Details

sample18.0ms

Algorithm

intervals

Results

8.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

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)
36.4b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite20.0ms

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

series241.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* x x) (* y y))
51.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
164.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify130.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (122.0ms)

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

prune216.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.3b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
36.4b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite28.0ms

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))
16.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series280.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* x x) (* y y))
159.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
95.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify120.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (112.0ms)

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

prune212.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
36.4b	(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)))

series345.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* x x) (* y y))
220.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify93.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

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

prune217.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.2b

localize4.0ms

Local error

Found 1 expressions with local error:

0.4b	(* x (sqrt (/ 1 3.0)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
16×	`associate-r` `sqrt-prod`
11×	`*-un-lft-identity` `times-frac`
10×	`add-cube-cbrt`
4×	`unswap-sqr`
3×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
1×	`sqrt-div` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `div-inv` `add-log-exp`

Counts

1 → 35

Calls

1 calls:

8.0ms

(* x (sqrt (/ 1 3.0)))

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

(* x (sqrt (/ 1 3.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	133	185
1	443	172
2	1117	156
3	1916	145
4	5001	145

prune60.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 21.2b

regimes421.0ms

Accuracy

62.9% (7.3b remaining)

Error of 25.6b against oracle of 18.2b and baseline of 38.0b

bsearch63.0ms

Steps

Iters	Range		Point
7	1.5208757723416256e+124	2.9879744889931395e+125	1.4103613175797002e+125
7	-9.30187801373195e+97	-1.0095689469955089e+96	-6.600093290421653e+97

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	16
1	34	16
2	37	16
3	37	16

end0.0ms

sample447.0ms

Algorithm

intervals

Results

279.0ms

8000×

body

valid