Details

analyze272.0ms (7.3%)

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

sample40.0ms (1.1%)

Algorithm

1×

intervals

Results

14.0ms	144×	body	160	valid
10.0ms	277×	pre	80	true
5.0ms	112×	body	80	valid
1.0ms	21×	body	80	nan

simplify244.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (243.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune8.0ms (0.2%)

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: 27.9b

Counts

2 → 1

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
0.3b	(- (* b b) (* (* 4.0 a) c))
27.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite29.0ms (0.8%)

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:

10.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
7.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(- (* b b) (* (* 4.0 a) c))

series64.0ms (1.7%)

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)))
9.0ms	(- (* b b) (* (* 4.0 a) c))

simplify46.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4921	1309
1	4921	1309

prune163.0ms (4.4%)

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: 0.3b

Counts

83 → 5

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite37.0ms (1%)

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)))))
5.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))

series126.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
43.0ms	(/ (/ (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))

simplify58.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4978	3969
1	4978	3969

prune436.0ms (11.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	156	11	167
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	161	11	172

Merged error: 0.0b

Counts

172 → 11

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite23.0ms (0.6%)

Algorithm

1×	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 (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))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series85.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(- (* b b) (* (* 4.0 a) c))

simplify70.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4930	1299
1	4930	1299

prune197.0ms (5.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	83	11	94

Merged error: 0b

Counts

94 → 11

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(/ c (+ b (cbrt (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.5b	(cbrt (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))
0.6b	(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)

rewrite30.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity`
23×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`cbrt-prod`
12×	`unpow-prod-down` `times-frac` `cube-prod` `sqrt-prod`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`cube-div` `sqrt-div` `associate-/r*` `distribute-lft-out`
3×	`pow-unpow` `flip3--` `pow-pow` `flip--` `associate-/l*`
2×	`cube-mult` `cbrt-div` `unpow3` `associate-/r/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `sqrt-pow2` `rem-cbrt-cube` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 107

Calls

4 calls:

11.0ms	(/ c (+ b (cbrt (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))))
6.0ms	(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)
6.0ms	(cbrt (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))
4.0ms	(- (* b b) (* (* 4.0 a) c))

series83.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ c (+ b (cbrt (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))))
14.0ms	(cbrt (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))
11.0ms	(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)
9.0ms	(- (* b b) (* (* 4.0 a) c))

simplify42.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4937	1858
1	4937	1858

prune247.0ms (6.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	119	11	130

Merged error: 0b

Counts

130 → 11

regimes246.0ms (6.6%)

Accuracy

Total 0.4b remaining (96.4%)

Threshold costs 0.4b (96.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	87	22
1	87	22

end0.0ms (0%)

sample1.1s (29.9%)

Algorithm

1×

intervals

Results

431.0ms	4424×	body	160	valid
261.0ms	8829×	pre	80	true
180.0ms	3576×	body	80	valid
41.0ms	829×	body	80	nan

Details

analyze272.0ms (7.3%)

sample40.0ms (1.1%)

simplify244.0ms (6.6%)

prune8.0ms (0.2%)

localize10.0ms (0.3%)

rewrite29.0ms (0.8%)

series64.0ms (1.7%)

simplify46.0ms (1.2%)

prune163.0ms (4.4%)

localize12.0ms (0.3%)

rewrite37.0ms (1%)

series126.0ms (3.4%)

simplify58.0ms (1.6%)

prune436.0ms (11.8%)

localize12.0ms (0.3%)

rewrite23.0ms (0.6%)

series85.0ms (2.3%)

simplify70.0ms (1.9%)

prune197.0ms (5.3%)

localize18.0ms (0.5%)

rewrite30.0ms (0.8%)

series83.0ms (2.2%)

simplify42.0ms (1.1%)

prune247.0ms (6.7%)

regimes246.0ms (6.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (29.9%)

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