Details

sample55.0ms

Algorithm

intervals

Results

10.0ms	195×	body	80	valid
8.0ms	28×	body	2560	valid
5.0ms	22×	body	1280	valid
4.0ms	75×	body	80	nan
3.0ms	17×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 32.8b

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))
1.4b	(- (* b b) (* 4.0 (* a c)))
1.9b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

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

series60.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms	(- (* 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))))

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	398	888
1	1466	803
2	5001	798

prune165.0ms

Filtered

89 candidates to 65 candidates (27.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	9	90

Merged error: 6.3b

Counts

90 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.4b	(- (* b b) (* 4.0 (* a c)))
1.9b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

15.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify71.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	538	1801
1	2573	1602
2	5002	1528

prune155.0ms

Filtered

137 candidates to 73 candidates (46.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	139	7	146

Merged error: 6.2b

Counts

146 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.4b	(- (* b b) (* 4.0 (* a c)))
7.3b	(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

7.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	418	881
1	1485	823
2	5002	813

prune138.0ms

Filtered

88 candidates to 68 candidates (22.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	88	7	95

Merged error: 6.2b

Counts

95 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* 4.0 (* a c)))
13.8b	(- (pow b 2) (pow b 2))
14.8b	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
22×	`unpow-prod-down`
19×	`add-exp-log` `*-un-lft-identity`
16×	`difference-of-squares`
15×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--`
8×	`distribute-lft-out--` `add-log-exp`
7×	`div-exp`
5×	`pow1` `associate-/l/`
4×	`cbrt-undiv` `prod-exp`
3×	`flip3--` `times-frac` `associate-/r*` `sqrt-prod` `flip--`
2×	`frac-times` `sub-neg` `flip3-+` `sqrt-div` `diff-log` `associate-*r/` `cbrt-unprod` `flip-+`
1×	`rem-sqrt-square` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `+-inverses` `1-exp` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 104

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (pow b 2) (pow b 2))
21.0ms	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
3.0ms	(- (pow b 2) (pow b 2))
4.0ms	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify172.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (163.0ms)

Iter	Nodes	Cost
0	522	717
1	3461	529
2	5002	480

prune157.0ms

Filtered

116 candidates to 73 candidates (37.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	116	7	123

Merged error: 6.2b

Counts

123 → 7

regimes239.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.0b against oracle of 5.0b and baseline of 29.2b

bsearch96.0ms

Steps

Iters	Range	Point
8	1.2099936426732458e+107	2.3384458119324726e+110	1.3604106813735005e+110
9	-5.1943839769957087e-306	1.0385722684675478e-305	1.7937395549211e-310
7	-6.682283173913537e+118	-3.724757707733592e+117	-4.2599201187066844e+117

Iters

Range

Point

1.2099936426732458e+107

2.3384458119324726e+110

1.3604106813735005e+110

-5.1943839769957087e-306

1.0385722684675478e-305

1.7937395549211e-310

-6.682283173913537e+118

-3.724757707733592e+117

-4.2599201187066844e+117

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	26
1	43	26

end0.0ms

sample1.7s

Algorithm

intervals

Results

307.0ms	5773×	body	80	valid
305.0ms	1009×	body	2560	valid
235.0ms	964×	body	1280	valid
156.0ms	3007×	body	80	nan
92.0ms	470×	body	640	valid
43.0ms	120×	body	5120	valid
32.0ms	216×	body	320	valid
12.0ms	125×	body	160	valid

Details

sample55.0ms

simplify14.0ms

prune4.0ms

localize11.0ms

rewrite28.0ms

series60.0ms

simplify43.0ms

prune165.0ms

localize13.0ms

rewrite34.0ms

series71.0ms

simplify71.0ms

prune155.0ms

localize15.0ms

rewrite31.0ms

series81.0ms

simplify45.0ms

prune138.0ms

localize18.0ms

rewrite39.0ms

series30.0ms

simplify172.0ms

prune157.0ms

regimes239.0ms

bsearch96.0ms

simplify2.0ms

end0.0ms

sample1.7s

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