Details

sample108.0ms

Algorithm

intervals

Results

43.0ms	764×	body	80	nan
11.0ms	182×	body	80	valid
7.0ms	22×	body	640	valid
6.0ms	10×	body	1280	valid
5.0ms	25×	body	320	valid
2.0ms	18×	body	160	valid

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	7
1	30	7
2	39	7
3	45	7
4	60	7
5	88	7
6	125	7
7	176	7
8	208	7
9	225	7
10	293	7
11	293	7

prune2.0ms

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: 10.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (log y)) (* z (log (- 1.0 y))))
0.0b	(* z (log (- 1.0 y)))
0.2b	(* x (log y))
5.7b	(log (- 1.0 y))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

37×	`log-prod`
31×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow1`
10×	`associate-+r+`
9×	`add-exp-log`
8×	`associate-r` `add-cbrt-cube`
6×	`associate-+l+` `associate-l` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
3×	`log-pow`
2×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3--` `flip3-+` `rem-log-exp` `sum-log` `flip--` `flip-+`

Counts

4 → 97

Calls

4 calls:

7.0ms	(+ (* x (log y)) (* z (log (- 1.0 y))))
6.0ms	(* z (log (- 1.0 y)))
4.0ms	(* x (log y))
3.0ms	(log (- 1.0 y))

series229.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (* x (log y)) (* z (log (- 1.0 y))))
67.0ms	(* z (log (- 1.0 y)))
36.0ms	(* x (log y))
46.0ms	(log (- 1.0 y))

simplify50.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	449	675
1	1570	619
2	5002	588

prune259.0ms

Filtered

109 candidates to 76 candidates (69.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	103	6	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	6	110

Merged error: 0.1b

Counts

110 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `log-prod`
21×	`*-un-lft-identity`
16×	`distribute-rgt-in` `add-cube-cbrt` `distribute-lft-in`
13×	`associate--l+`
11×	`add-log-exp`
10×	`pow1` `associate-+r+` `associate-r`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-+l+` `associate-l`
5×	`sub-neg`
3×	`distribute-lft-out--`
2×	`flip3--` `diff-log` `associate-r/` `pow-prod-down` `prod-exp` `sum-log` `log-pow` `-commutative` `flip--` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `flip3-+` `flip-+`

Counts

4 → 101

Calls

4 calls:

7.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
6.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
13.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
4.0ms	(* x (log y))

series445.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
129.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
101.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
37.0ms	(* x (log y))

simplify56.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	435	1202
1	1650	1138
2	5002	1111

prune340.0ms

Filtered

113 candidates to 75 candidates (66.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	110	9	119

Merged error: 0.1b

Counts

119 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt y) (cbrt y))
0.7b	(cbrt y)
0.7b	(cbrt y)
0.7b	(cbrt y)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (cbrt y) (cbrt y))
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series879.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (cbrt y) (cbrt y))
180.0ms	(cbrt y)
319.0ms	(cbrt y)
181.0ms	(cbrt y)

simplify97.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	115	288
1	472	261
2	2959	238
3	5003	235

prune362.0ms

Filtered

85 candidates to 64 candidates (75.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	85	9	94

Merged error: 0.1b

Counts

94 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
0.2b	(* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.2b	(* x (log y))
0.3b	(* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`associate-r`
17×	`pow1`
15×	`sqrt-prod`
13×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt`
10×	`associate-*r/`
7×	`associate-l`
6×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
5×	`flip3-+` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
4×	`frac-times` `add-log-exp` `difference-of-squares`
3×	`flip3--` `log-pow` `*-commutative` `flip--` `distribute-lft-out` `distribute-lft-out--`
2×	`sub-neg` `sqrt-div` `associate-*l/` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 102

Calls

4 calls:

3.0ms	(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
10.0ms	(* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
4.0ms	(* x (log y))
19.0ms	(* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series766.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
193.0ms	(* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
43.0ms	(* x (log y))
462.0ms	(* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify95.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	688	1792
1	3425	1492
2	5001	1471

prune412.0ms

Filtered

114 candidates to 75 candidates (65.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	6	6
Picked	0	1	1
Done	1	1	2
Total	114	9	123

Merged error: 0.1b

Counts

123 → 9

regimes205.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	20
1	33	20

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	24440×	body	80	nan
343.0ms	5555×	body	80	valid
303.0ms	902×	body	640	valid
265.0ms	411×	body	1280	valid
141.0ms	684×	body	320	valid
63.0ms	479×	body	160	valid