Details

analyze623.0ms (15.5%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample43.0ms (1.1%)

Algorithm

1×

intervals

Results

11.0ms	43×	body	2560	valid
7.0ms	29×	body	1280	valid
7.0ms	154×	body	80	valid
2.0ms	13×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	9×	body	160	valid
1.0ms	16×	body	80	nan
1.0ms	5×	body	320	valid
0.0ms	5×	body	80	invalid

simplify515.0ms (12.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune11.0ms (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: 36.0b

Counts

2 → 1

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (* b_2 b_2) (* a c))
1.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 82

Calls

4 calls:

10.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(- (* b_2 b_2) (* a c))

series82.0ms (2%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (- (* b_2 b_2) (* a c)))
22.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))

simplify55.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5743	1403

prune164.0ms (4.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	82	12	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	12	95

Merged error: 6.9b

Counts

95 → 12

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
4.0b	(/ (/ (neg (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
9.8b	(/ (neg (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac`
154×	`*-un-lft-identity`
93×	`add-sqr-sqrt`
92×	`add-cube-cbrt`
36×	`associate-/l*`
31×	`distribute-lft-out`
21×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`div-inv` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp`
3×	`div-sub` `distribute-frac-neg` `sqrt-prod`
2×	`neg-sub0` `flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 216

Calls

4 calls:

13.0ms	(/ (/ (neg (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
8.0ms	(/ (neg (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(- (* b_2 b_2) (* a c))

series119.0ms (3%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (neg (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
44.0ms	(/ (/ (neg (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(- (* b_2 b_2) (* a c))

simplify69.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5864	5186

prune253.0ms (6.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	231	9	240

Merged error: 6.8b

Counts

240 → 9

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
0.5b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite22.0ms (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_2 (sqrt (- (* b_2 b_2) (* a c)))))
6.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(- (* b_2 b_2) (* a c))

series83.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
14.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(- (* b_2 b_2) (* a c))

simplify47.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5326	1109

prune115.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	83	9	92

Merged error: 6.8b

Counts

92 → 9

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(* c (/ 1 (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
0.5b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
18×	`associate-r`
14×	`add-cube-cbrt` `times-frac`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`prod-exp` `distribute-lft-out`
3×	`associate-l` `sqrt-prod` `unswap-sqr`
2×	`flip3--` `flip3-+` `sqrt-div` `div-exp` `associate-/r/` `flip--` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 79

Calls

4 calls:

12.0ms	(* c (/ 1 (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
6.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(- (* b_2 b_2) (* a c))

series82.0ms (2%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(* c (/ 1 (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
14.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(- (* b_2 b_2) (* a c))

simplify52.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4906	1078
1	4906	1078

prune106.0ms (2.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	91	9	100

Merged error: 6.8b

Counts

100 → 9

regimes241.0ms (6%)

Accuracy

Total 0.8b remaining (12.4%)

Threshold costs 0.8b (12.4%)

bsearch92.0ms (2.3%)

Steps

Iters	Range	Point
10	6.4851974710934e+151	6.7846503122979244e+162	8.828154833930211e+151
7	-3.588378087479768e-211	-3.8670254222860854e-213	-9.281927902223943e-213
10	-1.9898668609638904e+139	-6.411886552711472e+128	-9.444009031655424e+133

Iters

Range

Point

6.4851974710934e+151

6.7846503122979244e+162

8.828154833930211e+151

-3.588378087479768e-211

-3.8670254222860854e-213

-9.281927902223943e-213

-1.9898668609638904e+139

-6.411886552711472e+128

-9.444009031655424e+133

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	100	55
1	100	55

end0.0ms (0%)

sample1.1s (27.6%)

Algorithm

1×

intervals

Results

273.0ms	1057×	body	2560	valid
232.0ms	5073×	body	80	valid
189.0ms	907×	body	1280	valid
85.0ms	484×	body	640	valid
40.0ms	130×	body	5120	valid
30.0ms	731×	body	80	nan
28.0ms	224×	body	320	valid
12.0ms	268×	body	80	invalid
10.0ms	125×	body	160	valid

Details

analyze623.0ms (15.5%)

sample43.0ms (1.1%)

simplify515.0ms (12.8%)

prune11.0ms (0.3%)

localize10.0ms (0.3%)

rewrite31.0ms (0.8%)

series82.0ms (2%)

simplify55.0ms (1.4%)

prune164.0ms (4.1%)

localize11.0ms (0.3%)

rewrite41.0ms (1%)

series119.0ms (3%)

simplify69.0ms (1.7%)

prune253.0ms (6.3%)

localize9.0ms (0.2%)

rewrite22.0ms (0.6%)

series83.0ms (2.1%)

simplify47.0ms (1.2%)

prune115.0ms (2.9%)

localize11.0ms (0.3%)

rewrite28.0ms (0.7%)

series82.0ms (2%)

simplify52.0ms (1.3%)

prune106.0ms (2.6%)

regimes241.0ms (6%)

bsearch92.0ms (2.3%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (27.6%)

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