Details

sample71.0ms

Algorithm

intervals

Results

39.0ms

620×

body

valid

simplify99.0ms

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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.2b

Counts

2 → 1

localize16.0ms

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)
0.6b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite33.0ms

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

series383.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
65.0ms	(* (* a a) (+ 1.0 a))
123.0ms	(pow (+ (* a a) (* b b)) 2.0)
67.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify72.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	504	702
1	2520	622
2	5003	622

prune542.0ms

Filtered

91 candidates to 61 candidates (33.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	5	92

Merged error: 0.0b

Counts

92 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0))
0.1b	(* (* a a) (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.6b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite31.0ms

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×	`associate-*r/`
3×	`distribute-rgt-in` `unpow-prod-down` `pow-unpow` `distribute-lft-in`
2×	`sub-neg` `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 → 77

Calls

4 calls:

7.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0))
8.0ms	(* (* a a) (+ 1.0 a))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
10.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0))
67.0ms	(* (* a a) (+ 1.0 a))
127.0ms	(pow (+ (* a a) (* b b)) 2.0)
67.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify66.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	484	599
1	2423	527
2	5003	527

prune532.0ms

Filtered

89 candidates to 59 candidates (33.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	90	4	94

Merged error: 0.0b

Counts

94 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (- 1.0 (* 3.0 a)))
10.1b	(cbrt (+ (* a a) (* b b)))
10.1b	(cbrt (+ (* a a) (* b b)))
10.1b	(cbrt (+ (* a a) (* b b)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
3.0ms	(cbrt (+ (* a a) (* b b)))
3.0ms	(cbrt (+ (* a a) (* b b)))
3.0ms	(cbrt (+ (* a a) (* b b)))

series412.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
112.0ms	(cbrt (+ (* a a) (* b b)))
120.0ms	(cbrt (+ (* a a) (* b b)))
111.0ms	(cbrt (+ (* a a) (* b b)))

simplify44.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	277	537
1	1234	483
2	5002	474

prune595.0ms

Filtered

76 candidates to 58 candidates (23.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	76	4	80

Merged error: 0.0b

Counts

80 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a)))))
0.0b	(- 1.0 (* 3.0 a))
0.6b	(* (* b b) (- 1.0 (* 3.0 a)))
1.6b	(* (pow a 2) (pow b 2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`add-exp-log`
17×	`unswap-sqr`
15×	`add-log-exp`
14×	`unpow-prod-down`
12×	`prod-exp`
11×	`associate-r` `add-cbrt-cube`
10×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/` `unpow2` `sqr-pow`
9×	`pow1` `add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`associate-+r+`
7×	`sub-neg`
6×	`pow-to-exp` `pow-exp` `sum-log`
4×	`flip3--` `pow-prod-down` `frac-add` `flip--` `cbrt-unprod`
3×	`flip3-+` `flip-+`
2×	`*-commutative`
1×	`+-commutative` `associate-+l+` `diff-log`

Counts

4 → 114

Calls

4 calls:

13.0ms	(+ (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a)))))
3.0ms	(- 1.0 (* 3.0 a))
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
8.0ms	(* (pow a 2) (pow b 2))

series271.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a)))))
43.0ms	(- 1.0 (* 3.0 a))
67.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
42.0ms	(* (pow a 2) (pow b 2))

simplify104.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	651	1149
1	3179	1030
2	5001	1026

prune1.1s

Filtered

126 candidates to 73 candidates (42.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	126	4	130

Merged error: 0.0b

Counts

130 → 4

regimes145.0ms

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	29	16
1	29	16

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.3s

20249×

body

valid

Details

sample71.0ms

simplify99.0ms

prune5.0ms

localize16.0ms

rewrite33.0ms

series383.0ms

simplify72.0ms

prune542.0ms

localize16.0ms

rewrite31.0ms

series374.0ms

simplify66.0ms

prune532.0ms

localize21.0ms

rewrite19.0ms

series412.0ms

simplify44.0ms

prune595.0ms

localize19.0ms

rewrite34.0ms

series271.0ms

simplify104.0ms

prune1.1s

regimes145.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.8s

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