Details

analyze733.0ms (16.2%)

Algorithm

1×

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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

sample38.0ms (0.8%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	80	valid
1.0ms	14×	body	80	nan
1.0ms	7×	body	80	invalid

simplify654.0ms (14.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (216.0ms)

Iter	Nodes	Cost
0	3270	37
1	3270	37

prune13.0ms (0.3%)

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: 19.3b

Counts

2 → 1

localize24.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
1.6b	(- (neg b) (sqrt (- (* b b) (* c (* 4.0 a)))))
22.5b	(sqrt (- (* b b) (* c (* 4.0 a))))
22.5b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 61

Calls

4 calls:

9.0ms	(- (neg b) (sqrt (- (* b b) (* c (* 4.0 a)))))
7.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
6.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series68.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
16.0ms	(- (neg b) (sqrt (- (* b b) (* c (* 4.0 a)))))
15.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify89.0ms (2%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4877	1082
1	4877	1082

prune217.0ms (4.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	6	74

Merged error: 6.3b

Counts

74 → 6

localize24.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.6b	(- (neg b) (sqrt (- (* b b) (* c (* 4.0 a)))))
3.2b	(exp (log (- (sqrt (- (* b b) (* c (* 4.0 a)))) b)))
22.5b	(sqrt (- (* b b) (* c (* 4.0 a))))
22.5b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
8×	`add-cube-cbrt` `sqrt-prod` `add-log-exp`
7×	`pow1`
6×	`log-prod` `exp-sum`
4×	`add-exp-log` `exp-prod` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
3×	`distribute-lft-out--`
2×	`rem-sqrt-square` `log-div` `sqrt-pow1` `pow1/2` `exp-diff` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `neg-log` `log-pow` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

9.0ms	(- (neg b) (sqrt (- (* b b) (* c (* 4.0 a)))))
9.0ms	(exp (log (- (sqrt (- (* b b) (* c (* 4.0 a)))) b)))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series61.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
15.0ms	(- (neg b) (sqrt (- (* b b) (* c (* 4.0 a)))))
15.0ms	(exp (log (- (sqrt (- (* b b) (* c (* 4.0 a)))) b)))
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4895	1170
1	4895	1170

prune243.0ms (5.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	78	7	85

Merged error: 6.3b

Counts

85 → 7

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
4.0b	(/ c (- (neg b) (- b (* 2.0 (* c (/ a b))))))
6.6b	(* c (/ a b))
22.5b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

9.0ms	(/ c (- (neg b) (- b (* 2.0 (* c (/ a b))))))
8.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
7.0ms	(* c (/ a b))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series59.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ c (- (neg b) (- b (* 2.0 (* c (/ a b))))))
17.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
15.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
5.0ms	(* c (/ a b))

simplify45.0ms (1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5107	1546

prune262.0ms (5.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	115	6	121

Merged error: 6.3b

Counts

121 → 6

localize31.0ms (0.7%)

Local error

Found 4 expressions with local error:

2.1b	(exp (log (- (- (* 2.0 (* c (/ a b))) b) b)))
2.2b	(log (- (- (* 2.0 (* c (/ a b))) b) b))
6.6b	(* c (/ a b))
22.5b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
16×	`add-cube-cbrt`
13×	`associate-r`
10×	`add-exp-log` `log-prod` `times-frac`
9×	`pow1` `add-cbrt-cube`
5×	`exp-sum`
4×	`log-div` `exp-prod` `add-log-exp`
3×	`flip3--` `associate-l` `sqrt-prod` `flip--`
2×	`exp-diff` `sqrt-div` `prod-exp` `log-pow` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `div-exp` `rem-log-exp` `pow-prod-down` `-commutative` `div-inv` `rem-exp-log`

Counts

4 → 82

Calls

4 calls:

11.0ms	(exp (log (- (- (* 2.0 (* c (/ a b))) b) b)))
10.0ms	(log (- (- (* 2.0 (* c (/ a b))) b) b))
7.0ms	(* c (/ a b))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series49.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(log (- (- (* 2.0 (* c (/ a b))) b) b))
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
11.0ms	(exp (log (- (- (* 2.0 (* c (/ a b))) b) b)))
5.0ms	(* c (/ a b))

simplify60.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4948	1112
1	4948	1112

prune242.0ms (5.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	93	7	100

Merged error: 6.3b

Counts

100 → 7

regimes259.0ms (5.7%)

Accuracy

Total 0.9b remaining (13.1%)

Threshold costs 0.9b (13.1%)

bsearch107.0ms (2.4%)

Steps

Iters	Range	Point
9	1.1832726428531494e+121	1.4545663394930315e+128	2.838341990170196e+126
9	-1.1435203403412755e-293	-2.7481330108391266e-300	-2.780192689850507e-300
10	-2.9936197355724482e+134	-2.185187917165607e+122	-4.1275090717025735e+127

Iters

Range

Point

1.1832726428531494e+121

1.4545663394930315e+128

2.838341990170196e+126

-1.1435203403412755e-293

-2.7481330108391266e-300

-2.780192689850507e-300

-2.9936197355724482e+134

-2.185187917165607e+122

-4.1275090717025735e+127

simplify17.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	882	160
1	882	160

end0.0ms (0%)

sample1.0s (22.3%)

Algorithm

1×

intervals

Results

704.0ms	8000×	body	80	valid
62.0ms	708×	body	80	nan
34.0ms	398×	body	80	invalid

Details

analyze733.0ms (16.2%)

sample38.0ms (0.8%)

simplify654.0ms (14.5%)

prune13.0ms (0.3%)

localize24.0ms (0.5%)

rewrite38.0ms (0.8%)

series68.0ms (1.5%)

simplify89.0ms (2%)

prune217.0ms (4.8%)

localize24.0ms (0.5%)

rewrite28.0ms (0.6%)

series61.0ms (1.3%)

simplify56.0ms (1.3%)

prune243.0ms (5.4%)

localize25.0ms (0.6%)

rewrite30.0ms (0.7%)

series59.0ms (1.3%)

simplify45.0ms (1%)

prune262.0ms (5.8%)

localize31.0ms (0.7%)

rewrite35.0ms (0.8%)

series49.0ms (1.1%)

simplify60.0ms (1.3%)

prune242.0ms (5.4%)

regimes259.0ms (5.7%)

bsearch107.0ms (2.4%)

simplify17.0ms (0.4%)

end0.0ms (0%)

sample1.0s (22.3%)

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