Details

sample2.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 62.5%

Guaranteed chance to sample good point: 33.333333%

Results

34.0ms	380×	body	80	valid
16.0ms	196×	body	80	nan
8.0ms	19×	body	640	valid
4.0ms	15×	body	320	valid
2.0ms	3×	body	1280	valid
1.0ms	5×	body	160	valid

simplify36.0ms

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

prune5.0ms

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: 3.3b

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))))
0.1b	(* y (- (log z) t))
0.8b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.7b	(log (- 1.0 z))

rewrite57.0ms

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:

17.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
12.0ms	(* y (- (log z) t))
18.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series112.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
13.0ms	(* y (- (log z) t))
43.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.0ms	(log (- 1.0 z))

simplify64.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	657	992
1	2473	924
2	5001	894

prune192.0ms

Filtered

83 candidates to 113 candidates (-36.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	3	114

Merged error: 0.3b

Counts

114 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
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	(* y (- (log z) t))
0.8b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

20.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
17.0ms	(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))
19.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
60.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
16.0ms	(* y (- (log z) t))
62.0ms	(+ (* 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

135 → 135

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	662	1755
1	2763	1645
2	5002	1626

prune301.0ms

Filtered

87 candidates to 135 candidates (-55.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	135	3	138

Merged error: 0.0b

Counts

138 → 3

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
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	(* y (- (log z) t))
0.8b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

19.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
20.0ms	(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))
20.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
61.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
13.0ms	(* y (- (log z) t))
58.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify80.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	662	1755
1	2763	1645
2	5002	1626

prune369.0ms

Filtered

88 candidates to 135 candidates (-53.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	135	3	138

Merged error: 0.0b

Counts

138 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

10.0ms	(* x (exp (+ (* y (- (log z) t)) (* (log 1.0) a))))
4.0ms	(- (log z) t)
7.0ms	(exp (+ (* y (- (log z) t)) (* (log 1.0) a)))
7.0ms	(* y (- (log z) t))

series120.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* x (exp (+ (* y (- (log z) t)) (* (log 1.0) a))))
18.0ms	(- (log z) t)
23.0ms	(exp (+ (* y (- (log z) t)) (* (log 1.0) a)))
13.0ms	(* y (- (log z) t))

simplify158.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (146.0ms)

Iter	Nodes	Cost
0	351	647
1	1274	561
2	4303	519
3	5001	517

prune136.0ms

Filtered

66 candidates to 95 candidates (-43.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	95	3	98

Merged error: 0.0b

Counts

98 → 3

regimes422.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	18
1	35	18

end0.0ms

sample6.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 62.5%

Guaranteed chance to sample good point: 33.333333%

Results

1.1s	12615×	body	80	valid
559.0ms	6714×	body	80	nan
161.0ms	367×	body	640	valid
116.0ms	384×	body	320	valid
63.0ms	76×	body	1280	valid
47.0ms	262×	body	160	valid

Details

sample2.9s

simplify36.0ms

prune5.0ms

localize16.0ms

rewrite57.0ms

series112.0ms

simplify64.0ms

prune192.0ms

localize22.0ms

rewrite68.0ms

series158.0ms

simplify78.0ms

prune301.0ms

localize24.0ms

rewrite70.0ms

series156.0ms

simplify80.0ms

prune369.0ms

localize12.0ms

rewrite30.0ms

series120.0ms

simplify158.0ms

prune136.0ms

regimes422.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.1s

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