Details

sample50.0ms

Algorithm

intervals

Results

10.0ms	33×	body	2560	valid
9.0ms	172×	body	80	valid
7.0ms	31×	body	1280	valid
4.0ms	73×	body	80	nan
3.0ms	14×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	11×	body	160	valid

simplify15.0ms

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 36.1b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.4b	(- (* b b) (* 4.0 (* a c)))
2.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

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	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune230.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	8	90

Merged error: 5.5b

Counts

90 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.2b	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
18.5b	(- (pow b 2) (pow b 2))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 175

Calls

4 calls:

29.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
29.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
8.0ms	(- (pow b 2) (pow b 2))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series354.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
161.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
1.0ms	(- (pow b 2) (pow b 2))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify179.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (154.0ms)

Iter	Nodes	Cost
0	761	2839
1	3905	2393
2	5002	2366

prune442.0ms

Filtered

187 candidates to 124 candidates (66.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	188	7	195

Merged error: 5.5b

Counts

195 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b	(- (* b b) (* 4.0 (* a c)))
14.8b	(/ (* 4.0 (* a c)) a)
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
6.0ms	(/ (* 4.0 (* a c)) a)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
287.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(/ (* 4.0 (* a c)) a)
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	344	518
1	1520	468
2	5001	450

prune175.0ms

Filtered

77 candidates to 54 candidates (70.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	77	7	84

Merged error: 5.5b

Counts

84 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b	(- (* b b) (* 4.0 (* a c)))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

11.0ms	(/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
83.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
45.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	346	764
1	1376	681
2	5001	678

prune181.0ms

Filtered

83 candidates to 61 candidates (73.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	83	7	90

Merged error: 5.5b

Counts

90 → 7

regimes170.0ms

Accuracy

94.6% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.7b

bsearch200.0ms

Steps

Iters	Range	Point
7	6.011887282010727e+43	5.675568733030414e+45	5.6015260252764486e+45
9	-1.3767648779983776e-304	9.315340853673907e-306	5.658228075089988e-307
8	-3.270551254255918e+118	-2.131753517190888e+115	-9.646585596466915e+117

Iters

Range

Point

6.011887282010727e+43

5.675568733030414e+45

5.6015260252764486e+45

-1.3767648779983776e-304

9.315340853673907e-306

5.658228075089988e-307

-3.270551254255918e+118

-2.131753517190888e+115

-9.646585596466915e+117

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	26
1	47	26

end0.0ms

sample1.4s

Algorithm

intervals

Results

327.0ms	1062×	body	2560	valid
301.0ms	5799×	body	80	valid
224.0ms	927×	body	1280	valid
147.0ms	2900×	body	80	nan
92.0ms	463×	body	640	valid
34.0ms	238×	body	320	valid
32.0ms	90×	body	5120	valid
12.0ms	120×	body	160	valid

Details

sample50.0ms

simplify15.0ms

prune3.0ms

localize16.0ms

rewrite31.0ms

series301.0ms

simplify46.0ms

prune230.0ms

localize16.0ms

rewrite78.0ms

series354.0ms

simplify179.0ms

prune442.0ms

localize13.0ms

rewrite22.0ms

series461.0ms

simplify43.0ms

prune175.0ms

localize18.0ms

rewrite28.0ms

series396.0ms

simplify43.0ms

prune181.0ms

regimes170.0ms

bsearch200.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling