Details

sample56.0ms

Algorithm

intervals

Results

10.0ms	36×	body	2560	valid
10.0ms	184×	body	80	valid
5.0ms	23×	body	1280	valid
4.0ms	89×	body	80	nan
3.0ms	18×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	8×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

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: 36.0b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b	(- (* b b) (* (* 3.0 a) c))
1.7b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	391	774
1	1518	684
2	5001	674

prune170.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	72	11	83

Merged error: 5.7b

Counts

83 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.9b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.3b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 154

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
17.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series129.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
44.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
56.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	644	2693
1	3143	2447
2	5001	2434

prune475.0ms

Filtered

111 candidates to 166 candidates (-49.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	165	12	177

Merged error: 5.6b

Counts

177 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

15.3b	(cbrt (+ 0 (* 3.0 (* a c))))
15.3b	(cbrt (+ 0 (* 3.0 (* a c))))
15.3b	(cbrt (+ 0 (* 3.0 (* a c))))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `sqrt-prod` `flip-+`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 54

Calls

4 calls:

2.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
2.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
2.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
16.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
18.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	257	548
1	1011	508
2	5001	492

prune218.0ms

Filtered

61 candidates to 66 candidates (-8.2%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	66	12	78

Merged error: 5.6b

Counts

78 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
1.7b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
4.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 3.0 a) c)
8.0ms	(- (* b b) (* (* 3.0 a) c))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	302	468
1	1299	428
2	5002	417

prune89.0ms

Filtered

52 candidates to 72 candidates (-38.5%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	71	13	84

Merged error: 5.6b

Counts

84 → 13

regimes815.0ms

Accuracy

87.2% (3.5b remaining)

Error of 9.0b against oracle of 5.6b and baseline of 32.8b

bsearch105.0ms

Steps

Iters	Range	Point
7	7.012417207579252e+108	1.3633655355432952e+110	7.091702199968928e+108
10	2.6835842014060276e-138	1.2377688018938939e-119	1.2326174769211632e-137
9	-8.123118303304505e+80	-8.66777673642249e+74	-3.453036615513107e+80

Iters

Range

Point

7.012417207579252e+108

1.3633655355432952e+110

7.091702199968928e+108

2.6835842014060276e-138

1.2377688018938939e-119

1.2326174769211632e-137

-8.123118303304505e+80

-8.66777673642249e+74

-3.453036615513107e+80

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	29
1	48	29
2	48	29

end0.0ms

sample1.6s

Algorithm

intervals

Results

325.0ms	1104×	body	2560	valid
301.0ms	5835×	body	80	valid
202.0ms	854×	body	1280	valid
145.0ms	2894×	body	80	nan
88.0ms	470×	body	640	valid
39.0ms	112×	body	5120	valid
35.0ms	234×	body	320	valid
13.0ms	124×	body	160	valid

Details

sample56.0ms

simplify9.0ms

prune4.0ms

localize10.0ms

rewrite27.0ms

series64.0ms

simplify43.0ms

prune170.0ms

localize17.0ms

rewrite47.0ms

series129.0ms

simplify114.0ms

prune475.0ms

localize24.0ms

rewrite11.0ms

series64.0ms

simplify57.0ms

prune218.0ms

localize13.0ms

rewrite21.0ms

series40.0ms

simplify40.0ms

prune89.0ms

regimes815.0ms

bsearch105.0ms

simplify2.0ms

end0.0ms

sample1.6s

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