Details

sample20.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	7
1	48	7
2	104	7
3	196	7
4	359	7
5	686	7
6	1355	7
7	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(* (- x y) (+ x y))
20.9b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `flip3-+` `flip-+` `associate-/l/`
7×	`add-cube-cbrt`
6×	`flip3--` `flip--`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-r/` `associate-r` `associate-l/`
3×	`times-frac` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `sum-log` `-commutative` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 73

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
8.0ms	(* (- x y) (+ x y))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series133.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* x x) (* y y))
40.0ms	(* (- x y) (+ x y))
66.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify65.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	419	577
1	2448	504
2	5003	497

prune191.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(* (- x y) (+ x y))
0.0b	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
20.9b	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
41×	`associate-/r/`
36×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`add-exp-log` `add-cube-cbrt`
24×	`frac-times`
20×	`flip3-+` `add-cbrt-cube` `flip-+`
18×	`flip3--` `flip--`
16×	`associate-/r*`
14×	`div-exp`
12×	`associate-r/` `associate-l/`
7×	`pow1` `cbrt-undiv`
6×	`div-inv` `associate-/l*` `add-log-exp`
5×	`associate-l` `prod-exp`
4×	`associate-r`
3×	`rec-exp` `1-exp` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`+-commutative` `distribute-rgt-in` `pow-flip` `distribute-lft-in` `pow-prod-down` `sum-log` `*-commutative` `distribute-lft-out` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 161

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
8.0ms	(* (- x y) (+ x y))
13.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
12.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

series194.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* x x) (* y y))
40.0ms	(* (- x y) (+ x y))
63.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
59.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

simplify97.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	656	1830
1	3964	1623
2	5001	1542

prune324.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (sqrt (+ (* x x) (* y y))))
0.0b	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ 1 (/ (sqrt (+ (* x x) (* y y))) (+ x y))))
20.1b	(sqrt (+ (* x x) (* y y)))
20.1b	(sqrt (+ (* x x) (* y y)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

266×	`times-frac`
223×	`add-sqr-sqrt`
189×	`*-un-lft-identity`
118×	`add-cube-cbrt`
95×	`associate-r`
88×	`sqrt-prod`
51×	`add-exp-log`
36×	`associate-l`
27×	`add-cbrt-cube`
22×	`div-exp`
21×	`unswap-sqr`
18×	`distribute-lft-out`
14×	`prod-exp`
13×	`distribute-lft-out--` `difference-of-squares`
11×	`associate-/r/`
10×	`cbrt-undiv`
8×	`pow1` `sqrt-div`
7×	`flip3-+` `flip-+`
6×	`associate-/r*` `cbrt-unprod` `div-inv`
5×	`associate-/l*`
4×	`rec-exp` `1-exp` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip--`

Counts

4 → 273

Calls

4 calls:

8.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
69.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ 1 (/ (sqrt (+ (* x x) (* y y))) (+ x y))))
3.0ms	(sqrt (+ (* x x) (* y y)))
4.0ms	(sqrt (+ (* x x) (* y y)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
66.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ 1 (/ (sqrt (+ (* x x) (* y y))) (+ x y))))
36.0ms	(sqrt (+ (* x x) (* y y)))
41.0ms	(sqrt (+ (* x x) (* y y)))

simplify61.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1146	4261
1	5001	3841

prune607.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(* (- x y) (+ x y))
0.4b	(/ 1 (+ (* x x) (* y y)))
22.0b	(* (/ 1 (+ (* x x) (* y y))) (* (- x y) (+ x y)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`frac-times` `associate-l` `add-cbrt-cube`
18×	`times-frac`
14×	`associate-*r/`
13×	`prod-exp`
12×	`pow1` `flip3-+` `flip-+`
9×	`flip3--` `flip--`
7×	`associate-*l/` `cbrt-unprod`
6×	`div-exp` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
4×	`pow-prod-down` `associate-/r/`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r` `associate-/l`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `clear-num` `sum-log` `distribute-lft-out` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
9.0ms	(* (- x y) (+ x y))
5.0ms	(/ 1 (+ (* x x) (* y y)))
20.0ms	(* (/ 1 (+ (* x x) (* y y))) (* (- x y) (+ x y)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* x x) (* y y))
40.0ms	(* (- x y) (+ x y))
39.0ms	(/ 1 (+ (* x x) (* y y)))
66.0ms	(* (/ 1 (+ (* x x) (* y y))) (* (- x y) (+ x y)))

simplify101.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	635	1171
1	4031	1017
2	5001	996

prune287.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.7b

regimes228.0ms

Accuracy

77.1% (4.5b remaining)

Error of 5.0b against oracle of 0.5b and baseline of 20.2b

bsearch101.0ms

Steps

Iters	Range		Point
7	7.493051701410122e-163	1.3624675667085591e-161	2.1854699112047555e-162
7	-3.9633239496367584e-187	-2.1653087995485248e-188	-3.925464791081515e-187
6	-1.3821575310249933e-163	-1.361823673782187e-164	-2.5188680969543457e-164
9	-9.80925815183762e+155	-5.17073721832495e+150	-1.0551763464365888e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	19
1	31	19

end0.0ms

sample486.0ms

Algorithm

intervals

Results

240.0ms	8000×	body	80	valid
106.0ms	8000×	pre	80	true