Details

sample57.0ms

Algorithm

intervals

Results

37.0ms

670×

body

valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	55	15
1	179	14
2	561	13
3	1824	13
4	5002	13

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.2b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b	(* (* a a) (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

316×	`associate-+r+`
216×	`prod-diff`
211×	`add-sqr-sqrt`
202×	`distribute-rgt-in` `distribute-lft-in`
180×	`*-un-lft-identity`
146×	`add-cube-cbrt`
100×	`associate-l`
71×	`associate-r`
33×	`unswap-sqr`
24×	`*-commutative`
16×	`unpow-prod-down`
15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
13×	`distribute-lft-out`
12×	`fma-def` `swap-sqr`
9×	`+-commutative`
8×	`associate-+l+`
6×	`sub-neg` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`pow-unpow`
2×	`flip3-+` `flip-+` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--`

Counts

4 → 382

Calls

4 calls:

116.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
12.0ms	(* (* a a) (+ 1.0 a))
18.0ms	(pow (+ (* a a) (* b b)) 2.0)
20.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
56.0ms	(* (* a a) (+ 1.0 a))
116.0ms	(pow (+ (* a a) (* b b)) 2.0)
54.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify104.0ms

Algorithm

egg-herbie

Counts

394 → 394

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	2058	5347
1	5001	4066

prune1.1s

Filtered

394 candidates to 214 candidates (54.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	388	6	394
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	389	6	395

Merged error: 0.0b

Counts

395 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

188×	`add-sqr-sqrt`
144×	`prod-diff`
118×	`*-un-lft-identity`
102×	`add-cube-cbrt`
76×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
56×	`associate-r`
34×	`unswap-sqr`
18×	`*-commutative`
16×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
12×	`hypot-def`
10×	`sqrt-prod`
8×	`swap-sqr`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `sub-neg` `unpow-prod-down` `sqrt-div` `associate-*r/` `log1p-expm1-u` `distribute-lft-out` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `sqr-pow`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `flip--` `flip-+`

Counts

4 → 292

Calls

4 calls:

20.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
19.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
123.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
124.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
60.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
194.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
201.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify126.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	873	4208
1	3805	3160
2	5002	3154

prune742.0ms

Filtered

304 candidates to 118 candidates (38.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	300	4	304
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	304	6	310

Merged error: 0.0b

Counts

310 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite405.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
72×	`prod-diff`
71×	`*-un-lft-identity`
55×	`add-cube-cbrt`
40×	`associate-l`
38×	`distribute-rgt-in` `distribute-lft-in`
28×	`associate-r`
23×	`unswap-sqr`
18×	`hypot-def`
15×	`sqrt-prod`
12×	`pow1`
9×	`add-exp-log` `*-commutative` `add-cbrt-cube`
6×	`unpow-prod-down` `sqrt-div` `distribute-lft-out` `sqr-pow`
4×	`expm1-log1p-u` `swap-sqr` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
2×	`sub-neg` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`flip3--` `flip--`

Counts

4 → 196

Calls

4 calls:

19.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
125.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
125.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
125.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series651.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
197.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
196.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
197.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify118.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	873	2954
1	3805	2394
2	5002	2385

prune696.0ms

Filtered

208 candidates to 103 candidates (49.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	207	1	208
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	208	6	214

Merged error: 0.0b

Counts

214 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite508.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `hypot-def`
20×	`sqrt-prod`
12×	`unswap-sqr`
8×	`pow1` `add-cube-cbrt` `unpow-prod-down` `sqrt-div` `distribute-lft-out` `sqr-pow`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`

Counts

4 → 100

Calls

4 calls:

125.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
126.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
127.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
126.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series807.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
200.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
203.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
206.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify138.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	195	1700
1	746	1628
2	3881	1628
3	5001	1624

prune613.0ms

Filtered

112 candidates to 92 candidates (82.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	112	6	118

Merged error: 0.0b

Counts

118 → 6

regimes179.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	50
1	32	50

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

20277×

body

valid