Details

sample121.0ms

Algorithm

intervals

Results

50.0ms	846×	body	80	nan
13.0ms	199×	body	80	valid
9.0ms	26×	body	640	valid
8.0ms	6×	body	1280	valid
3.0ms	16×	body	320	valid
1.0ms	9×	body	160	valid

simplify137.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	9
1	49	9
2	118	9
3	256	9
4	533	9
5	1250	9
6	2637	9
7	4297	9
8	4573	9
9	4588	9
10	4588	9

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: 6.3b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

10.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
8.0ms	(* (- z 1.0) (log (- 1.0 y)))
7.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series310.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
47.0ms	(* (- z 1.0) (log (- 1.0 y)))
55.0ms	(* (- x 1.0) (log y))
47.0ms	(log (- 1.0 y))

simplify50.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	498	803
1	1805	714
2	5001	701

prune309.0ms

Filtered

106 candidates to 75 candidates (70.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	98	8	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	8	107

Merged error: 0.0b

Counts

107 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
80×	`times-frac`
78×	`associate-r`
57×	`*-un-lft-identity`
56×	`unpow-prod-down`
50×	`add-cube-cbrt`
31×	`add-exp-log`
27×	`flip3--` `flip--`
24×	`log-prod` `associate-*l/` `unpow2` `sqr-pow`
19×	`unswap-sqr`
16×	`distribute-rgt-in` `distribute-lft-in` `frac-add`
13×	`associate-l` `add-cbrt-cube`
12×	`pow1` `frac-times` `prod-exp` `associate--l+`
10×	`associate-+r+`
9×	`div-exp`
7×	`associate-*r/`
6×	`pow-to-exp` `associate-+l+` `pow-exp` `add-log-exp`
4×	`sub-neg` `cbrt-unprod` `distribute-lft-out--`
3×	`pow-prod-down` `*-commutative` `difference-of-squares`
2×	`log-pow`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `sum-log` `flip-+` `div-inv`

Counts

4 → 223

Calls

4 calls:

19.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
12.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
12.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
7.0ms	(* (- x 1.0) (log y))

series339.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
150.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
72.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
62.0ms	(* (- x 1.0) (log y))

simplify64.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1332	2812
1	5001	2662

prune898.0ms

Filtered

235 candidates to 163 candidates (69.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	231	4	235
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	234	9	243

Merged error: 0.0b

Counts

243 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- x 1.0) (log (cbrt y)))
0.3b	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

7.0ms	(* (- x 1.0) (log (cbrt y)))
11.0ms	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series779.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (- x 1.0) (log (cbrt y)))
292.0ms	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
182.0ms	(cbrt y)
179.0ms	(cbrt y)

simplify65.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	450	835
1	2041	746
2	5002	703

prune519.0ms

Filtered

101 candidates to 78 candidates (77.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	5	2	7
Picked	1	0	1
Done	0	1	1
Total	104	6	110

Merged error: 0.0b

Counts

110 → 6

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* 2 (log (cbrt y))) (log (cbrt (sqrt y))))
0.6b	(cbrt (sqrt y))
0.6b	(cbrt (sqrt y))
0.6b	(cbrt y)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
21×	`log-prod`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`associate-+l+`
9×	`associate-+r+` `sqrt-prod`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 71

Calls

4 calls:

8.0ms	(+ (* 2 (log (cbrt y))) (log (cbrt (sqrt y))))
2.0ms	(cbrt (sqrt y))
2.0ms	(cbrt (sqrt y))
1.0ms	(cbrt y)

series906.0ms

Counts

4 → 12

Calls

4 calls:

389.0ms	(+ (* 2 (log (cbrt y))) (log (cbrt (sqrt y))))
151.0ms	(cbrt (sqrt y))
179.0ms	(cbrt (sqrt y))
187.0ms	(cbrt y)

simplify98.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	282	529
1	791	474
2	3203	449
3	5001	425

prune497.0ms

Filtered

83 candidates to 69 candidates (83.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	83	6	89

Merged error: 0.0b

Counts

89 → 6

regimes260.0ms

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	28	15
1	28	15

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.4s	23742×	body	80	nan
386.0ms	5905×	body	80	valid
274.0ms	777×	body	640	valid
167.0ms	247×	body	1280	valid
146.0ms	672×	body	320	valid
58.0ms	434×	body	160	valid

Details

sample121.0ms

simplify137.0ms

prune3.0ms

localize13.0ms

rewrite31.0ms

series310.0ms

simplify50.0ms

prune309.0ms

localize26.0ms

rewrite61.0ms

series339.0ms

simplify64.0ms

prune898.0ms

localize24.0ms

rewrite24.0ms

series779.0ms

simplify65.0ms

prune519.0ms

localize35.0ms

rewrite15.0ms

series906.0ms

simplify98.0ms

prune497.0ms

regimes260.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.3s

Profiling