Details

sample20.0ms

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

prune2.0ms

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: 38.9b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.2b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite28.0ms

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:

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

series293.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (+ (* x x) (* y y)) (* z z))
28.0ms	(+ (* x x) (* y y))
50.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
173.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (30.0ms)

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

prune219.0ms

Filtered

90 candidates to 71 candidates (78.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Merged error: 19.8b

Counts

91 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.2b	(/ (+ (+ (* 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))))
36.2b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite47.0ms

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×	`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` `frac-2neg` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 155

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
9.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
22.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
7.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x x) (* y y))
329.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
360.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
374.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify69.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	467	2452
1	1797	2356
2	5001	2337

prune553.0ms

Filtered

167 candidates to 131 candidates (78.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	165	9	174

Merged error: 19.7b

Counts

174 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
0.4b	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

150×	`sqrt-prod`
130×	`add-sqr-sqrt`
106×	`times-frac`
64×	`add-cube-cbrt` `*-un-lft-identity`
47×	`cbrt-prod`
43×	`associate-r`
24×	`unswap-sqr`
13×	`associate-l`
10×	`pow1` `sqrt-div`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r` `associate-/l`
4×	`sqrt-pow1` `pow1/2` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `flip-+` `div-inv`
2×	`rem-sqrt-square` `associate-/l/`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 189

Calls

4 calls:

9.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
30.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series858.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
373.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
101.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
122.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify169.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 3 (124.0ms)

Iter	Nodes	Cost
0	414	3970
1	1331	3861
2	4398	3765
3	5001	3713

prune494.0ms

Filtered

201 candidates to 125 candidates (62.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	201	9	210

Merged error: 19.7b

Counts

210 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
0.4b	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

152×	`sqrt-prod`
122×	`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×	`add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`flip3-+` `flip-+`
1×	`frac-times` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 156

Calls

4 calls:

7.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
25.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
184.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
107.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
103.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify73.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	393	2966
1	1355	2835
2	5001	2785

prune393.0ms

Filtered

168 candidates to 109 candidates (64.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	168	9	177

Merged error: 19.7b

Counts

177 → 9

regimes546.0ms

Accuracy

60.5% (7.6b remaining)

Error of 25.8b against oracle of 18.2b and baseline of 37.4b

bsearch139.0ms

Steps

Iters	Range		Point
8	3.584984032206546e+131	1.933236461977481e+136	1.0270452633617047e+135
9	-4.86612890522375e-281	-8.637060737317073e-289	-4.658617051526522e-281
7	-4.845435935635627e-218	-1.1000449631184665e-219	-1.8518021247462165e-219
4	-2.8077428121399217e+107	-1.6342802683843278e+107	-2.7710721076475597e+107

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	45
1	55	45
2	58	45
3	58	45

end0.0ms

sample543.0ms

Algorithm

intervals

Results

365.0ms

8000×

body

valid

Details

sample20.0ms

simplify6.0ms

prune2.0ms

localize9.0ms

rewrite28.0ms

series293.0ms

simplify39.0ms

prune219.0ms

localize14.0ms

rewrite47.0ms

series1.1s

simplify69.0ms

prune553.0ms

localize19.0ms

rewrite59.0ms

series858.0ms

simplify169.0ms

prune494.0ms

localize13.0ms

rewrite52.0ms

series564.0ms

simplify73.0ms

prune393.0ms

regimes546.0ms

bsearch139.0ms

simplify3.0ms

end0.0ms

sample543.0ms

Profiling