Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.3%	0.2%	12
12.2%	87.5%	0.2%	13
21.9%	77.7%	0.4%	14

sample31.0ms

Algorithm

intervals

Results

8.0ms	214×	body	80	valid
2.0ms	12×	body	640	valid
2.0ms	40×	body	80	invalid
1.0ms	8×	body	1280	valid
1.0ms	13×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	2560	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4885	13
1	4885	13

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: 15.4b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.6b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.7b	(* (- y z) (/ (- t x) (- a z)))

rewrite38.0ms

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))
8.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
17.0ms	(* (- y z) (/ (- t x) (- a z)))

series98.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- t x) (- a z))
51.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
34.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify43.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5183	1602

prune171.0ms

Filtered

88 candidates to 128 candidates (-45.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	117	11	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	11	129

Merged error: 3.7b

Counts

129 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
3.4b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.8b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite52.0ms

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))
36.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
4.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series156.0ms

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

simplify37.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5314	2524

prune179.0ms

Filtered

108 candidates to 146 candidates (-35.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	144	13	157

Merged error: 3.7b

Counts

157 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
3.8b	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
6.7b	(* (- 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)))))
15.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

series100.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1 (- a z))
12.0ms	(* (- t x) (/ 1 (- a z)))
50.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
34.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

simplify47.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5717	1769

prune169.0ms

Filtered

99 candidates to 158 candidates (-59.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	158	13	171

Merged error: 3.7b

Counts

171 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

7.3b	(+ x (* (* (- y z) (* (cbrt (/ (- t x) (- a z))) (cbrt (/ (- t x) (- a z))))) (cbrt (/ (- t x) (- a z)))))
8.4b	(cbrt (/ (- t x) (- a z)))
8.4b	(cbrt (/ (- t x) (- a z)))
8.4b	(cbrt (/ (- t x) (- a z)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt` `*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
37×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 131

Calls

4 calls:

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

series193.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ x (* (* (- y z) (* (cbrt (/ (- t x) (- a z))) (cbrt (/ (- t x) (- a z))))) (cbrt (/ (- t x) (- a z)))))
47.0ms	(cbrt (/ (- t x) (- a z)))
46.0ms	(cbrt (/ (- t x) (- a z)))
49.0ms	(cbrt (/ (- t x) (- a z)))

simplify62.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4987	2296
1	4987	2296

prune129.0ms

Filtered

104 candidates to 143 candidates (-37.5%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	143	13	156

Merged error: 3.7b

Counts

156 → 13

regimes578.0ms

Accuracy

8% (8.5b remaining)

Error of 11.9b against oracle of 3.5b and baseline of 12.7b

bsearch48.0ms

Steps

Iters	Range	Point
8	4.2707657343345087e+139	1.0137489485420723e+143	1.1037859861347199e+142
7	7.359462582445854e-198	2.753613191197119e-196	1.291527251069965e-197
1	-8.378439745563182e-99	-7.628658141107354e-99	-7.816103542221312e-99

Iters

Range

Point

4.2707657343345087e+139

1.0137489485420723e+143

1.1037859861347199e+142

7.359462582445854e-198

2.753613191197119e-196

1.291527251069965e-197

-8.378439745563182e-99

-7.628658141107354e-99

-7.816103542221312e-99

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	76	95
1	76	95

end0.0ms

sample797.0ms

Algorithm

intervals

Results

267.0ms	6556×	body	80	valid
68.0ms	495×	body	640	valid
53.0ms	269×	body	1280	valid
45.0ms	1210×	body	80	invalid
44.0ms	425×	body	320	valid
17.0ms	242×	body	160	valid
3.0ms	13×	body	2560	valid

Details

analyze1.1s

sample31.0ms

simplify69.0ms

prune4.0ms

localize10.0ms

rewrite38.0ms

series98.0ms

simplify43.0ms

prune171.0ms

localize13.0ms

rewrite52.0ms

series156.0ms

simplify37.0ms

prune179.0ms

localize13.0ms

rewrite42.0ms

series100.0ms

simplify47.0ms

prune169.0ms

localize16.0ms

rewrite31.0ms

series193.0ms

simplify62.0ms

prune129.0ms

regimes578.0ms

bsearch48.0ms

simplify2.0ms

end0.0ms

sample797.0ms

Profiling