Details

sample69.0ms

Algorithm

intervals

Results

46.0ms

691×

body

valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	14
1	155	14
2	430	14
3	1195	14
4	2526	14
5	5001	14

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

localize20.0ms

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) (+ 3.0 a)))))
0.1b	(* (* a a) (- 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
1.4b	(* (* b b) (+ 3.0 a))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
12×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`associate-r`
8×	`add-cube-cbrt`
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` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 81

Calls

4 calls:

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

series62.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
6.0ms	(* (* a a) (- 1.0 a))
22.0ms	(pow (+ (* a a) (* b b)) 2.0)
6.0ms	(* (* b b) (+ 3.0 a))

simplify71.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	549	670
1	2714	602
2	5001	598

prune152.0ms

Filtered

63 candidates to 93 candidates (-47.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	6	94

Merged error: 0.0b

Counts

94 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (* b b) (+ 3.0 a))
11.9b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
11.9b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
11.9b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

8.0ms	(* (* b b) (+ 3.0 a))
6.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
6.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
6.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series129.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (* b b) (+ 3.0 a))
40.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
40.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
42.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	366	1390
1	1549	1264
2	5001	1228

prune323.0ms

Filtered

61 candidates to 75 candidates (-23.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	75	6	81

Merged error: 0.0b

Counts

81 → 6

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))))
8.0ms	(* 2 (* (pow a 2) (pow b 2)))
9.0ms	(* (pow a 2) (pow b 2))

simplify57.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (47.0ms)

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

prune140.0ms

Filtered

47 candidates to 96 candidates (-104.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	96	6	102

Merged error: 0.0b

Counts

102 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
1.4b	(* (* b b) (+ 3.0 a))
28.2b	(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`cbrt-prod`
11×	`pow1` `add-exp-log`
10×	`add-cbrt-cube`
9×	`unpow-prod-down`
6×	`pow-unpow` `cube-prod`
4×	`cube-div` `associate-r` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+` `sqr-pow`
2×	`cube-mult` `pow-to-exp` `cbrt-div` `pow-pow` `unpow3` `associate-*r/` `pow-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/3` `associate-l` `*-commutative` `rem-cbrt-cube` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

7.0ms	(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
11.0ms	(* (* b b) (+ 3.0 a))
7.0ms	(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))

series208.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)
22.0ms	(pow (+ (* a a) (* b b)) 2.0)
6.0ms	(* (* b b) (+ 3.0 a))
25.0ms	(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))

simplify80.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	561	1431
1	2807	1313
2	5002	1303

prune174.0ms

Filtered

59 candidates to 101 candidates (-71.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	1	2
Picked	1	0	1
Done	1	2	3
Total	103	4	107

Merged error: 0.0b

Counts

107 → 4

regimes249.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	45
1	29	45

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.4s

20575×

body

valid

Details

sample69.0ms

simplify73.0ms

prune3.0ms

localize20.0ms

rewrite30.0ms

series62.0ms

simplify71.0ms

prune152.0ms

localize22.0ms

rewrite27.0ms

series129.0ms

simplify51.0ms

prune323.0ms

localize13.0ms

rewrite22.0ms

series26.0ms

simplify57.0ms

prune140.0ms

localize20.0ms

rewrite32.0ms

series208.0ms

simplify80.0ms

prune174.0ms

regimes249.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.0s

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