Details

sample40.0ms

Algorithm

intervals

Results

18.0ms	383×	body	80	valid
6.0ms	146×	body	80	nan

simplify104.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	7
1	53	5
2	106	5
3	269	5
4	904	5
5	3976	5
6	5001	5

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.2b	(* a (pow k m))
2.9b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
14×	`add-sqr-sqrt`
10×	`add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-log-exp`
7×	`associate-r`
6×	`prod-exp`
4×	`unpow-prod-down` `div-exp`
3×	`pow1` `expm1-log1p-u` `fma-def` `times-frac` `associate-l` `associate-/r*` `sum-log` `log1p-expm1-u` `unswap-sqr`
2×	`cbrt-undiv` `pow-to-exp` `flip3-+` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`+-commutative` `associate-+l+` `frac-2neg` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

3 → 72

Calls

3 calls:

5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
5.0ms	(* a (pow k m))
9.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series211.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
59.0ms	(* a (pow k m))
127.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify58.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	419	575
1	2040	495
2	5002	476

prune252.0ms

Filtered

81 candidates to 63 candidates (77.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (sqrt (pow k m)))
0.2b	(sqrt (pow k m))
0.2b	(sqrt (pow k m))
2.9b	(/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`sqrt-prod`
15×	`add-exp-log` `add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
10×	`associate-r`
6×	`pow1` `rem-sqrt-square` `sqr-pow`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-l` `associate-/r*`
2×	`sqrt-pow1` `pow1/2` `associate-/r/`
1×	`frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

4 → 99

Calls

4 calls:

10.0ms	(* a (sqrt (pow k m)))
2.0ms	(sqrt (pow k m))
3.0ms	(sqrt (pow k m))
13.0ms	(/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* a (sqrt (pow k m)))
63.0ms	(sqrt (pow k m))
68.0ms	(sqrt (pow k m))
125.0ms	(/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify63.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	469	809
1	2337	693
2	5002	659

prune385.0ms

Filtered

111 candidates to 87 candidates (78.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.2b	(* a (pow k m))
2.9b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
14×	`add-sqr-sqrt`
10×	`add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-log-exp`
7×	`associate-r`
6×	`prod-exp`
4×	`unpow-prod-down` `div-exp`
3×	`pow1` `expm1-log1p-u` `fma-def` `times-frac` `associate-l` `associate-/r*` `sum-log` `log1p-expm1-u` `unswap-sqr`
2×	`cbrt-undiv` `pow-to-exp` `flip3-+` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`+-commutative` `associate-+l+` `frac-2neg` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

3 → 72

Calls

3 calls:

5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
5.0ms	(* a (pow k m))
9.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
60.0ms	(* a (pow k m))
125.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify63.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	419	575
1	2040	495
2	5002	476

prune231.0ms

Filtered

81 candidates to 59 candidates (72.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
2.9b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
5.6b	(sqrt (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))
5.6b	(sqrt (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
18×	`sqrt-prod`
14×	`add-sqr-sqrt` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
8×	`div-exp` `associate-/r/`
6×	`pow1` `prod-exp` `associate-/r*`
4×	`cbrt-undiv` `expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `pow-exp` `clear-num` `cbrt-unprod` `associate-/l*`

Counts

4 → 98

Calls

4 calls:

9.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
9.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
7.0ms	(sqrt (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))
7.0ms	(sqrt (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))

series692.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
124.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
225.0ms	(sqrt (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))
219.0ms	(sqrt (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))

simplify62.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	459	1338
1	2040	1200
2	5001	1158

prune455.0ms

Filtered

110 candidates to 90 candidates (81.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes122.0ms

Accuracy

98.5% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.3b

bsearch57.0ms

Steps

Iters	Range		Point
7	7.232028391489847e+54	8.011735395639846e+56	5.517677918177175e+56

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	34
1	54	34
2	54	34

end0.0ms

sample1.1s

Algorithm

intervals

Results

584.0ms	11882×	body	80	valid
171.0ms	4350×	body	80	nan