Details

sample64.0ms

Algorithm

intervals

Results

45.0ms

676×

body

valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	55	15
1	179	14
2	561	13
3	1824	13
4	5002	13

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize22.0ms

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)
0.8b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
12×	`add-cube-cbrt`
7×	`distribute-rgt-in` `fma-def` `distribute-lft-in` `associate-r`
6×	`unpow-prod-down` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`pow-unpow`
2×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out`

Counts

4 → 100

Calls

4 calls:

9.0ms	(+ (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)
8.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series558.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
49.0ms	(* (* a a) (+ 1.0 a))
342.0ms	(pow (+ (* a a) (* b b)) 2.0)
54.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify77.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	564	828
1	2826	724
2	5001	715

prune292.0ms

Filtered

112 candidates to 80 candidates (71.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	106	6	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	6	113

Merged error: 0.0b

Counts

113 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (* b b) (- 1.0 (* 3.0 a)))
0.8b	(* (* b b) (- 1.0 (* 3.0 a)))
9.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-sqr-sqrt`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity` `prod-diff`
10×	`distribute-rgt-in` `distribute-lft-in`
6×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `sub-neg` `sqrt-div` `associate-*r/` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l` `*-commutative` `flip--` `flip-+` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

8.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
8.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
6.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
56.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
175.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
166.0ms	(sqrt (+ (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

112 → 112

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	388	1304
1	1674	1186
2	5002	1176

prune330.0ms

Filtered

112 candidates to 72 candidates (64.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	112	6	118

Merged error: 0.0b

Counts

118 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (* b b) (- 1.0 (* 3.0 a)))
10.0b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.0b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.0b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `cbrt-prod` `add-cbrt-cube`
6×	`cbrt-div` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

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

series602.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
190.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
180.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
177.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	401	1582
1	1689	1442
2	5002	1408

prune375.0ms

Filtered

90 candidates to 74 candidates (82.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	90	6	96

Merged error: 0.0b

Counts

96 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (* 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)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `cbrt-prod` `add-cbrt-cube`
6×	`cbrt-div` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms	(cbrt (+ (* a a) (* b b)))
3.0ms	(cbrt (+ (* a a) (* b b)))
4.0ms	(cbrt (+ (* a a) (* b b)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
91.0ms	(cbrt (+ (* a a) (* b b)))
91.0ms	(cbrt (+ (* a a) (* b b)))
91.0ms	(cbrt (+ (* a a) (* b b)))

simplify46.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	331	646
1	1480	584
2	5001	567

prune319.0ms

Filtered

90 candidates to 71 candidates (78.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	90	6	96

Merged error: 0.0b

Counts

96 → 6

regimes143.0ms

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	32
1	29	32

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.4s

20540×

body

valid