Details

analyze786.0ms

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 74.65893%

Guaranteed chance to sample good point: 54.302885%

sample53.0ms

Algorithm

intervals

Results

15.0ms	185×	body	80	valid
9.0ms	12×	body	1280	valid
8.0ms	21×	body	640	valid
6.0ms	25×	body	320	valid
2.0ms	13×	body	160	valid
0.0ms	6×	body	80	nan
0.0ms	1×	body	80	invalid

simplify130.0ms

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: 6.9b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(* (- x 1.0) (log y))
4.3b	(log (- 1.0 y))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`log-prod`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
8×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `associate-r`
7×	`add-cbrt-cube`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`associate-*l/`
3×	`flip3--` `log-pow` `flip--` `add-log-exp`
2×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-log-exp`

Counts

3 → 78

Calls

3 calls:

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

series22.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- z 1.0) (log (- 1.0 y)))
10.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

simplify41.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	425	573
1	1502	511
2	5001	470

prune161.0ms

Filtered

60 candidates to 87 candidates (-45.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	7	88

Merged error: 0.1b

Counts

88 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

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	(* 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))

rewrite66.0ms

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:

15.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
21.0ms	(* 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))

series67.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
5.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
13.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
10.0ms	(* (- x 1.0) (log y))

simplify63.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1359	2834
1	5001	2680

prune741.0ms

Filtered

162 candidates to 235 candidates (-45.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	233	2	235
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	234	8	242

Merged error: 0.0b

Counts

242 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- z 1.0))
0.2b	(cbrt (- z 1.0))
0.2b	(cbrt (- z 1.0))
0.3b	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))

rewrite23.0ms

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))
3.0ms	(cbrt (- z 1.0))
3.0ms	(cbrt (- z 1.0))
11.0ms	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(cbrt (- z 1.0))
8.0ms	(cbrt (- z 1.0))
8.0ms	(cbrt (- z 1.0))
10.0ms	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

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

prune379.0ms

Filtered

81 candidates to 113 candidates (-39.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	113	8	121

Merged error: 0.0b

Counts

121 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 1.0) (log y))
7.4b	(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
10.8b	(log (+ (sqrt 1.0) (sqrt y)))
10.9b	(log (- (sqrt 1.0) (sqrt y)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

7.0ms	(* (- x 1.0) (log y))
15.0ms	(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
6.0ms	(log (+ (sqrt 1.0) (sqrt y)))
6.0ms	(log (- (sqrt 1.0) (sqrt y)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (- x 1.0) (log y))
19.0ms	(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
7.0ms	(log (+ (sqrt 1.0) (sqrt y)))
10.0ms	(log (- (sqrt 1.0) (sqrt y)))

simplify56.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	594	1098
1	2272	1027
2	5001	996

prune234.0ms

Filtered

74 candidates to 110 candidates (-48.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	110	8	118

Merged error: 0.0b

Counts

118 → 8

regimes499.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b 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

analyze785.0ms

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 74.65893%

Guaranteed chance to sample good point: 54.302885%

sample1.4s

Algorithm

intervals

Results

408.0ms	5824×	body	80	valid
291.0ms	787×	body	640	valid
184.0ms	270×	body	1280	valid
161.0ms	696×	body	320	valid
62.0ms	423×	body	160	valid
10.0ms	141×	body	80	nan
2.0ms	31×	body	80	invalid

Details

analyze786.0ms

sample53.0ms

simplify130.0ms

prune4.0ms

localize13.0ms

rewrite21.0ms

series22.0ms

simplify41.0ms

prune161.0ms

localize20.0ms

rewrite66.0ms

series67.0ms

simplify63.0ms

prune741.0ms

localize26.0ms

rewrite23.0ms

series33.0ms

simplify43.0ms

prune379.0ms

localize19.0ms

rewrite36.0ms

series46.0ms

simplify56.0ms

prune234.0ms

regimes499.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze785.0ms

sample1.4s

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