Details

sample26.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	7
1	48	7
2	104	7
3	196	7
4	359	7
5	686	7
6	1343	7
7	5001	7

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 19.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
19.6b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`pow1` `cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 42

Calls

2 calls:

8.0ms	(+ (* x x) (* y y))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series17.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(+ (* x x) (* y y))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify44.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	308	388
1	1848	330
2	5001	322

prune70.0ms

Filtered

48 candidates to 39 candidates (18.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	5	49

Merged error: 0.4b

Counts

49 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
19.0b	(sqrt (+ (* x x) (* y y)))
19.0b	(sqrt (+ (* x x) (* y y)))
19.6b	(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `sqrt-div`
24×	`sqrt-prod`
21×	`pow1`
18×	`add-exp-log` `add-cbrt-cube`
17×	`flip3-+` `flip-+`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`frac-times`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr` `associate-/r/` `associate-/l/`
6×	`associate-r/` `associate-r` `associate-l` `associate-l/`
5×	`prod-exp` `pow-prod-up` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `add-log-exp` `unswap-sqr`
3×	`flip3--` `pow-prod-down` `pow-sqr` `flip--`
2×	`rem-sqrt-square`
1×	`pow2` `frac-2neg` `times-frac` `pow-plus` `sqrt-unprod` `clear-num` `associate-/r` `rem-square-sqrt` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 124

Calls

4 calls:

11.0ms	(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
3.0ms	(sqrt (+ (* x x) (* y y)))
3.0ms	(sqrt (+ (* x x) (* y y)))
18.0ms	(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))

series29.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
6.0ms	(sqrt (+ (* x x) (* y y)))
6.0ms	(sqrt (+ (* x x) (* y y)))
11.0ms	(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))

simplify83.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	455	1205
1	2861	1021
2	5003	971

prune110.0ms

Filtered

136 candidates to 83 candidates (39.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	136	5	141

Merged error: 0.4b

Counts

141 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
0.0b	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
19.6b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
18×	`unpow-prod-down` `cube-prod`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`add-exp-log` `times-frac` `add-cbrt-cube`
10×	`associate-/r/`
9×	`flip3-+` `flip-+`
8×	`associate-/l/`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`cbrt-undiv` `frac-times` `div-exp`
3×	`pow-unpow` `flip3--` `pow-exp` `associate-/r*` `flip--` `rem-cube-cbrt`
2×	`cube-div` `cube-mult` `unpow3` `associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `sum-log` `rem-cbrt-cube` `associate-/l*`

Counts

4 → 116

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
6.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
12.0ms	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* x x) (* y y))
14.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
13.0ms	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
13.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify80.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	494	1238
1	2872	1167
2	5001	1161

prune127.0ms

Filtered

128 candidates to 79 candidates (38.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	128	5	133

Merged error: 0.4b

Counts

133 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow x 2) (pow y 2))
0.2b	(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
19.2b	(/ (+ x y) (+ (pow x 2) (pow y 2)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
41×	`times-frac`
32×	`add-sqr-sqrt`
31×	`distribute-lft-out`
26×	`associate-r`
25×	`add-cube-cbrt`
20×	`unpow-prod-down`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-l` `associate-/r*` `add-log-exp`
4×	`flip3-+` `associate-/r/` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 109

Calls

3 calls:

7.0ms	(+ (pow x 2) (pow y 2))
22.0ms	(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
12.0ms	(/ (+ x y) (+ (pow x 2) (pow y 2)))

series24.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (pow x 2) (pow y 2))
11.0ms	(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
8.0ms	(/ (+ x y) (+ (pow x 2) (pow y 2)))

simplify56.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	390	902
1	1953	823
2	5002	822

prune144.0ms

Filtered

118 candidates to 69 candidates (41.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

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

Merged error: 0.4b

Counts

123 → 5

regimes186.0ms

Accuracy

73.7% (5.2b remaining)

Error of 5.6b against oracle of 0.4b and baseline of 20.1b

bsearch71.0ms

Steps

Iters	Range		Point
7	9.800151347634042e-166	1.3101142461216004e-163	1.2909033881601822e-163
9	2.600114394822618e-211	1.0668008400028473e-205	2.6348364519402426e-211
9	1.3742240088631154e-238	3.655030600482554e-232	3.587898028403666e-232
7	-1.2323979110488597e-139	-1.480506819967351e-141	-2.341076919463086e-140
7	-6.117051845512837e+155	-3.2200190317659238e+153	-4.7585037269884815e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	22
1	37	22

end0.0ms

sample702.0ms

Algorithm

intervals

Results

324.0ms	8000×	body	80	valid
151.0ms	8000×	pre	80	true

Details

sample26.0ms

simplify65.0ms

prune3.0ms

localize9.0ms

rewrite22.0ms

series17.0ms

simplify44.0ms

prune70.0ms

localize11.0ms

rewrite42.0ms

series29.0ms

simplify83.0ms

prune110.0ms

localize12.0ms

rewrite37.0ms

series46.0ms

simplify80.0ms

prune127.0ms

localize10.0ms

rewrite46.0ms

series24.0ms

simplify56.0ms

prune144.0ms

regimes186.0ms

bsearch71.0ms

simplify2.0ms

end0.0ms

sample702.0ms

Profiling