Details

analyze474.0ms

Algorithm: search

sample44.0ms

Algorithm

intervals

Results

14.0ms	47×	body	2560	valid
8.0ms	157×	body	80	valid
5.0ms	22×	body	1280	valid
2.0ms	11×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	18×	body	80	nan
1.0ms	14×	body	80	invalid
0.0ms	4×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

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: 36.4b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
6.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* 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)))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5002	673

prune158.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 7.1b

Counts

83 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4.0 a) c))
3.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.7b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series122.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
43.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
57.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	637	2580
1	3184	2341
2	5001	2328

prune281.0ms

Filtered

106 candidates to 160 candidates (-50.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	158	10	168

Merged error: 7.0b

Counts

168 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4.0 a) c))
3.3b	(* (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
10.7b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
51×	`add-exp-log`
46×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-l` `add-cbrt-cube`
20×	`prod-exp`
16×	`div-exp`
14×	`distribute-lft-out--` `difference-of-squares`
10×	`sqrt-prod`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1` `distribute-rgt-neg-in` `associate-r` `associate-/r*`
6×	`add-log-exp`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 143

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
22.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
42.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
58.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify138.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	729	2303
1	3953	1983
2	5001	1976

prune247.0ms

Filtered

98 candidates to 155 candidates (-58.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	155	10	165

Merged error: 7.0b

Counts

165 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/r*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 69

Calls

4 calls:

13.0ms	(/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(- (* 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)))

simplify44.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	376	757
1	1594	658
2	5001	645

prune105.0ms

Filtered

61 candidates to 81 candidates (-32.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	80	11	91

Merged error: 7.0b

Counts

91 → 11

regimes461.0ms

Accuracy

82.7% (4.7b remaining)

Error of 10.0b against oracle of 5.4b and baseline of 32.4b

bsearch502.0ms

Steps

Iters	Range		Point
8	1.0121811463366305e-46	7.90619011418034e-44	4.2139677410752915e-45
8	-7.400135821921412e+97	-2.0353633612918009e+93	-3.9716980978113024e+95

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

analyze470.0ms

Algorithm: search

sample1.3s

Algorithm

intervals

Results

337.0ms	1104×	body	2560	valid
274.0ms	5158×	body	80	valid
219.0ms	875×	body	1280	valid
85.0ms	434×	body	640	valid
40.0ms	109×	body	5120	valid
33.0ms	660×	body	80	nan
29.0ms	202×	body	320	valid
21.0ms	368×	body	80	invalid
12.0ms	118×	body	160	valid

Details

analyze474.0ms

sample44.0ms

simplify10.0ms

prune3.0ms

localize11.0ms

rewrite29.0ms

series61.0ms

simplify46.0ms

prune158.0ms

localize16.0ms

rewrite41.0ms

series122.0ms

simplify109.0ms

prune281.0ms

localize18.0ms

rewrite47.0ms

series123.0ms

simplify138.0ms

prune247.0ms

localize13.0ms

rewrite29.0ms

series88.0ms

simplify44.0ms

prune105.0ms

regimes461.0ms

bsearch502.0ms

simplify2.0ms

end0.0ms

analyze470.0ms

sample1.3s

Profiling