Details

analyze259.0ms (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

sample50.0ms (1.4%)

Algorithm

1×

intervals

Results

13.0ms	99×	body	320	valid
10.0ms	115×	body	160	valid
10.0ms	288×	pre	80	true
3.0ms	15×	body	640	valid
1.0ms	32×	body	80	nan
1.0ms	27×	body	80	valid

simplify178.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (176.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	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: 51.7b

Counts

2 → 1

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* 3.0 (* a c)))
0.2b	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
0.3b	(* 3.0 (* a c))
29.4b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

rewrite28.0ms (0.8%)

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:

11.0ms	(/ (- (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)))

series53.0ms (1.5%)

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)
8.0ms	(- (* b b) (* 3.0 (* a c)))
3.0ms	(* 3.0 (* a c))

simplify47.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5461	1199

prune156.0ms (4.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	3	86

Merged error: 0.1b

Counts

86 → 3

localize15.0ms (0.4%)

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))))))
0.4b	(/ (/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

rewrite39.0ms (1.1%)

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))
11.0ms	(/ (* 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))

series105.0ms (3%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
44.0ms	(/ (/ (* 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))

simplify53.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4983	1982
1	4983	1982

prune242.0ms (6.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	125	4	129

Merged error: 0b

Counts

129 → 4

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite24.0ms (0.7%)

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))))))
6.0ms	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
5.0ms	(* 3.0 (* a c))
4.0ms	(- (* b b) (* 3.0 (* a c)))

series73.0ms (2%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ c (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
15.0ms	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
8.0ms	(- (* b b) (* 3.0 (* a c)))
3.0ms	(* 3.0 (* a c))

simplify64.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4925	1187
1	4925	1187

prune158.0ms (4.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Merged error: 0b

Counts

90 → 4

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-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`
7×	`prod-exp` `distribute-lft-out`
6×	`associate-l` `add-log-exp`
5×	`cbrt-unprod`
4×	`div-exp` `pow-prod-down` `associate-/r*` `associate-/r/`
3×	`associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `*-commutative` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `pow-flip` `frac-2neg` `diff-log` `associate-*r/` `clear-num` `un-div-inv` `flip--` `inv-pow`

Counts

4 → 107

Calls

4 calls:

13.0ms	(* c (/ 1 (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))))
8.0ms	(/ 1 (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
5.0ms	(* 3.0 (* a c))
4.0ms	(- (* b b) (* 3.0 (* a c)))

series83.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(* c (/ 1 (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))))
24.0ms	(/ 1 (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
8.0ms	(- (* b b) (* 3.0 (* a c)))
4.0ms	(* 3.0 (* a c))

simplify55.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5070	1621

prune211.0ms (5.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	119	4	123

Merged error: 0b

Counts

123 → 4

regimes142.0ms (4%)

Accuracy

Total 0.0b remaining (59.4%)

Threshold costs 0.0b (59.4%)

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%)

sample1.4s (40.3%)

Algorithm

1×

intervals

Results

503.0ms	3602×	body	320	valid
279.0ms	2958×	body	160	valid
256.0ms	8811×	pre	80	true
99.0ms	535×	body	640	valid
46.0ms	905×	body	80	valid
40.0ms	811×	body	80	nan

Details

analyze259.0ms (7.3%)

sample50.0ms (1.4%)

simplify178.0ms (5%)

prune8.0ms (0.2%)

localize11.0ms (0.3%)

rewrite28.0ms (0.8%)

series53.0ms (1.5%)

simplify47.0ms (1.3%)

prune156.0ms (4.4%)

localize15.0ms (0.4%)

rewrite39.0ms (1.1%)

series105.0ms (3%)

simplify53.0ms (1.5%)

prune242.0ms (6.8%)

localize15.0ms (0.4%)

rewrite24.0ms (0.7%)

series73.0ms (2%)

simplify64.0ms (1.8%)

prune158.0ms (4.5%)

localize13.0ms (0.4%)

rewrite33.0ms (0.9%)

series83.0ms (2.3%)

simplify55.0ms (1.5%)

prune211.0ms (5.9%)

regimes142.0ms (4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.4s (40.3%)

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