 1.0 z))
44.0ms	(log (- 1.0 z))

simplify54.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	492	1248
1	1639	1194
2	5001	1194

prune615.0ms

Filtered

122 candidates to 100 candidates (82.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	122	6	128

Merged error: 0.1b

Counts

128 → 6

regimes424.0ms

Accuracy

70.3% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 2.0b

bsearch3.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	41
1	66	41
2	78	41
3	88	41
4	88	41

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.9s	40324×	body	80	nan
994.0ms	12433×	body	80	valid
152.0ms	361×	body	640	valid
108.0ms	405×	body	320	valid
49.0ms	61×	body	1280	valid
47.0ms	276×	body	160	valid