Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	7
1	27	7
2	33	7
3	34	7
4	34	7

prune3.0ms

Filtered

1 candidates to 0 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: 36.2b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.5b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`times-frac`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`sqrt-prod`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num` `sum-log`

Counts

3 → 72

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
15.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series279.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* x x) (* y y))
62.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
186.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify156.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	310	729
1	1303	650
2	4811	634
3	5001	634

prune265.0ms

Filtered

81 candidates to 68 candidates (84.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	7	82

Merged error: 17.4b

Counts

82 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
0.4b	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
33.5b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
75×	`times-frac` `sqrt-prod`
53×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`cbrt-prod`
25×	`associate-r`
16×	`unswap-sqr`
10×	`associate-l`
9×	`pow1`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r*` `add-log-exp`
5×	`sqrt-div`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-/l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-times` `fma-def` `frac-2neg` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 164

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
11.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
29.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
8.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series988.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* x x) (* y y))
155.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
389.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
414.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	483	2511
1	1869	2385
2	5001	2351

prune655.0ms

Filtered

176 candidates to 141 candidates (80.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	173	3	176
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	173	10	183

Merged error: 17.3b

Counts

183 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
0.3b	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
33.4b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.4b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

152×	`sqrt-prod`
124×	`add-sqr-sqrt`
84×	`times-frac`
55×	`*-un-lft-identity`
47×	`add-cube-cbrt`
25×	`associate-r` `associate-l`
24×	`unswap-sqr`
11×	`pow1`
9×	`sqrt-div`
6×	`add-exp-log` `add-cbrt-cube`
5×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`flip3-+` `flip-+` `hypot-def`
1×	`frac-times` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 166

Calls

4 calls:

7.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
26.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
6.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
6.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series599.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
192.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
115.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
120.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify87.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	403	3047
1	1364	2901
2	5001	2851

prune536.0ms

Filtered

178 candidates to 119 candidates (66.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	178	10	188

Merged error: 17.3b

Counts

188 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.9b	(exp (log (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))))
33.5b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
26×	`sqrt-prod`
16×	`log-prod` `exp-sum`
7×	`pow1`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `log-pow` `div-inv` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `log-div` `fma-def` `frac-2neg` `exp-diff` `div-exp` `clear-num` `sum-log` `rem-exp-log`

Counts

4 → 105

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
10.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
8.0ms	(exp (log (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))))
6.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series474.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* x x) (* y y))
55.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
189.0ms	(exp (log (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))))
189.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	389	1119
1	1425	1017
2	5001	981

prune347.0ms

Filtered

117 candidates to 90 candidates (76.9%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	114	13	127

Merged error: 17.3b

Counts

127 → 13

regimes742.0ms

Accuracy

60.4% (7.6b remaining)

Error of 26.5b against oracle of 18.9b and baseline of 38.1b

bsearch78.0ms

Steps

Iters	Range		Point
6	1.6006938423459802e+44	1.2467605670924074e+45	1.2302990277777622e+45
6	-2.4019015718107501e+145	-5.684541088404978e+144	-5.9409360080047396e+144

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	28
1	45	28
2	48	28
3	48	28

end0.0ms

sample560.0ms

Algorithm

intervals

Results

378.0ms

8000×

body

valid