Details

sample19.0ms

Algorithm

intervals

Results

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

simplify59.0ms

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: 21.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- x y) (+ x y))
0.0b	(+ (* x x) (* y y))
21.1b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite29.0ms

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:

8.0ms	(* (- x y) (+ x y))
4.0ms	(+ (* x x) (* y y))
15.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series128.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* (- x y) (+ x y))
30.0ms	(+ (* x x) (* y y))
58.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify61.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (54.0ms)

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

prune182.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune8.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize11.0ms

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)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
20.0b	(sqrt (+ (* x x) (* y y)))
20.0b	(sqrt (+ (* x x) (* y y)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

115×	`add-sqr-sqrt`
96×	`times-frac`
95×	`*-un-lft-identity`
57×	`add-cube-cbrt` `sqrt-prod`
36×	`associate-l`
30×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--` `difference-of-squares`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`associate-/r*` `associate-/r/` `distribute-lft-out`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `associate-/l*`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv`
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` `*-commutative` `flip--`

Counts

4 → 183

Calls

4 calls:

9.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
38.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
4.0ms	(sqrt (+ (* x x) (* y y)))
4.0ms	(sqrt (+ (* x x) (* y y)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
59.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
40.0ms	(sqrt (+ (* x x) (* y y)))
35.0ms	(sqrt (+ (* x x) (* y y)))

simplify76.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	628	2483
1	2598	2290
2	5002	2205

prune393.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- x y) (+ x y))
0.0b	(+ (* x x) (* y y))
0.0b	(log (exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
21.1b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

10.0ms	(* (- x y) (+ x y))
4.0ms	(+ (* x x) (* y y))
6.0ms	(log (exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (- x y) (+ x y))
26.0ms	(+ (* x x) (* y y))
63.0ms	(log (exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
62.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify63.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	456	788
1	2506	689
2	5001	677

prune255.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

regimes85.0ms

Accuracy

76.8% (4.9b remaining)

Error of 5.3b against oracle of 0.4b and baseline of 21.4b

bsearch102.0ms

Steps

Iters	Range	Point
10	1.8200255209229016e-180	9.43569343256252e-170	9.320749723812436e-170
10	-1.2783656621827507e-151	-8.482014366978142e-163	-3.392889983223758e-156
9	-1.6993806662071022e+156	-1.292778264002251e+151	-2.0372639617288886e+151

Iters

Range

Point

1.8200255209229016e-180

9.43569343256252e-170

9.320749723812436e-170

-1.2783656621827507e-151

-8.482014366978142e-163

-3.392889983223758e-156

-1.6993806662071022e+156

-1.292778264002251e+151

-2.0372639617288886e+151

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	26
1	35	26

end0.0ms

sample473.0ms

Algorithm

intervals

Results

233.0ms	8000×	body	80	valid
104.0ms	8000×	pre	80	true