Details

sample39.0ms

Algorithm

intervals

Results

10.0ms	259×	body	80	valid
2.0ms	14×	body	640	valid
2.0ms	8×	body	1280	valid
1.0ms	11×	body	320	valid
1.0ms	7×	body	160	valid

simplify72.0ms

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: 12.5b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.1b	(+ x (* (- y z) (/ (- t x) (- a z))))
4.5b	(* (- y z) (/ (- t x) (- a z)))

rewrite31.0ms

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))))
16.0ms	(* (- y z) (/ (- t x) (- a z)))

series97.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- t x) (- a z))
49.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
36.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (11.0ms)

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

prune165.0ms

Filtered

88 candidates to 128 candidates (-45.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	118	10	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	10	129

Merged error: 3.1b

Counts

129 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
3.2b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.0b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
34.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- a z))
25.0ms	(cbrt (- a z))
54.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
47.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify86.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	752	1839
1	3320	1671
2	5001	1580

prune163.0ms

Filtered

103 candidates to 146 candidates (-41.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	146	10	156

Merged error: 3.1b

Counts

156 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
4.3b	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
4.5b	(* (- y z) (* (- t x) (/ 1 (- a z))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`frac-times` `add-cbrt-cube`
17×	`flip3--` `flip--`
13×	`prod-exp`
12×	`pow1`
10×	`associate-r/` `associate-l` `associate-l/`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `add-log-exp`
5×	`associate-/r*`
4×	`pow-prod-down` `associate-/r/` `un-div-inv`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 146

Calls

4 calls:

5.0ms	(/ 1 (- a z))
13.0ms	(* (- t x) (/ 1 (- a z)))
4.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
14.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

series102.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1 (- a z))
12.0ms	(* (- t x) (/ 1 (- a z)))
48.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
37.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

simplify72.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	585	1025
1	2810	908
2	5003	863

prune154.0ms

Filtered

98 candidates to 158 candidates (-61.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	158	10	168

Merged error: 3.1b

Counts

168 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
2.2b	(* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z))))
2.7b	(* (cbrt (- y z)) (/ (- t x) (- a z)))
7.0b	(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

114×	`cbrt-div`
84×	`frac-times`
58×	`flip3--` `flip--`
52×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`associate-*l/`
32×	`associate-r`
30×	`add-exp-log`
27×	`times-frac` `associate-*r/`
18×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
15×	`prod-exp` `cbrt-unprod`
12×	`cbrt-prod` `distribute-lft-out--` `difference-of-squares`
9×	`associate-l` `pow-prod-down`
6×	`add-log-exp`
4×	`unswap-sqr`
3×	`cbrt-undiv` `div-exp`
2×	`associate-/r/` `*-commutative`
1×	`+-commutative` `flip3-+` `pow1/3` `sum-log` `flip-+` `div-inv`

Counts

4 → 166

Calls

4 calls:

3.0ms	(cbrt (- y z))
23.0ms	(* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z))))
17.0ms	(* (cbrt (- y z)) (/ (- t x) (- a z)))
3.0ms	(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z)))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- y z))
35.0ms	(* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z))))
127.0ms	(* (cbrt (- y z)) (/ (- t x) (- a z)))
51.0ms	(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	903	2530
1	3334	2280
2	5001	2235

prune138.0ms

Filtered

102 candidates to 178 candidates (-74.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	177	11	188

Merged error: 3.1b

Counts

188 → 11

regimes616.0ms

Accuracy

55.9% (4.2b remaining)

Error of 8.5b against oracle of 4.4b and baseline of 13.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	58
1	50	58

end0.0ms

sample995.0ms

Algorithm

intervals

Results

303.0ms	7809×	body	80	valid
72.0ms	495×	body	640	valid
54.0ms	271×	body	1280	valid
47.0ms	430×	body	320	valid
19.0ms	258×	body	160	valid
5.0ms	23×	body	2560	valid

Details

sample39.0ms

simplify72.0ms

prune4.0ms

localize9.0ms

rewrite31.0ms

series97.0ms

simplify54.0ms

prune165.0ms

localize13.0ms

rewrite51.0ms

series151.0ms

simplify86.0ms

prune163.0ms

localize13.0ms

rewrite42.0ms

series102.0ms

simplify72.0ms

prune154.0ms

localize15.0ms

rewrite55.0ms

series238.0ms

simplify88.0ms

prune138.0ms

regimes616.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample995.0ms

Profiling