Details

analyze459.0ms

Algorithm: search

sample41.0ms

Algorithm

intervals

Results

9.0ms	181×	body	80	valid
8.0ms	28×	body	2560	valid
6.0ms	26×	body	1280	valid
2.0ms	10×	body	640	valid
1.0ms	19×	body	80	nan
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	10×	body	80	invalid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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: 32.4b

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))
0.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
24.1b	(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:

12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
17.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (34.0ms)

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

prune177.0ms

Filtered

65 candidates to 89 candidates (-36.9%)

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: 7.5b

Counts

90 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
24.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

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

series75.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
16.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify68.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (51.0ms)

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

prune171.0ms

Filtered

73 candidates to 137 candidates (-87.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	137	9	146

Merged error: 7.5b

Counts

146 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
7.6b	(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
24.1b	(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))
3.0ms	(- (* 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:

34.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
24.0ms	(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

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

prune153.0ms

Filtered

68 candidates to 88 candidates (-29.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	88	9	97

Merged error: 7.5b

Counts

97 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.5b	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
17.0b	(- (pow b 2) (pow b 2))
24.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`unpow-prod-down`
19×	`add-exp-log`
16×	`difference-of-squares`
15×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--` `add-log-exp`
8×	`distribute-lft-out--`
7×	`div-exp`
5×	`pow1` `associate-/l/`
4×	`cbrt-undiv` `prod-exp`
3×	`flip3-+` `times-frac` `associate-/r*` `sqrt-prod` `flip-+`
2×	`frac-times` `flip3--` `sqrt-div` `associate-*r/` `sum-log` `flip--` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `rec-exp` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `+-inverses` `diff-log` `1-exp` `neg-log` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 107

Calls

4 calls:

7.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0ms	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
7.0ms	(- (pow b 2) (pow b 2))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series34.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
1.0ms	(- (pow b 2) (pow b 2))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify198.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (188.0ms)

Iter	Nodes	Cost
0	590	777
1	3981	571
2	5002	555

prune187.0ms

Filtered

79 candidates to 119 candidates (-50.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	118	10	128

Merged error: 7.5b

Counts

128 → 10

regimes389.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.3b

bsearch884.0ms

Steps

Iters	Range	Point
10	1.3276812284778394e+80	7.239746687445401e+95	7.112223899555998e+94
9	6.316571832843378e-268	1.5817710304477146e-259	2.4401530635164625e-262
10	-4.8908751238470227e+154	-7.181262992992344e+144	-1.164448204895336e+151

Iters

Range

Point

1.3276812284778394e+80

7.239746687445401e+95

7.112223899555998e+94

6.316571832843378e-268

1.5817710304477146e-259

2.4401530635164625e-262

-4.8908751238470227e+154

-7.181262992992344e+144

-1.164448204895336e+151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	26
1	43	26

end0.0ms

analyze451.0ms

Algorithm: search

sample1.2s

Algorithm

intervals

Results

325.0ms	1059×	body	2560	valid
272.0ms	5123×	body	80	valid
218.0ms	883×	body	1280	valid
89.0ms	464×	body	640	valid
42.0ms	115×	body	5120	valid
37.0ms	251×	body	320	valid
33.0ms	627×	body	80	nan
23.0ms	420×	body	80	invalid
10.0ms	105×	body	160	valid

Details

analyze459.0ms

sample41.0ms

simplify12.0ms

prune4.0ms

localize11.0ms

rewrite28.0ms

series60.0ms

simplify44.0ms

prune177.0ms

localize12.0ms

rewrite35.0ms

series75.0ms

simplify68.0ms

prune171.0ms

localize12.0ms

rewrite31.0ms

series81.0ms

simplify50.0ms

prune153.0ms

localize17.0ms

rewrite44.0ms

series34.0ms

simplify198.0ms

prune187.0ms

regimes389.0ms

bsearch884.0ms

simplify2.0ms

end0.0ms

analyze451.0ms

sample1.2s

Profiling