Details

analyze588.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample40.0ms

Algorithm

intervals

Results

8.0ms	173×	body	80	valid
8.0ms	31×	body	2560	valid
5.0ms	23×	body	1280	valid
3.0ms	17×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	26×	body	80	nan
1.0ms	6×	body	320	valid
0.0ms	9×	body	80	invalid
0.0ms	1×	body	160	valid

simplify478.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 32.6b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

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` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 82

Calls

4 calls:

10.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5743	1403

prune140.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 5.4b

Counts

95 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

3.1b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
4.1b	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
9.4b	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
40×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l*`
10×	`associate-/r/`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `distribute-lft-out`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
3×	`distribute-frac-neg` `sqrt-prod`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `distribute-rgt-neg-out` `cbrt-unprod`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `sum-log` `flip--` `associate-/l/`

Counts

4 → 114

Calls

4 calls:

5.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
9.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
37.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
51.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4948	2297
1	4948	2297

prune135.0ms

Filtered

98 candidates to 126 candidates (-28.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	128	7	135

Merged error: 5.3b

Counts

135 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
1.2b	(- (* b_2 b_2) (* a c))
3.1b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out`
4×	`associate-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 71

Calls

4 calls:

7.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5326	1109

prune100.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	81	9	90

Merged error: 5.3b

Counts

90 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
1.2b	(- (* b_2 b_2) (* a c))
5.5b	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

6.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
4.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
7.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4888	1599
1	4888	1599

prune91.0ms

Filtered

79 candidates to 103 candidates (-30.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	103	9	112

Merged error: 5.3b

Counts

112 → 9

regimes258.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.5b

bsearch95.0ms

Steps

Iters	Range	Point
9	7.142695134840945e+79	4.060737640007043e+87	1.8760651202363554e+87
10	-3.813210180097129e-281	-1.918300208831901e-291	-2.9621340593023486e-291
8	-4.6673400924698946e+114	-2.649039100327638e+111	-4.361350987131594e+113

Iters

Range

Point

7.142695134840945e+79

4.060737640007043e+87

1.8760651202363554e+87

-3.813210180097129e-281

-1.918300208831901e-291

-2.9621340593023486e-291

-4.6673400924698946e+114

-2.649039100327638e+111

-4.361350987131594e+113

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	55
1	83	55

end0.0ms

sample1.1s

Algorithm

intervals

Results

274.0ms	1106×	body	2560	valid
225.0ms	5098×	body	80	valid
185.0ms	927×	body	1280	valid
70.0ms	433×	body	640	valid
34.0ms	799×	body	80	nan
29.0ms	227×	body	320	valid
27.0ms	92×	body	5120	valid
12.0ms	271×	body	80	invalid
9.0ms	117×	body	160	valid

Details

analyze588.0ms

sample40.0ms

simplify478.0ms

prune11.0ms

localize11.0ms

rewrite30.0ms

series69.0ms

simplify52.0ms

prune140.0ms

localize12.0ms

rewrite36.0ms

series113.0ms

simplify53.0ms

prune135.0ms

localize10.0ms

rewrite23.0ms

series76.0ms

simplify49.0ms

prune100.0ms

localize10.0ms

rewrite37.0ms

series65.0ms

simplify46.0ms

prune91.0ms

regimes258.0ms

bsearch95.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling