Details

analyze15.0ms

Algorithm: search

sample25.0ms

Algorithm

intervals

Results

11.0ms

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: 38.1b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.5b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

3.0ms	(+ (* x x) (* y y))
5.0ms	(+ (+ (* x x) (* y y)) (* z z))
8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series57.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* x x) (* y y))
10.0ms	(+ (+ (* x x) (* y y)) (* z z))
15.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
26.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	325	828
1	1345	761
2	5001	755

prune157.0ms

Filtered

71 candidates to 90 candidates (-26.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	83	7	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	7	91

Merged error: 17.1b

Counts

91 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
35.5b	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-log-exp`
9×	`pow1`
8×	`add-sqr-sqrt`
6×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`flip3-+` `associate-*r/` `sum-log` `flip-+`
3×	`associate-r` `associate-l`
2×	`+-commutative` `sqrt-pow1` `sqrt-div` `pow-prod-down`
1×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

3.0ms	(+ (* x x) (* y y))
5.0ms	(+ (+ (* x x) (* y y)) (* z z))
7.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
6.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* x x) (* y y))
10.0ms	(+ (+ (* x x) (* y y)) (* z z))
13.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
26.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify44.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	310	539
1	1615	492
2	5001	492

prune99.0ms

Filtered

50 candidates to 71 candidates (-42.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	71	7	78

Merged error: 17.1b

Counts

78 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.4b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-log-exp`
6×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `sum-log` `flip-+`
2×	`+-commutative` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `associate-+l+` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 102

Calls

4 calls:

3.0ms	(+ (* x x) (* y y))
5.0ms	(+ (+ (* x x) (* y y)) (* z z))
9.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* x x) (* y y))
10.0ms	(+ (+ (* x x) (* y y)) (* z z))
30.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
18.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify44.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	330	1316
1	1338	1241
2	5002	1218

prune147.0ms

Filtered

73 candidates to 114 candidates (-56.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	111	10	121

Merged error: 17.0b

Counts

121 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
0.5b	(* (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))) (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))))
35.5b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))
35.5b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

194×	`sqrt-prod`
120×	`add-sqr-sqrt`
73×	`times-frac`
62×	`add-cube-cbrt` `*-un-lft-identity`
34×	`sqrt-pow1`
29×	`pow1`
25×	`swap-sqr`
19×	`associate-r` `associate-l`
18×	`pow1/2`
16×	`unswap-sqr`
10×	`sqrt-div`
9×	`pow-prod-up`
8×	`add-exp-log` `add-cbrt-cube`
7×	`div-inv`
5×	`pow-prod-down` `pow-sqr`
4×	`rem-sqrt-square` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `flip3-+` `pow-plus` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 194

Calls

4 calls:

8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
21.0ms	(* (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))) (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))))
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series94.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
27.0ms	(* (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))) (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))))
26.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))
27.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	388	2590
1	1746	2405
2	5001	2350

prune299.0ms

Filtered

128 candidates to 206 candidates (-60.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	206	10	216

Merged error: 17.0b

Counts

216 → 10

regimes1.0s

Accuracy

61.8% (7.7b remaining)

Error of 26.2b against oracle of 18.6b and baseline of 38.6b

bsearch147.0ms

Steps

Iters	Range		Point
7	6.212776018882463e+93	1.6524904715370627e+95	1.6277273401591426e+95
9	-2.135496755353017e-196	-2.2726329204290766e-204	-7.003463090911537e-197
8	-4.291637353470548e-178	-1.8386109251777073e-181	-1.865000523584714e-181
9	-7.961393899382742e+120	-2.52842479968767e+111	-6.84965762204123e+120

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	21
1	42	21
2	42	21

end0.0ms

analyze14.0ms

Algorithm: search

sample535.0ms

Algorithm

intervals

Results

381.0ms

8000×

body

valid

Details

analyze15.0ms

sample25.0ms

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite24.0ms

series57.0ms

simplify39.0ms

prune157.0ms

localize10.0ms

rewrite23.0ms

series54.0ms

simplify44.0ms

prune99.0ms

localize10.0ms

rewrite28.0ms

series63.0ms

simplify44.0ms

prune147.0ms

localize13.0ms

rewrite50.0ms

series94.0ms

simplify71.0ms

prune299.0ms

regimes1.0s

bsearch147.0ms

simplify2.0ms

end0.0ms

analyze14.0ms

sample535.0ms

Profiling