Details

sample2.9s

Algorithm

intervals

sampling

Space saved by range analysis: 1.437274%

Space saved by search: 0.243902%

Guaranteed chance to sample good point: 0%

Results

8.0ms	203×	body	80	valid
3.0ms	21×	body	640	valid
2.0ms	10×	body	1280	valid
1.0ms	32×	body	80	invalid
1.0ms	11×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	2560	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	6
1	44	6
2	122	6
3	327	6
4	868	6
5	1727	6
6	3544	6
7	5001	6

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: 17.1b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
5.1b	(+ x (* (- y z) (/ (- t x) (- a z))))
7.2b	(* (- y z) (/ (- t x) (- a z)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

7.0ms	(/ (- t x) (- a z))
3.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
17.0ms	(* (- y z) (/ (- t x) (- a z)))

series103.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- t x) (- a z))
54.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
36.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify51.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	473	869
1	2012	820
2	5002	820

prune190.0ms

Filtered

88 candidates to 128 candidates (-45.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	114	14	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	14	129

Merged error: 4.2b

Counts

129 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.3b	(/ 1 (/ (- a z) (- t x)))
7.1b	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
7.2b	(* (- y z) (/ 1 (/ (- a z) (- t x))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

392×	`times-frac`
338×	`add-sqr-sqrt`
326×	`*-un-lft-identity`
158×	`add-cube-cbrt`
98×	`associate-r`
83×	`distribute-lft-out--` `difference-of-squares`
36×	`add-exp-log` `associate-/r*`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
11×	`flip3--` `flip--`
10×	`div-inv`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`associate-l` `unswap-sqr`
4×	`rec-exp` `1-exp`
3×	`cbrt-unprod`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 344

Calls

4 calls:

8.0ms	(/ (- a z) (- t x))
11.0ms	(/ 1 (/ (- a z) (- t x)))
3.0ms	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
36.0ms	(* (- y z) (/ 1 (/ (- a z) (- t x))))

series152.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (- a z) (- t x))
30.0ms	(/ 1 (/ (- a z) (- t x)))
51.0ms	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
59.0ms	(* (- y z) (/ 1 (/ (- a z) (- t x))))

simplify58.0ms

Algorithm

egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1010	3035
1	5002	2738

prune347.0ms

Filtered

206 candidates to 356 candidates (-72.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	352	4	356
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	359	11	370

Merged error: 4.2b

Counts

370 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.8b	(* (/ (- y z) (- a z)) (- t x))
3.2b	(+ x (* (/ (- y z) (- a z)) (- t x)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-l`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-r` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in` `associate-/r/`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 127

Calls

3 calls:

7.0ms	(/ (- y z) (- a z))
14.0ms	(* (/ (- y z) (- a z)) (- t x))
4.0ms	(+ x (* (/ (- y z) (- a z)) (- t x)))

series115.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(/ (- y z) (- a z))
56.0ms	(* (/ (- y z) (- a z)) (- t x))
49.0ms	(+ x (* (/ (- y z) (- a z)) (- t x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	522	929
1	1920	879
2	5003	879

prune149.0ms

Filtered

90 candidates to 136 candidates (-51.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	136	11	147

Merged error: 4.2b

Counts

147 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ 1 (/ (- t x) (- a z))))
0.3b	(/ 1 (/ (- t x) (- a z)))
6.8b	(+ x (* (- y z) (/ 1 (/ 1 (/ (- t x) (- a z))))))
7.2b	(* (- y z) (/ 1 (/ 1 (/ (- t x) (- a z)))))

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

1979×	`times-frac`
1271×	`add-sqr-sqrt`
1245×	`*-un-lft-identity`
734×	`add-cube-cbrt`
299×	`associate-r`
251×	`distribute-lft-out--` `difference-of-squares`
129×	`associate-/r*`
124×	`add-exp-log`
77×	`div-exp`
60×	`associate-/r/`
35×	`div-inv`
32×	`add-cbrt-cube`
28×	`rec-exp` `1-exp`
27×	`flip3--` `flip--`
22×	`prod-exp`
15×	`cbrt-undiv`
11×	`unswap-sqr`
9×	`pow1`
6×	`associate-/l*` `add-log-exp`
5×	`pow-flip` `associate-l`
4×	`cbrt-unprod`
3×	`inv-pow`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`
1×	`+-commutative` `flip3-+` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `flip-+` `remove-double-div`

Counts

4 → 950

Calls

4 calls:

43.0ms	(/ 1 (/ 1 (/ (- t x) (- a z))))
20.0ms	(/ 1 (/ (- t x) (- a z)))
5.0ms	(+ x (* (- y z) (/ 1 (/ 1 (/ (- t x) (- a z))))))
131.0ms	(* (- y z) (/ 1 (/ 1 (/ (- t x) (- a z)))))

series142.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ 1 (/ 1 (/ (- t x) (- a z))))
33.0ms	(/ 1 (/ (- t x) (- a z)))
52.0ms	(+ x (* (- y z) (/ 1 (/ 1 (/ (- t x) (- a z))))))
44.0ms	(* (- y z) (/ 1 (/ 1 (/ (- t x) (- a z)))))

simplify158.0ms

Algorithm

egg-herbie

Counts

962 → 962

Iterations

Useful iterations: 1 (54.0ms)

Iter	Nodes	Cost
0	2439	10603
1	5002	8505

prune771.0ms

Filtered

444 candidates to 962 candidates (-116.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	960	2	962
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	961	12	973

Merged error: 4.2b

Counts

973 → 12

regimes521.0ms

Accuracy

6.3% (7.3b remaining)

Error of 11.5b against oracle of 4.3b and baseline of 12.0b

bsearch84.0ms

Steps

Iters	Range		Point
5	3.800410401564134e-54	7.979560675918499e-54	3.844152459745298e-54
9	-2.4315902976857002e-202	-2.659848610047237e-208	-4.0381246062167965e-207

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	12
1	31	12

end0.0ms

sample3.4s

Algorithm

intervals

sampling

Space saved by range analysis: 1.437274%

Space saved by search: 0.243902%

Guaranteed chance to sample good point: 0%

Results

283.0ms	6513×	body	80	valid
80.0ms	521×	body	640	valid
49.0ms	1154×	body	80	invalid
44.0ms	415×	body	320	valid
44.0ms	250×	body	1280	valid
20.0ms	281×	body	160	valid
5.0ms	20×	body	2560	valid

Details

sample2.9s

simplify74.0ms

prune4.0ms

localize14.0ms

rewrite33.0ms

series103.0ms

simplify51.0ms

prune190.0ms

localize10.0ms

rewrite81.0ms

series152.0ms

simplify58.0ms

prune347.0ms

localize9.0ms

rewrite33.0ms

series115.0ms

simplify50.0ms

prune149.0ms

localize12.0ms

rewrite296.0ms

series142.0ms

simplify158.0ms

prune771.0ms

regimes521.0ms

bsearch84.0ms

simplify1.0ms

end0.0ms

sample3.4s

Profiling