Details

sample41.0ms

Algorithm

intervals

Results

11.0ms	263×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	7×	body	1280	valid
1.0ms	9×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	2560	valid

simplify111.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	5503	13

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 10.0b

Counts

2 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.9b	(+ x (* (- y z) (/ (- t x) (- a z))))
4.5b	(* (- y z) (/ (- t x) (- a z)))

rewrite34.0ms

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)))

series95.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ (- t x) (- a z))
49.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
33.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify28.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5022	1602

prune171.0ms

Filtered

87 candidates to 128 candidates (-47.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	117	11	128
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	117	13	130

Merged error: 2.8b

Counts

130 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
1.2b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
5.8b	(+ 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))
36.0ms	(* (/ (- 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)))))

series158.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- a z))
28.0ms	(cbrt (- a z))
54.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
50.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify38.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5188	2532

prune172.0ms

Filtered

108 candidates to 146 candidates (-35.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	147	12	159

Merged error: 2.8b

Counts

159 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
4.5b	(* (- y z) (* (- t x) (/ 1 (- a z))))
4.9b	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

rewrite43.0ms

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:

7.0ms	(/ 1 (- a z))
12.0ms	(* (- t x) (/ 1 (- a z)))
14.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))
4.0ms	(+ x (* (- 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)))
36.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))
48.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5477	1770

prune160.0ms

Filtered

98 candidates to 158 candidates (-61.2%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	158	12	170

Merged error: 2.8b

Counts

170 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

5.8b	(cbrt (/ (- t x) (- a z)))
5.8b	(cbrt (/ (- t x) (- a z)))
5.8b	(cbrt (/ (- t x) (- a z)))
8.5b	(+ x (* (* (- y z) (* (cbrt (/ (- t x) (- a z))) (cbrt (/ (- t x) (- a z))))) (cbrt (/ (- t x) (- a z)))))

rewrite29.0ms

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:

7.0ms	(cbrt (/ (- t x) (- a z)))
7.0ms	(cbrt (/ (- t x) (- a z)))
6.0ms	(cbrt (/ (- t x) (- a z)))
3.0ms	(+ x (* (* (- y z) (* (cbrt (/ (- t x) (- a z))) (cbrt (/ (- t x) (- a z))))) (cbrt (/ (- t x) (- a z)))))

series189.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(cbrt (/ (- t x) (- a z)))
45.0ms	(cbrt (/ (- t x) (- a z)))
46.0ms	(cbrt (/ (- t x) (- a z)))
51.0ms	(+ x (* (* (- y z) (* (cbrt (/ (- t x) (- a z))) (cbrt (/ (- t x) (- a z))))) (cbrt (/ (- t x) (- a z)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5041	2289

prune131.0ms

Filtered

105 candidates to 143 candidates (-36.2%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	1	7	8
Picked	0	1	1
Done	0	3	3
Total	142	13	155

Merged error: 2.8b

Counts

155 → 13

regimes697.0ms

Accuracy

21.5% (7.2b remaining)

Error of 10.5b against oracle of 3.3b and baseline of 12.5b

bsearch74.0ms

Steps

Iters	Range		Point
6	7.177187781932268e-220	2.9989312324481596e-219	2.953667556710652e-219
5	-6.089909595908471e-141	-2.635853615644637e-141	-5.995119860382596e-141
1	-6.436865004956038e-122	-5.939000455178526e-122	-6.063466592622904e-122
10	-1.2946721603137682e-17	-2.677193310051518e-35	-8.804268970560579e-31

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	99
1	50	99

end0.0ms

sample979.0ms

Algorithm

intervals

Results

307.0ms	7779×	body	80	valid
70.0ms	485×	body	640	valid
48.0ms	266×	body	1280	valid
46.0ms	400×	body	320	valid
20.0ms	266×	body	160	valid
2.0ms	10×	body	2560	valid

Details

sample41.0ms

simplify111.0ms

prune13.0ms

localize9.0ms

rewrite34.0ms

series95.0ms

simplify28.0ms

prune171.0ms

localize13.0ms

rewrite51.0ms

series158.0ms

simplify38.0ms

prune172.0ms

localize10.0ms

rewrite43.0ms

series100.0ms

simplify44.0ms

prune160.0ms

localize13.0ms

rewrite29.0ms

series189.0ms

simplify69.0ms

prune131.0ms

regimes697.0ms

bsearch74.0ms

simplify1.0ms

end0.0ms

sample979.0ms

Profiling