Details

sample25.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	22	7
2	24	7
3	24	7

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: 38.7b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.0b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite18.0ms

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×	`associate-/r` `associate-/l`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num` `sum-log`

Counts

3 → 65

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series48.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
13.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
30.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify119.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	294	707
1	1224	644
2	4391	642
3	5001	640

prune135.0ms

Filtered

60 candidates to 74 candidates (-23.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	67	7	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	7	75

Merged error: 18.2b

Counts

75 → 7

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
35.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`sqrt-prod`
16×	`-un-lft-identity` `associate-r*`
14×	`add-cube-cbrt`
13×	`times-frac`
9×	`sqrt-div`
8×	`pow1` `unswap-sqr`
6×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`frac-times` `associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `associate-r/` `prod-exp` `sum-log` `-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 75

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
13.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series50.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
26.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify117.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	318	858
1	1226	828
2	4716	804
3	5001	796

prune116.0ms

Filtered

59 candidates to 84 candidates (-42.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	83	8	91

Merged error: 18.2b

Counts

91 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
0.2b	(* (/ 1 (sqrt 3.0)) (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))
1.0b	(/ 1 (sqrt 3.0))
36.0b	(sqrt (* (/ 1 (sqrt 3.0)) (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
94×	`times-frac`
66×	`*-un-lft-identity`
60×	`add-cube-cbrt`
54×	`sqrt-prod`
32×	`add-exp-log`
22×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`unswap-sqr`
12×	`associate-/r*`
11×	`pow1` `div-exp`
8×	`prod-exp`
6×	`cbrt-undiv` `associate-/l*`
4×	`cbrt-unprod` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `sqrt-pow1` `sqrt-div` `1-exp`
2×	`frac-times` `frac-2neg` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/l/`
1×	`flip3-+` `*-commutative` `flip-+` `inv-pow`

Counts

4 → 183

Calls

4 calls:

9.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
19.0ms	(* (/ 1 (sqrt 3.0)) (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))
4.0ms	(/ 1 (sqrt 3.0))
10.0ms	(sqrt (* (/ 1 (sqrt 3.0)) (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))

series76.0ms

Counts

4 → 10

Calls

4 calls:

18.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
25.0ms	(* (/ 1 (sqrt 3.0)) (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))
0.0ms	(/ 1 (sqrt 3.0))
33.0ms	(sqrt (* (/ 1 (sqrt 3.0)) (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))

simplify82.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	564	2203
1	3826	1965
2	5002	1859

prune255.0ms

Filtered

107 candidates to 193 candidates (-80.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	190	3	193
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	190	11	201

Merged error: 18.0b

Counts

201 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
0.3b	(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
1.0b	(/ 1 (sqrt 3.0))
36.0b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

170×	`sqrt-prod`
148×	`add-sqr-sqrt`
120×	`times-frac`
83×	`*-un-lft-identity`
75×	`add-cube-cbrt`
25×	`associate-r` `associate-l`
24×	`unswap-sqr`
12×	`add-exp-log` `associate-/r*`
11×	`pow1`
10×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`sqrt-div` `div-inv`
4×	`sqrt-pow1` `pow1/2` `add-log-exp`
3×	`rem-sqrt-square` `pow-flip` `div-exp` `pow-prod-down`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `rec-exp` `flip3-+` `sqrt-unprod` `1-exp` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `inv-pow`

Counts

4 → 212

Calls

4 calls:

9.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
23.0ms	(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
4.0ms	(/ 1 (sqrt 3.0))
6.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

series87.0ms

Counts

4 → 10

Calls

4 calls:

21.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
29.0ms	(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
0.0ms	(/ 1 (sqrt 3.0))
37.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

simplify65.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	452	2919
1	1938	2730
2	5001	2684

prune312.0ms

Filtered

126 candidates to 222 candidates (-76.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	216	6	222
Fresh	0	8	8
Picked	1	0	1
Done	1	1	2
Total	218	15	233

Merged error: 18.0b

Counts

233 → 15

regimes1.1s

Accuracy

63.5% (7.2b remaining)

Error of 25.8b against oracle of 18.6b and baseline of 38.2b

bsearch18.0ms

Steps

Iters	Range		Point
3	5.531458983737382e+103	6.9401487626072185e+103	6.8521056514278536e+103
5	-2.548340863580925e+115	-1.126098718845409e+115	-2.5129308052104592e+115

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	14
1	39	14
2	39	14

end0.0ms

sample667.0ms

Algorithm

intervals

Results

368.0ms

8000×

body

valid

Details

sample25.0ms

simplify6.0ms

prune4.0ms

localize9.0ms

rewrite18.0ms

series48.0ms

simplify119.0ms

prune135.0ms

localize13.0ms

rewrite24.0ms

series50.0ms

simplify117.0ms

prune116.0ms

localize15.0ms

rewrite48.0ms

series76.0ms

simplify82.0ms

prune255.0ms

localize14.0ms

rewrite53.0ms

series87.0ms

simplify65.0ms

prune312.0ms

regimes1.1s

bsearch18.0ms

simplify2.0ms

end0.0ms

sample667.0ms

Profiling