Details

sample22.0ms

Algorithm

intervals

Results

8.0ms	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

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: 20.6b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
20.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

3.0ms	(+ (* x x) (* y y))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series91.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (* x x) (* y y))
65.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify43.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	308	388
1	1848	330
2	5001	322

prune119.0ms

Filtered

48 candidates to 39 candidates (81.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Merged error: 0.3b

Counts

49 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
0.0b	(/ (- x y) (sqrt (+ (* x x) (* y y))))
19.4b	(sqrt (+ (* x x) (* y y)))
19.4b	(sqrt (+ (* x x) (* y y)))

rewrite59.0ms

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:

32.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
9.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
3.0ms	(sqrt (+ (* x x) (* y y)))
4.0ms	(sqrt (+ (* x x) (* y y)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
84.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
34.0ms	(sqrt (+ (* x x) (* y y)))
36.0ms	(sqrt (+ (* x x) (* y y)))

simplify71.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (50.0ms)

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

prune379.0ms

Filtered

195 candidates to 125 candidates (64.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	195	4	199

Merged error: 0.3b

Counts

199 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
0.0b	(+ (* x x) (* y y))
0.0b	(log (exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
20.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

5.0ms	(exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
4.0ms	(+ (* x x) (* y y))
6.0ms	(log (exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
29.0ms	(+ (* x x) (* y y))
58.0ms	(log (exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
62.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify51.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	355	761
1	1949	662
2	5001	647

prune226.0ms

Filtered

92 candidates to 74 candidates (80.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	92	4	96

Merged error: 0.3b

Counts

96 → 4

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

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Merged error: 0.3b

Counts

4 → 4

regimes86.0ms

Accuracy

76.8% (4.6b remaining)

Error of 5.2b against oracle of 0.6b and baseline of 20.5b

bsearch79.0ms

Steps

Iters	Range	Point
8	4.6392126302617956e-172	3.3746055148489886e-168	3.3216144882269104e-168
5	-7.101451878346312e-157	-3.155267202466709e-157	-4.654600319030996e-157
9	-1.2994787762702041e+157	-1.865346764731705e+152	-1.1011563348006714e+153

Iters

Range

Point

4.6392126302617956e-172

3.3746055148489886e-168

3.3216144882269104e-168

-7.101451878346312e-157

-3.155267202466709e-157

-4.654600319030996e-157

-1.2994787762702041e+157

-1.865346764731705e+152

-1.1011563348006714e+153

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	20
1	33	20

end0.0ms

sample499.0ms

Algorithm

intervals

Results

252.0ms	8000×	body	80	valid
110.0ms	8000×	pre	80	true