Details

analyze258.0ms (7.6%)

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

sample43.0ms (1.3%)

Algorithm

1×

intervals

Results

15.0ms	158×	body	160	valid
8.0ms	280×	pre	80	true
6.0ms	44×	body	320	valid
3.0ms	54×	body	80	valid
1.0ms	24×	body	80	nan

simplify176.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (174.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune10.0ms (0.3%)

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: 44.1b

Counts

2 → 2

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* 3.0 (* a c)))
0.3b	(* 3.0 (* a c))
0.3b	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
38.7b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

13.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
7.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
5.0ms	(* 3.0 (* a c))
4.0ms	(- (* b b) (* 3.0 (* a c)))

series55.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
15.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
9.0ms	(- (* b b) (* 3.0 (* a c)))
3.0ms	(* 3.0 (* a c))

simplify47.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5461	1199

prune160.0ms (4.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	80	5	85
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	82	5	87

Merged error: 0.2b

Counts

87 → 5

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(* 3.0 (* a c))
0.3b	(* 3.0 (* a (neg c)))
0.3b	(/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
0.3b	(/ (/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

rewrite40.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-exp-log` `add-cbrt-cube`
22×	`times-frac`
20×	`*-un-lft-identity`
19×	`prod-exp` `cbrt-unprod`
17×	`cbrt-undiv` `div-exp`
14×	`pow1`
12×	`add-sqr-sqrt` `add-cube-cbrt`
11×	`associate-/l*`
6×	`associate-l` `pow-prod-down` `associate-/r/` `distribute-rgt-neg-out`
5×	`associate-/r*`
4×	`div-inv` `distribute-lft-out` `add-log-exp`
3×	`flip3-+` `distribute-frac-neg` `flip-+`
2×	`frac-2neg` `associate-r` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 114

Calls

4 calls:

14.0ms	(/ (/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
12.0ms	(/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
5.0ms	(* 3.0 (* a (neg c)))
5.0ms	(* 3.0 (* a c))

series107.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
47.0ms	(/ (/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
3.0ms	(* 3.0 (* a (neg c)))
3.0ms	(* 3.0 (* a c))

simplify51.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4983	1982
1	4983	1982

prune246.0ms (7.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	6	126
Fresh	4	0	4
Picked	0	1	1
Done	0	0	0
Total	124	7	131

Merged error: 0b

Counts

131 → 7

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* 3.0 (* a c)))
0.1b	(/ c (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
0.1b	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
0.3b	(* 3.0 (* a c))

rewrite27.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

7.0ms	(/ c (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
7.0ms	(- (* b b) (* 3.0 (* a c)))
6.0ms	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
5.0ms	(* 3.0 (* a c))

series73.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ c (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
16.0ms	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
9.0ms	(- (* b b) (* 3.0 (* a c)))
4.0ms	(* 3.0 (* a c))

simplify65.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4925	1187
1	4925	1187

prune156.0ms (4.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	2	3	5
Picked	0	1	1
Done	1	0	1
Total	87	6	93

Merged error: 0b

Counts

93 → 6

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
0.1b	(/ 1 (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
0.3b	(* 3.0 (* a c))
0.3b	(* c (/ 1 (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))))

rewrite35.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
26×	`times-frac`
23×	`add-cube-cbrt`
22×	`add-exp-log`
19×	`associate-r`
16×	`add-cbrt-cube`
12×	`pow1`
8×	`distribute-lft-out`
7×	`prod-exp`
6×	`associate-l` `add-log-exp`
5×	`cbrt-unprod`
4×	`div-exp` `pow-prod-down` `associate-/r*` `associate-/r/`
3×	`flip3-+` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `associate-*r/` `clear-num` `sum-log` `un-div-inv` `inv-pow`

Counts

4 → 108

Calls

4 calls:

12.0ms	(* c (/ 1 (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))))
8.0ms	(/ 1 (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
6.0ms	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
5.0ms	(* 3.0 (* a c))

series94.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(* c (/ 1 (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))))
25.0ms	(/ 1 (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
15.0ms	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(* 3.0 (* a c))

simplify56.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5029	1661

prune212.0ms (6.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	120	6	126

Merged error: 0b

Counts

126 → 6

regimes160.0ms (4.7%)

Accuracy

Total 0.1b remaining (82.2%)

Threshold costs 0.1b (82.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	94	15
1	94	15

end0.0ms (0%)

sample1.2s (36.6%)

Algorithm

1×

intervals

Results

469.0ms	4886×	body	160	valid
256.0ms	8900×	pre	80	true
185.0ms	1347×	body	320	valid
86.0ms	1767×	body	80	valid
43.0ms	900×	body	80	nan

Details

analyze258.0ms (7.6%)

sample43.0ms (1.3%)

simplify176.0ms (5.2%)

prune10.0ms (0.3%)

localize10.0ms (0.3%)

rewrite32.0ms (0.9%)

series55.0ms (1.6%)

simplify47.0ms (1.4%)

prune160.0ms (4.7%)

localize17.0ms (0.5%)

rewrite40.0ms (1.2%)

series107.0ms (3.1%)

simplify51.0ms (1.5%)

prune246.0ms (7.2%)

localize12.0ms (0.4%)

rewrite27.0ms (0.8%)

series73.0ms (2.1%)

simplify65.0ms (1.9%)

prune156.0ms (4.6%)

localize15.0ms (0.5%)

rewrite35.0ms (1%)

series94.0ms (2.8%)

simplify56.0ms (1.6%)

prune212.0ms (6.2%)

regimes160.0ms (4.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (36.6%)

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