Details

analyze128.0ms

Algorithm: search

sample25.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify66.0ms

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

localize15.0ms

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)
0.9b	(* (* b b) (+ 3.0 a))

rewrite29.0ms

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))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
8.0ms	(* (* b b) (+ 3.0 a))

series58.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
5.0ms	(* (* a a) (- 1.0 a))
23.0ms	(pow (+ (* a a) (* b b)) 2.0)
5.0ms	(* (* b b) (+ 3.0 a))

simplify68.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (59.0ms)

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

prune164.0ms

Filtered

63 candidates to 93 candidates (-47.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	7	94

Merged error: 0.0b

Counts

94 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (+ 1.0 a))
0.1b	(* (* a a) (- (* 1.0 1.0) (* a a)))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.9b	(* (* b b) (+ 3.0 a))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
23×	`add-cbrt-cube`
16×	`*-un-lft-identity`
15×	`pow1`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`prod-exp` `cbrt-unprod`
8×	`associate-r`
6×	`associate-*r/` `pow-prod-down`
4×	`times-frac` `associate-/r*` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `unpow-prod-down` `pow-unpow` `distribute-lft-in` `div-exp` `distribute-lft-out`
2×	`sub-neg` `flip3--` `flip3-+` `associate-l` `associate-/r/` `*-commutative` `flip--` `flip-+` `associate-/l/` `unswap-sqr`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `pow-exp` `clear-num` `div-inv` `associate-/l*` `difference-of-squares` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

13.0ms	(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (+ 1.0 a))
8.0ms	(* (* a a) (- (* 1.0 1.0) (* a a)))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
8.0ms	(* (* b b) (+ 3.0 a))

series46.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (+ 1.0 a))
8.0ms	(* (* a a) (- (* 1.0 1.0) (* a a)))
23.0ms	(pow (+ (* a a) (* b b)) 2.0)
6.0ms	(* (* b b) (+ 3.0 a))

simplify87.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	603	754
1	3242	635
2	5001	633

prune169.0ms

Filtered

70 candidates to 108 candidates (-54.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	108	7	115

Merged error: 0.0b

Counts

115 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (* b b) (+ 3.0 a))
0.9b	(* (* b b) (+ 3.0 a))
9.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
9.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

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

series73.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (* b b) (+ 3.0 a))
5.0ms	(* (* b b) (+ 3.0 a))
32.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
30.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	321	932
1	1454	858
2	5002	856

prune240.0ms

Filtered

60 candidates to 90 candidates (-50.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	90	7	97

Merged error: 0.0b

Counts

97 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (* b b) (+ 3.0 a))
24.1b	(cbrt (* (* a a) (- 1.0 a)))
24.1b	(cbrt (* (* a a) (- 1.0 a)))
24.1b	(cbrt (* (* a a) (- 1.0 a)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

12.0ms	(* (* b b) (+ 3.0 a))
10.0ms	(cbrt (* (* a a) (- 1.0 a)))
10.0ms	(cbrt (* (* a a) (- 1.0 a)))
11.0ms	(cbrt (* (* a a) (- 1.0 a)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (* b b) (+ 3.0 a))
13.0ms	(cbrt (* (* a a) (- 1.0 a)))
15.0ms	(cbrt (* (* a a) (- 1.0 a)))
13.0ms	(cbrt (* (* a a) (- 1.0 a)))

simplify41.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	343	625
1	1372	559
2	5001	523

prune181.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	69	7	76

Merged error: 0.0b

Counts

76 → 7

regimes234.0ms

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	18
1	29	18

end0.0ms

analyze122.0ms

Algorithm: search

sample615.0ms

Algorithm

intervals

Results

487.0ms	8000×	body	80	valid
0.0ms	6×	body	80	invalid

Details

analyze128.0ms

sample25.0ms

simplify66.0ms

prune3.0ms

localize15.0ms

rewrite29.0ms

series58.0ms

simplify68.0ms

prune164.0ms

localize19.0ms

rewrite36.0ms

series46.0ms

simplify87.0ms

prune169.0ms

localize21.0ms

rewrite29.0ms

series73.0ms

simplify45.0ms

prune240.0ms

localize21.0ms

rewrite46.0ms

series51.0ms

simplify41.0ms

prune181.0ms

regimes234.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze122.0ms

sample615.0ms

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