Details

sample96.0ms

Algorithm

intervals

Results

18.0ms	192×	body	80	valid
17.0ms	31×	body	2560	valid
16.0ms	35×	body	1280	valid
8.0ms	89×	body	80	nan
4.0ms	11×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	5×	body	160	valid

simplify400.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (397.0ms)

Iter	Nodes	Cost
0	1931	17
1	1931	17

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 38.3b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b	(- (* b b) (* 4.0 (* a c)))
1.8b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite59.0ms

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:

22.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
7.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series105.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms	(- (* b b) (* 4.0 (* a c)))
27.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify90.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5946	1465

prune333.0ms

Filtered

64 candidates to 89 candidates (-39.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	11	90

Merged error: 6.1b

Counts

90 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0b	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.3b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
28.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
23.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series241.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
82.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
106.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
26.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify81.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5232	2499

prune381.0ms

Filtered

84 candidates to 125 candidates (-48.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	6	3	9
Picked	1	0	1
Done	0	1	1
Total	127	9	136

Merged error: 6.0b

Counts

136 → 9

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
1.2b	(- (* b b) (* 4.0 (* a c)))
1.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

19.0ms	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series157.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
15.0ms	(- (* b b) (* 4.0 (* a c)))
25.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
29.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify132.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4943	1608
1	4943	1608

prune319.0ms

Filtered

69 candidates to 95 candidates (-37.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	95	9	104

Merged error: 5.9b

Counts

104 → 9

localize36.0ms

Local error

Found 4 expressions with local error:

3.8b	(* (/ 4.0 (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* (/ c (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) a))
4.0b	(/ (* (/ 4.0 (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* (/ c (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) a)) (* 2.0 a))
24.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-exp-log` `add-cbrt-cube`
37×	`prod-exp` `cbrt-unprod`
36×	`add-sqr-sqrt`
33×	`associate-l`
29×	`cbrt-undiv` `div-exp`
28×	`*-un-lft-identity` `times-frac`
27×	`sqrt-prod`
22×	`add-cube-cbrt`
11×	`pow1`
6×	`sqrt-div` `associate-*l/` `difference-of-squares`
4×	`add-log-exp`
3×	`flip3--` `pow-prod-down` `flip--` `associate-/l/` `distribute-lft-out--`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `associate-/r/` `div-inv`
1×	`frac-2neg` `associate-r` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

4 → 133

Calls

4 calls:

58.0ms	(* (/ 4.0 (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* (/ c (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) a))
58.0ms	(/ (* (/ 4.0 (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* (/ c (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) a)) (* 2.0 a))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (/ 4.0 (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* (/ c (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) a))
59.0ms	(/ (* (/ 4.0 (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* (/ c (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) a)) (* 2.0 a))
27.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
26.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify90.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5180	3957

prune511.0ms

Filtered

86 candidates to 145 candidates (-68.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	144	10	154

Merged error: 5.9b

Counts

154 → 10

regimes917.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 30.0b

bsearch157.0ms

Steps

Iters	Range		Point
5	1.1994113433831075e+59	2.551497614016684e+59	2.517726559601462e+59
9	8.181651543211295e-234	3.895310942336471e-227	8.727612177657317e-234
8	-9.755383452814402e+129	-1.823895620004969e+126	-2.2204211290805433e+129

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	137	73
1	137	73

end0.0ms

sample2.9s

Algorithm

intervals

Results

576.0ms	1016×	body	2560	valid
547.0ms	5870×	body	80	valid
418.0ms	923×	body	1280	valid
270.0ms	2935×	body	80	nan
173.0ms	463×	body	640	valid
66.0ms	98×	body	5120	valid
61.0ms	227×	body	320	valid
20.0ms	110×	body	160	valid

Details

sample96.0ms

simplify400.0ms

prune13.0ms

localize22.0ms

rewrite59.0ms

series105.0ms

simplify90.0ms

prune333.0ms

localize28.0ms

rewrite81.0ms

series241.0ms

simplify81.0ms

prune381.0ms

localize31.0ms

rewrite55.0ms

series157.0ms

simplify132.0ms

prune319.0ms

localize36.0ms

rewrite147.0ms

series174.0ms

simplify90.0ms

prune511.0ms

regimes917.0ms

bsearch157.0ms

simplify4.0ms

end0.0ms

sample2.9s

Profiling