Details

sample67.0ms

Algorithm

intervals

Results

13.0ms	194×	body	80	valid
8.0ms	34×	body	1280	valid
7.0ms	25×	body	2560	valid
4.0ms	92×	body	80	nan
2.0ms	13×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	5×	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: 31.7b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.1b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

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))
3.0ms	(- (* 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)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

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

prune154.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 4.4b

Counts

83 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
3.5b	(/ (/ (+ 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)))))
20.7b	(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))
15.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms	(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))))) (* 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)))

simplify111.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (87.0ms)

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

prune266.0ms

Filtered

106 candidates to 160 candidates (-50.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	156	4	160
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	161	9	170

Merged error: 4.3b

Counts

170 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
3.6b	(* (/ (+ 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)))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

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:

3.0ms	(- (* b b) (* (* 4.0 a) c))
19.0ms	(* (/ (+ 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)))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
45.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
98.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify136.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (117.0ms)

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

prune235.0ms

Filtered

99 candidates to 155 candidates (-56.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	155	9	164

Merged error: 4.3b

Counts

164 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
3.5b	(/ (* 1 (/ 4.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
10.5b	(/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(/ (* 1 (/ 4.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
32.0ms	(/ (* 1 (/ 4.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
21.0ms	(/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify91.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	762	1550
1	4074	1210
2	5001	1198

prune114.0ms

Filtered

63 candidates to 113 candidates (-79.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	113	9	122

Merged error: 4.3b

Counts

122 → 9

regimes262.0ms

Accuracy

82.2% (4.8b remaining)

Error of 10.3b against oracle of 5.5b and baseline of 32.6b

bsearch66.0ms

Steps

Iters	Range		Point
8	4.6842429409994347e-64	1.8297242317365662e-59	9.486198483324874e-62
10	-1.1906535729190708e+67	-5.5606112961667094e+54	-8.165795190759411e+60

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	16
1	38	16

end0.0ms

sample1.5s

Algorithm

intervals

Results

298.0ms	5840×	body	80	valid
298.0ms	1041×	body	2560	valid
217.0ms	914×	body	1280	valid
136.0ms	2767×	body	80	nan
90.0ms	471×	body	640	valid
38.0ms	106×	body	5120	valid
31.0ms	226×	body	320	valid
11.0ms	121×	body	160	valid

Details

sample67.0ms

simplify10.0ms

prune3.0ms

localize11.0ms

rewrite26.0ms

series64.0ms

simplify44.0ms

prune154.0ms

localize16.0ms

rewrite41.0ms

series123.0ms

simplify111.0ms

prune266.0ms

localize16.0ms

rewrite44.0ms

series172.0ms

simplify136.0ms

prune235.0ms

localize16.0ms

rewrite40.0ms

series78.0ms

simplify91.0ms

prune114.0ms

regimes262.0ms

bsearch66.0ms

simplify1.0ms

end0.0ms

sample1.5s

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