Details

sample36.0ms

Algorithm

intervals

Results

11.0ms	287×	body	80	valid
9.0ms	302×	body	80	nan

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	26	5
1	57	5
2	121	5
3	241	5
4	364	5
5	490	5
6	641	5
7	1023	5
8	1797	5
9	2155	5
10	2161	5
11	2161	5

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x 0.5) (* y (+ (- 1.0 z) (log z))))
0.0b	(+ (- 1.0 z) (log z))
0.1b	(* y (+ (- 1.0 z) (log z)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
55×	`associate-+l+`
50×	`add-sqr-sqrt`
47×	`associate-+r+`
45×	`prod-diff`
44×	`add-cube-cbrt`
32×	`distribute-rgt-in` `distribute-lft-in`
17×	`fma-def`
15×	`log-prod`
13×	`add-log-exp`
12×	`distribute-lft-out`
10×	`associate-r` `associate-l`
9×	`pow1`
6×	`+-commutative`
5×	`add-exp-log` `sub-neg` `sum-log` `add-cbrt-cube` `distribute-lft-out--`
4×	`log-pow`
3×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
2×	`diff-log` `associate-r/` `-commutative` `unswap-sqr`
1×	`associate-+l-` `pow-prod-down` `prod-exp` `cbrt-unprod` `difference-of-squares`

Counts

3 → 159

Calls

3 calls:

23.0ms	(+ (* x 0.5) (* y (+ (- 1.0 z) (log z))))
8.0ms	(+ (- 1.0 z) (log z))
14.0ms	(* y (+ (- 1.0 z) (log z)))

series307.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(+ (* x 0.5) (* y (+ (- 1.0 z) (log z))))
160.0ms	(+ (- 1.0 z) (log z))
80.0ms	(* y (+ (- 1.0 z) (log z)))

simplify68.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	584	1102
1	2282	832
2	5001	817

prune270.0ms

Filtered

168 candidates to 103 candidates (61.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	163	5	168
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	5	169

Merged error: 0.0b

Counts

169 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- 1.0 z) (log (sqrt z)))
0.1b	(* y (+ (- 1.0 z) (log (sqrt z))))
0.1b	(+ (* y (+ (- 1.0 z) (log (sqrt z)))) (* y (log (sqrt z))))
0.3b	(* y (log (sqrt z)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

117×	`*-un-lft-identity`
93×	`associate-+l+`
70×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
54×	`log-prod`
50×	`distribute-rgt-in` `distribute-lft-in`
45×	`prod-diff`
42×	`associate-+r+`
40×	`associate-r`
37×	`distribute-lft-out`
27×	`sqrt-prod`
25×	`pow1`
21×	`fma-def`
18×	`log-pow`
17×	`associate-l`
14×	`add-log-exp`
11×	`distribute-lft-out--`
8×	`add-exp-log` `add-cbrt-cube`
6×	`+-commutative`
5×	`sub-neg` `sum-log` `*-commutative`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3-+` `flip-+` `unswap-sqr`
2×	`diff-log` `associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`associate-+l-` `distribute-rgt-out` `sqrt-pow1` `pow1/2` `difference-of-squares`

Counts

4 → 239

Calls

4 calls:

9.0ms	(+ (- 1.0 z) (log (sqrt z)))
13.0ms	(* y (+ (- 1.0 z) (log (sqrt z))))
35.0ms	(+ (* y (+ (- 1.0 z) (log (sqrt z)))) (* y (log (sqrt z))))
5.0ms	(* y (log (sqrt z)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (- 1.0 z) (log (sqrt z)))
92.0ms	(* y (+ (- 1.0 z) (log (sqrt z))))
123.0ms	(+ (* y (+ (- 1.0 z) (log (sqrt z)))) (* y (log (sqrt z))))
91.0ms	(* y (log (sqrt z)))

simplify93.0ms

Algorithm

egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	734	1954
1	3029	1554
2	5001	1483

prune507.0ms

Filtered

251 candidates to 162 candidates (64.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	248	3	251
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	251	5	256

Merged error: 0b

Counts

256 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt z) (cbrt z))
0.6b	(cbrt z)
0.6b	(cbrt z)
0.6b	(cbrt z)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
8×	`add-cbrt-cube`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 84

Calls

4 calls:

6.0ms	(* (cbrt z) (cbrt z))
1.0ms	(cbrt z)
1.0ms	(cbrt z)
1.0ms	(cbrt z)

series756.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(* (cbrt z) (cbrt z))
179.0ms	(cbrt z)
189.0ms	(cbrt z)
180.0ms	(cbrt z)

simplify93.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	128	331
1	526	287
2	3251	261
3	5002	258

prune365.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	96	5	101

Merged error: 0b

Counts

101 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (fma x 0.5 (* (fma (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0) (- (* z 1))) y)) (* (+ (fma (- (sqrt z)) (sqrt z) (* (sqrt z) (sqrt z))) (log z)) y))
0.3b	(* (+ (fma (- (sqrt z)) (sqrt z) (* (sqrt z) (sqrt z))) (log z)) y)
0.5b	(* (sqrt z) (sqrt z))
60.2b	(fma (- (sqrt z)) (sqrt z) (* (sqrt z) (sqrt z)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
23×	`pow1`
18×	`sqrt-prod`
15×	`add-cube-cbrt`
14×	`associate-l`
9×	`associate-r`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `swap-sqr` `add-cbrt-cube` `distribute-lft-out`
6×	`add-log-exp`
5×	`pow-prod-up` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`fma-def` `pow-sqr`
2×	`flip3-+` `associate-l/` `prod-exp` `log-pow` `-commutative` `cbrt-unprod` `flip-+` `fma-udef`
1×	`+-commutative` `pow2` `associate-+l+` `pow-plus` `sqrt-unprod` `sum-log` `rem-square-sqrt`

Counts

4 → 106

Calls

4 calls:

9.0ms	(+ (fma x 0.5 (* (fma (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0) (- (* z 1))) y)) (* (+ (fma (- (sqrt z)) (sqrt z) (* (sqrt z) (sqrt z))) (log z)) y))
6.0ms	(* (+ (fma (- (sqrt z)) (sqrt z) (* (sqrt z) (sqrt z))) (log z)) y)
6.0ms	(* (sqrt z) (sqrt z))
1.0ms	(fma (- (sqrt z)) (sqrt z) (* (sqrt z) (sqrt z)))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.3s	(+ (fma x 0.5 (* (fma (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0) (- (* z 1))) y)) (* (+ (fma (- (sqrt z)) (sqrt z) (* (sqrt z) (sqrt z))) (log z)) y))
180.0ms	(* (+ (fma (- (sqrt z)) (sqrt z) (* (sqrt z) (sqrt z))) (log z)) y)
16.0ms	(* (sqrt z) (sqrt z))
120.0ms	(fma (- (sqrt z)) (sqrt z) (* (sqrt z) (sqrt z)))

simplify75.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	481	1085
1	2163	881
2	5001	826

prune348.0ms

Filtered

118 candidates to 80 candidates (67.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	118	5	123

Merged error: 0b

Counts

123 → 5

regimes142.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	19
1	30	19

end0.0ms

sample1.0s

Algorithm

intervals

Results

339.0ms	9125×	body	80	valid
271.0ms	9098×	body	80	nan