Details

analyze278.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

sample49.0ms (0.1%)

Algorithm

1×

intervals

Results

17.0ms	148×	body	160	valid
9.0ms	294×	pre	80	true
7.0ms	47×	body	320	valid
3.0ms	61×	body	80	valid
2.0ms	38×	body	80	nan

simplify250.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (249.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune8.0ms (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: 44.8b

Counts

2 → 1

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
38.2b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite30.0ms (0%)

Algorithm

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

Counts

4 → 70

Calls

4 calls:

11.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
7.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
6.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series62.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
15.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(- (* b b) (* (* 4.0 a) c))

simplify47.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4921	1309
1	4921	1309

prune161.0ms (0.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 0.2b

Counts

83 → 5

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a 2.0))

rewrite39.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac`
78×	`*-un-lft-identity`
38×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`associate-/l*`
20×	`distribute-lft-out`
18×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`associate-/r*`
4×	`pow1` `flip3-+` `flip-+` `div-inv`
3×	`div-sub` `distribute-frac-neg`
2×	`neg-sub0` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `flip--` `associate-/l/`

Counts

4 → 155

Calls

4 calls:

14.0ms	(/ (/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a 2.0))
9.0ms	(/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
6.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))

series126.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
46.0ms	(/ (/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a 2.0))
16.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))

simplify59.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4978	3969
1	4978	3969

prune408.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	160	7	167
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	165	7	172

Merged error: 0b

Counts

172 → 7

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b	(/ a (/ (/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))
0.3b	(/ (/ (neg (* 4.0 a)) 1) (/ a (/ (/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0)))

rewrite965.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

17936×	`times-frac`
7690×	`*-un-lft-identity`
6368×	`add-sqr-sqrt` `add-cube-cbrt`
661×	`distribute-lft-out`
540×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
498×	`div-inv`
465×	`associate-/r/`
241×	`associate-/r*`
220×	`flip3-+` `flip-+`
61×	`add-exp-log`
47×	`add-cbrt-cube`
45×	`div-exp`
31×	`cbrt-undiv`
28×	`associate-/l*`
6×	`add-log-exp`
4×	`pow1` `1-exp`
3×	`frac-2neg` `clear-num`
2×	`div-sub` `distribute-frac-neg`
1×	`neg-sub0` `sub-neg` `flip3--` `diff-log` `flip--` `associate-/l/`

Counts

4 → 4469

Calls

4 calls:

112.0ms	(/ (/ (neg (* 4.0 a)) 1) (/ a (/ (/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0)))
19.0ms	(/ a (/ (/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))
7.0ms	(/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(- (* b b) (* (* 4.0 a) c))

series147.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (/ (neg (* 4.0 a)) 1) (/ a (/ (/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0)))
45.0ms	(/ a (/ (/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))
45.0ms	(/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(- (* b b) (* (* 4.0 a) c))

simplify1.4s (1.8%)

Algorithm

1×	egg-herbie

Counts

4481 → 4481

Iterations

Useful iterations: 0 (181.0ms)

Iter	Nodes	Cost
0	4995	233354
1	4995	233354

prune1.2min (92.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	4480	1	4481
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	4482	6	4488

Merged error: 0b

Counts

4488 → 6

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b	(/ 2.0 (* 4.0 (/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))))
0.3b	(/ 1 (/ 2.0 (* 4.0 (/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))))

rewrite48.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`times-frac`
71×	`*-un-lft-identity`
49×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt`
29×	`add-cbrt-cube`
25×	`div-exp`
16×	`associate-/l*`
15×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
13×	`cbrt-undiv` `associate-/r*`
11×	`distribute-lft-out`
8×	`prod-exp` `associate-/r/`
7×	`div-inv`
6×	`add-log-exp`
5×	`pow1` `neg-mul-1` `associate-*r/`
4×	`rec-exp` `1-exp` `cbrt-unprod`
3×	`frac-2neg` `clear-num`
1×	`neg-sub0` `sub-neg` `flip3--` `pow-flip` `flip3-+` `diff-log` `div-sub` `distribute-frac-neg` `flip--` `flip-+` `inv-pow`

Counts

4 → 169

Calls

4 calls:

16.0ms	(/ 1 (/ 2.0 (* 4.0 (/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))))
13.0ms	(/ 2.0 (* 4.0 (/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))))
9.0ms	(/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(- (* b b) (* (* 4.0 a) c))

series133.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ 1 (/ 2.0 (* 4.0 (/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))))
45.0ms	(/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
31.0ms	(/ 2.0 (* 4.0 (/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))))
8.0ms	(- (* b b) (* (* 4.0 a) c))

simplify69.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4946	3812
1	4946	3812

prune387.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	181	6	187

Merged error: 0b

Counts

187 → 6

regimes174.0ms (0.2%)

Accuracy

Total 0.2b remaining (84.6%)

Threshold costs 0.2b (84.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	23
1	70	23

end0.0ms (0%)

sample1.3s (1.6%)

Algorithm

1×

intervals

Results

475.0ms	4848×	body	160	valid
262.0ms	8975×	pre	80	true
204.0ms	1360×	body	320	valid
96.0ms	1792×	body	80	valid
49.0ms	975×	body	80	nan

Details

analyze278.0ms (0.4%)

sample49.0ms (0.1%)

simplify250.0ms (0.3%)

prune8.0ms (0%)

localize10.0ms (0%)

rewrite30.0ms (0%)

series62.0ms (0.1%)

simplify47.0ms (0.1%)

prune161.0ms (0.2%)

localize15.0ms (0%)

rewrite39.0ms (0%)

series126.0ms (0.2%)

simplify59.0ms (0.1%)

prune408.0ms (0.5%)

localize17.0ms (0%)

rewrite965.0ms (1.2%)

series147.0ms (0.2%)

simplify1.4s (1.8%)

prune1.2min (92.2%)

localize15.0ms (0%)

rewrite48.0ms (0.1%)

series133.0ms (0.2%)

simplify69.0ms (0.1%)

prune387.0ms (0.5%)

regimes174.0ms (0.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.3s (1.6%)

Profiling