Details

sample73.0ms

Algorithm

intervals

Results

48.0ms

691×

body

valid

simplify96.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	15
1	161	15
2	459	15
3	1323	15
4	2992	15
5	5001	15

prune3.0ms

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: 0.2b

Counts

2 → 1

localize17.0ms

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)
1.3b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
3×	`unpow-prod-down` `pow-unpow`
2×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

7.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms	(* (* a a) (+ 1.0 a))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms	(* (* a a) (+ 1.0 a))
21.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify72.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	547	721
1	2714	641
2	5001	637

prune149.0ms

Filtered

61 candidates to 91 candidates (-49.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	87	5	92

Merged error: 0.0b

Counts

92 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2.0)
1.3b	(* (* b b) (- 1.0 (* 3.0 a)))
4.5b	(exp (log (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))))
11.5b	(log (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
11×	`add-exp-log` `add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-cbrt-cube`
6×	`log-prod`
4×	`log-div` `exp-prod` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-r` `exp-sum` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `exp-diff` `associate-*r/` `log-pow` `flip-+`
1×	`pow-to-exp` `flip3--` `pow-pow` `rem-log-exp` `associate-l` `pow-exp` `*-commutative` `flip--` `rem-exp-log` `unswap-sqr` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

5.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
7.0ms	(exp (log (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))))
6.0ms	(log (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
27.0ms	(exp (log (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))))
26.0ms	(log (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	486	1125
1	2066	1009
2	5003	977

prune161.0ms

Filtered

57 candidates to 85 candidates (-49.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	85	5	90

Merged error: 0.0b

Counts

90 → 5

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
3.4b	(* (pow a 2) (pow b 2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
28×	`prod-exp`
24×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
12×	`pow-to-exp` `pow-exp`
11×	`associate-l`
10×	`add-cbrt-cube` `unpow2` `sqr-pow`
9×	`associate-r`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-log-exp`
4×	`cbrt-unprod`
2×	`pow-prod-down` `*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

3 → 87

Calls

3 calls:

4.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
7.0ms	(* 2 (* (pow a 2) (pow b 2)))
7.0ms	(* (pow a 2) (pow b 2))

series26.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
10.0ms	(* 2 (* (pow a 2) (pow b 2)))
7.0ms	(* (pow a 2) (pow b 2))

simplify47.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	297	518
1	1270	444
2	5001	432

prune131.0ms

Filtered

47 candidates to 96 candidates (-104.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	96	5	101

Merged error: 0.0b

Counts

101 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
1.3b	(* (* b b) (- 1.0 (* 3.0 a)))
24.8b	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

29×	`unpow-prod-down`
20×	`cbrt-prod`
18×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`cube-prod`
12×	`add-exp-log`
10×	`pow1` `add-cbrt-cube`
7×	`sqr-pow`
6×	`pow-unpow`
5×	`pow-exp`
4×	`add-log-exp`
3×	`pow-to-exp` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `cube-mult` `sub-neg` `pow-pow` `distribute-lft-in` `unpow3` `associate-*r/`
1×	`flip3--` `pow1/3` `associate-l` `*-commutative` `flip--` `rem-cbrt-cube` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

6.0ms	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
6.0ms	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

series91.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
21.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
33.0ms	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

simplify59.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	428	862
1	1816	824
2	5002	804

prune162.0ms

Filtered

66 candidates to 116 candidates (-75.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	116	5	121

Merged error: 0.0b

Counts

121 → 5

regimes250.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	15
1	27	15

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.5s

20575×

body

valid

Details

sample73.0ms

simplify96.0ms

prune3.0ms

localize17.0ms

rewrite28.0ms

series61.0ms

simplify72.0ms

prune149.0ms

localize22.0ms

rewrite28.0ms

series81.0ms

simplify62.0ms

prune161.0ms

localize13.0ms

rewrite22.0ms

series26.0ms

simplify47.0ms

prune131.0ms

localize20.0ms

rewrite29.0ms

series91.0ms

simplify59.0ms

prune162.0ms

regimes250.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.0s

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