Details

sample52.0ms

Algorithm

intervals

Results

27.0ms	278×	body	80	valid
7.0ms	88×	body	80	nan

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	18
1	79	18
2	136	18
3	161	18
4	173	18
5	177	18
6	177	18

prune4.0ms

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: 22.7b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.7b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 63

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	248	644
1	898	606
2	3865	590
3	5001	586

prune191.0ms

Filtered

60 candidates to 75 candidates (-25.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	7	76

Merged error: 7.8b

Counts

76 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.1b	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
5.2b	(/ (* a c) b)
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
13×	`*-un-lft-identity`
9×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`times-frac` `associate-/r*`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `sqrt-prod`
3×	`flip3--` `flip--`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 77

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.0ms	(/ (* a c) b)
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
5.0ms	(/ (* a c) b)
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	447	687
1	2162	609
2	5001	607

prune168.0ms

Filtered

65 candidates to 89 candidates (-36.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	89	7	96

Merged error: 6.8b

Counts

96 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.3b	(* a (/ c b))
4.1b	(/ (* 2.0 c) (- (* 2.0 (* a (/ c b))) (* 2 b)))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
14×	`add-exp-log` `add-cbrt-cube`
13×	`times-frac` `associate-r`
8×	`add-log-exp`
7×	`pow1`
4×	`sqrt-prod`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-l` `prod-exp` `associate-/r*` `flip--` `cbrt-unprod`
2×	`sqrt-div` `diff-log` `associate-/r/` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `clear-num` `-commutative` `associate-/l*`

Counts

4 → 88

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(* a (/ c b))
9.0ms	(/ (* 2.0 c) (- (* 2.0 (* a (/ c b))) (* 2 b)))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(* a (/ c b))
16.0ms	(/ (* 2.0 c) (- (* 2.0 (* a (/ c b))) (* 2 b)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	511	735
1	2479	657
2	5002	655

prune186.0ms

Filtered

73 candidates to 100 candidates (-37.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	99	8	107

Merged error: 6.8b

Counts

107 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (cbrt a) (/ c b))
2.4b	(* (* (cbrt a) (cbrt a)) (* (cbrt a) (/ c b)))
4.1b	(/ (* 2.0 c) (- (* 2.0 (* (* (cbrt a) (cbrt a)) (* (cbrt a) (/ c b)))) (* 2 b)))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
27×	`add-sqr-sqrt`
23×	`add-cbrt-cube`
19×	`pow1`
16×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp` `cbrt-unprod`
14×	`times-frac` `associate-r`
9×	`pow-prod-down`
7×	`associate-l`
5×	`cbrt-undiv` `cbrt-prod` `div-exp`
4×	`add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-/r` `sqrt-prod`
2×	`flip3--` `sqrt-div` `associate-/r/` `*-commutative` `flip--` `div-inv`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l*`

Counts

4 → 102

Calls

4 calls:

7.0ms	(* (cbrt a) (/ c b))
10.0ms	(* (* (cbrt a) (cbrt a)) (* (cbrt a) (/ c b)))
16.0ms	(/ (* 2.0 c) (- (* 2.0 (* (* (cbrt a) (cbrt a)) (* (cbrt a) (/ c b)))) (* 2 b)))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (cbrt a) (/ c b))
8.0ms	(* (* (cbrt a) (cbrt a)) (* (cbrt a) (/ c b)))
21.0ms	(/ (* 2.0 c) (- (* 2.0 (* (* (cbrt a) (cbrt a)) (* (cbrt a) (/ c b)))) (* 2 b)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	604	1041
1	2731	851
2	5001	816

prune160.0ms

Filtered

77 candidates to 114 candidates (-48.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	114	8	122

Merged error: 6.8b

Counts

122 → 8

regimes279.0ms

Accuracy

92.4% (1.2b remaining)

Error of 7.8b against oracle of 6.6b and baseline of 22.2b

bsearch70.0ms

Steps

Iters	Range		Point
9	7.012417207579252e+108	6.866534780894548e+114	1.2836931049081647e+114
9	-7.21165770739688e+50	-1.2355930349392776e+42	-5.400759275415969e+50

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	42
1	54	42

end0.0ms

sample1.4s

Algorithm

intervals

Results

746.0ms	8764×	body	80	valid
234.0ms	2909×	body	80	nan

Details

sample52.0ms

simplify13.0ms

prune4.0ms

localize21.0ms

rewrite23.0ms

series61.0ms

simplify112.0ms

prune191.0ms

localize24.0ms

rewrite27.0ms

series50.0ms

simplify52.0ms

prune168.0ms

localize24.0ms

rewrite30.0ms

series51.0ms

simplify64.0ms

prune186.0ms

localize29.0ms

rewrite41.0ms

series73.0ms

simplify70.0ms

prune160.0ms

regimes279.0ms

bsearch70.0ms

simplify2.0ms

end0.0ms

sample1.4s

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