Details

analyze14.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
93.6%	6.2%	0.1%	8
96.7%	3.1%	0.1%	9
98.3%	1.6%	0.1%	10
99.1%	0.8%	0.1%	11
99.5%	0.4%	0.1%	12
99.7%	0.2%	0.1%	13
99.8%	0.1%	0.1%	14

sample22.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	317	14
1	317	14

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 36.7b

Counts

2 → 1

localize9.0ms

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)
34.1b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite26.0ms

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:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* 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))

series56.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* x x) (* y y))
10.0ms	(+ (+ (* x x) (* y y)) (* z z))
12.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
29.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4961	1458
1	4961	1458

prune168.0ms

Filtered

72 candidates to 90 candidates (-25.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	6	91

Merged error: 18.0b

Counts

91 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (+ (* y y) (* z z)))
0.1b	(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
34.1b	(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 46

Calls

3 calls:

6.0ms	(+ (* x x) (+ (* y y) (* z z)))
10.0ms	(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
7.0ms	(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

series48.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(+ (* x x) (+ (* y y) (* z z)))
12.0ms	(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
26.0ms	(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

simplify55.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5723	797

prune90.0ms

Filtered

37 candidates to 55 candidates (-48.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	55	6	61

Merged error: 18.0b

Counts

61 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (+ (* y y) (* z z)))
0.4b	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
34.0b	(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 91

Calls

3 calls:

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

series60.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(+ (* 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))))

simplify65.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4997	2042
1	4997	2042

prune137.0ms

Filtered

61 candidates to 100 candidates (-63.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	97	9	106

Merged error: 17.9b

Counts

106 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* y y) (* z z))
10.8b	(- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4))
34.1b	(sqrt (/ (/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (+ (* x x) (- (* y y) (* z z)))) 3.0))
40.8b	(/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (+ (* x x) (- (* y y) (* z z))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
104×	`add-sqr-sqrt`
76×	`sqrt-prod`
70×	`add-cube-cbrt` `*-un-lft-identity`
43×	`difference-of-squares`
14×	`unpow-prod-down` `sqr-pow`
8×	`associate-/r/` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `div-inv`
4×	`flip3-+` `flip-+`
3×	`rem-sqrt-square` `flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `diff-log` `associate--l+` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 161

Calls

4 calls:

4.0ms	(- (* y y) (* z z))
11.0ms	(- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4))
24.0ms	(sqrt (/ (/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (+ (* x x) (- (* y y) (* z z)))) 3.0))
19.0ms	(/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (+ (* x x) (- (* y y) (* z z))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* y y) (* z z))
31.0ms	(- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4))
59.0ms	(sqrt (/ (/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (+ (* x x) (- (* y y) (* z z)))) 3.0))
32.0ms	(/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (+ (* x x) (- (* y y) (* z z))))

simplify91.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4994	7218
1	4994	7218

prune346.0ms

Filtered

138 candidates to 173 candidates (-25.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	173	9	182

Merged error: 17.9b

Counts

182 → 9

regimes614.0ms

Accuracy

59.7% (7.9b remaining)

Error of 25.3b against oracle of 17.4b and baseline of 37.1b

bsearch24.0ms

Steps

Iters	Range		Point
9	9.720001440918833e+93	1.0553719062659764e+102	9.823181246466244e+101
3	-3.9601196506411914e+100	-3.1030253180085583e+100	-3.881765264748886e+100

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	100	31
1	100	31

end0.0ms

sample565.0ms

Algorithm

intervals

Results

385.0ms

8000×

body

valid

Details

analyze14.0ms

sample22.0ms

simplify8.0ms

prune7.0ms

localize9.0ms

rewrite26.0ms

series56.0ms

simplify63.0ms

prune168.0ms

localize9.0ms

rewrite24.0ms

series48.0ms

simplify55.0ms

prune90.0ms

localize10.0ms

rewrite24.0ms

series60.0ms

simplify65.0ms

prune137.0ms

localize16.0ms

rewrite65.0ms

series127.0ms

simplify91.0ms

prune346.0ms

regimes614.0ms

bsearch24.0ms

simplify2.0ms

end0.0ms

sample565.0ms

Profiling