Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 36.2b

Counts

2 → 1

localize11.0ms

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))

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:

4.0ms	(+ (* 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))

series235.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* x x) (* y y))
47.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
159.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify116.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	294	707
1	1224	644
2	4405	642
3	5001	640

prune186.0ms

Filtered

74 candidates to 60 candidates (81.1%)

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: 17.4b

Counts

75 → 7

localize11.0ms

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)))
33.4b	(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:

4.0ms	(+ (* 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)))

series289.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* x x) (* y y))
160.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
100.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify119.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	318	858
1	1226	828
2	4730	804
3	5002	796

prune190.0ms

Filtered

84 candidates to 58 candidates (69.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

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

Merged error: 17.4b

Counts

91 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.3b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
33.4b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 89

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
9.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series353.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* x x) (* y y))
226.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
100.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify100.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	294	1188
1	1083	1124
2	4083	1101
3	5001	1101

prune189.0ms

Filtered

98 candidates to 62 candidates (63.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	95	10	105

Merged error: 17.3b

Counts

105 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (* (cbrt (sqrt 3.0)) (cbrt (sqrt 3.0))))
1.0b	(* (cbrt (sqrt 3.0)) (cbrt (sqrt 3.0)))
33.4b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.4b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
44×	`sqrt-prod`
40×	`cbrt-prod`
24×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1`
11×	`add-exp-log` `swap-sqr`
9×	`times-frac` `associate-r` `associate-l` `associate-/l*` `unswap-sqr`
8×	`sqrt-div`
7×	`add-cbrt-cube`
6×	`pow1/3`
4×	`add-log-exp`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod` `associate-/l/`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num` `associate-/r` `-commutative` `div-inv`

Counts

4 → 121

Calls

4 calls:

13.0ms	(/ (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (* (cbrt (sqrt 3.0)) (cbrt (sqrt 3.0))))
7.0ms	(* (cbrt (sqrt 3.0)) (cbrt (sqrt 3.0)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series820.0ms

Counts

4 → 10

Calls

4 calls:

620.0ms	(/ (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (* (cbrt (sqrt 3.0)) (cbrt (sqrt 3.0))))
0.0ms	(* (cbrt (sqrt 3.0)) (cbrt (sqrt 3.0)))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
101.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify50.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	326	1389
1	1309	1283
2	5001	1238

prune365.0ms

Filtered

131 candidates to 86 candidates (65.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	131	10	141

Merged error: 17.3b

Counts

141 → 10

regimes567.0ms

Accuracy

60% (7.7b remaining)

Error of 26.6b against oracle of 18.9b and baseline of 38.2b

bsearch54.0ms

Steps

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	14
1	37	14
2	37	14

end0.0ms

sample527.0ms

Algorithm

intervals

Results

357.0ms

8000×

body

valid