Details

sample1.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 68.75%

Guaranteed chance to sample good point: 41.210938%

Results

14.0ms	191×	body	80	valid
9.0ms	23×	body	640	valid
7.0ms	9×	body	1280	valid
5.0ms	20×	body	320	valid
4.0ms	60×	body	80	nan
2.0ms	13×	body	160	valid

simplify129.0ms

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

prune4.0ms

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: 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))))
0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(* (- x 1.0) (log y))
6.6b	(log (- 1.0 y))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

14.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
9.0ms	(* (- z 1.0) (log (- 1.0 y)))
7.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series44.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
6.0ms	(* (- z 1.0) (log (- 1.0 y)))
9.0ms	(* (- x 1.0) (log y))
4.0ms	(log (- 1.0 y))

simplify67.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	673	1005
1	2529	936
2	5001	886

prune214.0ms

Filtered

87 candidates to 121 candidates (-39.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	115	6	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	6	122

Merged error: 0.0b

Counts

122 → 6

localize22.0ms

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))))))
0.1b	(* (- x 1.0) (log y))

rewrite59.0ms

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)))
11.0ms	(+ (* (- 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))

series68.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
36.0ms	(+ (* (- 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))))))
14.0ms	(* (- x 1.0) (log y))

simplify57.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1359	2834
1	5001	2680

prune794.0ms

Filtered

162 candidates to 235 candidates (-45.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	232	3	235
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	234	7	241

Merged error: 0.0b

Counts

241 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- z 1.0))
0.3b	(cbrt (- z 1.0))
0.3b	(cbrt (- z 1.0))
0.3b	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 101

Calls

4 calls:

3.0ms	(cbrt (- z 1.0))
5.0ms	(cbrt (- z 1.0))
3.0ms	(cbrt (- z 1.0))
10.0ms	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(cbrt (- z 1.0))
7.0ms	(cbrt (- z 1.0))
8.0ms	(cbrt (- z 1.0))
11.0ms	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	368	950
1	1220	913
2	5001	853

prune379.0ms

Filtered

81 candidates to 113 candidates (-39.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	113	7	120

Merged error: 0.0b

Counts

120 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
0.3b	(cbrt (- x 1.0))
0.3b	(cbrt (- x 1.0))
0.3b	(cbrt (- x 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 101

Calls

4 calls:

10.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
3.0ms	(cbrt (- x 1.0))
3.0ms	(cbrt (- x 1.0))
3.0ms	(cbrt (- x 1.0))

series32.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
8.0ms	(cbrt (- x 1.0))
7.0ms	(cbrt (- x 1.0))
8.0ms	(cbrt (- x 1.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	368	950
1	1208	913
2	5001	853

prune349.0ms

Filtered

81 candidates to 113 candidates (-39.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	113	7	120

Merged error: 0.0b

Counts

120 → 7

regimes474.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	22
1	32	22

end0.0ms

sample3.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 68.75%

Guaranteed chance to sample good point: 41.210938%

Results

432.0ms	5855×	body	80	valid
294.0ms	789×	body	640	valid
164.0ms	234×	body	1280	valid
161.0ms	676×	body	320	valid
150.0ms	1952×	body	80	nan
72.0ms	446×	body	160	valid
2.0ms	35×	body	80	invalid

Details

sample1.5s

simplify129.0ms

prune4.0ms

localize13.0ms

rewrite36.0ms

series44.0ms

simplify67.0ms

prune214.0ms

localize22.0ms

rewrite59.0ms

series68.0ms

simplify57.0ms

prune794.0ms

localize24.0ms

rewrite25.0ms

series34.0ms

simplify45.0ms

prune379.0ms

localize25.0ms

rewrite22.0ms

series32.0ms

simplify49.0ms

prune349.0ms

regimes474.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.4s

Profiling