Details

analyze462.0ms (6.9%)

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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	171×	body	128	valid
8.0ms	34×	body	2048	valid
5.0ms	28×	body	1024	valid
3.0ms	11×	body	4096	valid
1.0ms	24×	body	128	nan
1.0ms	7×	body	512	valid
0.0ms	5×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify241.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune5.0ms (0.1%)

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: 34.4b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 4 a) c)
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1477`
10×	`pow1_binary64_1516`
9×	`add-cbrt-cube_binary64_1491` `*-un-lft-identity_binary64_1455` `add-exp-log_binary64_1493`
8×	`add-log-exp_binary64_1494`
7×	`add-cube-cbrt_binary64_1490`
4×	`sqrt-prod_binary64_1471` `cancel-sign-sub-inv_binary64_1421`
3×	`prod-exp_binary64_1504` `associate-r_binary64_1395` `flip--_binary64_1430` `cbrt-unprod_binary64_1488` `flip3--_binary64_1459` `pow-prod-down_binary64_1526`
2×	`sqrt-div_binary64_1472` `difference-of-squares_binary64_1424` `diff-log_binary64_1547` `sub-neg_binary64_1448`
1×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `distribute-lft-out--_binary64_1407` `-commutative_binary64_1386` `pow1/2_binary64_1535` `associate-l*_binary64_1396`

Counts

4 → 62

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
6.0ms	(.f64 (.f64 4 a) c)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series356.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
128.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
28.0ms	(.f64 (.f64 4 a) c)

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4883	1223
1	4883	1223

prune265.0ms (4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	66	8	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	9	75

Merged error: 12.9b

Counts

75 → 9

Compiler

Compiled 5188 to 3621 computations (30.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.4b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
8.0b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
22×	`times-frac_binary64_1461`
21×	`*-un-lft-identity_binary64_1455`
17×	`div-exp_binary64_1506` `cbrt-undiv_binary64_1489`
13×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488`
12×	`add-sqr-sqrt_binary64_1477`
11×	`add-cube-cbrt_binary64_1490` `associate-/l*_binary64_1400`
6×	`associate-/r/_binary64_1401` `add-log-exp_binary64_1494`
5×	`distribute-lft-out_binary64_1406` `pow1_binary64_1516` `associate-/r*_binary64_1399`
4×	`flip-+_binary64_1429` `flip3-+_binary64_1458` `div-inv_binary64_1452`
3×	`sqrt-prod_binary64_1471`
2×	`sqrt-div_binary64_1472` `clear-num_binary64_1454` `frac-2neg_binary64_1466`
1×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `associate-/l/_binary64_1402` `flip--_binary64_1430` `pow1/2_binary64_1535` `sum-log_binary64_1546` `+-commutative_binary64_1385` `flip3--_binary64_1459`

Counts

4 → 102

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series953.0ms (14.3%)

Counts

4 → 12

Calls

4 calls:

382.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
321.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
130.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5005	3121

prune430.0ms (6.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	107	7	114
Fresh	6	1	7
Picked	1	0	1
Done	0	1	1
Total	114	9	123

Merged error: 8.2b

Counts

123 → 9

Compiler

Compiled 8832 to 6188 computations (29.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 4 a) c)
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64_1516`
9×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
8×	`add-log-exp_binary64_1494` `*-un-lft-identity_binary64_1455`
7×	`add-sqr-sqrt_binary64_1477`
6×	`add-cube-cbrt_binary64_1490`
3×	`prod-exp_binary64_1504` `associate-r_binary64_1395` `sqrt-prod_binary64_1471` `cbrt-unprod_binary64_1488` `pow-prod-down_binary64_1526`
2×	`sqrt-div_binary64_1472` `flip--_binary64_1430` `flip3--_binary64_1459`
1×	`sqrt-pow1_binary64_1473` `distribute-lft-out_binary64_1406` `rem-sqrt-square_binary64_1468` `flip-+_binary64_1429` `-commutative_binary64_1386` `diff-log_binary64_1547` `cancel-sign-sub-inv_binary64_1421` `sub-neg_binary64_1448` `pow1/2_binary64_1535` `flip3-+_binary64_1458` `sum-log_binary64_1546` `+-commutative_binary64_1385` `associate-l*_binary64_1396`

Counts

4 → 57

Calls

4 calls:

7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
6.0ms	(.f64 (.f64 4 a) c)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series330.0ms (5%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
26.0ms	(.f64 (.f64 4 a) c)

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4908	1123
1	4908	1123

prune108.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	72	6	78

Merged error: 7.2b

Counts

78 → 6

Compiler

Compiled 2213 to 1498 computations (32.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4)))
1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.4b	(/.f64 (/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4))) (*.f64 a 2))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite64.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`times-frac_binary64_1461`
74×	`*-un-lft-identity_binary64_1455`
53×	`add-sqr-sqrt_binary64_1477`
52×	`add-cube-cbrt_binary64_1490`
45×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
32×	`associate-/l*_binary64_1400`
23×	`div-exp_binary64_1506` `cbrt-undiv_binary64_1489`
14×	`div-inv_binary64_1452`
11×	`distribute-lft-out_binary64_1406`
9×	`associate-/r*_binary64_1399`
7×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488`
6×	`add-log-exp_binary64_1494`
5×	`pow1_binary64_1516`
3×	`sqrt-prod_binary64_1471` `associate-/r/_binary64_1401`
2×	`sqrt-div_binary64_1472` `clear-num_binary64_1454` `frac-2neg_binary64_1466`
1×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `flip-+_binary64_1429` `associate-/l/_binary64_1402` `flip--_binary64_1430` `pow1/2_binary64_1535` `flip3-+_binary64_1458` `sum-log_binary64_1546` `+-commutative_binary64_1385` `flip3--_binary64_1459`

Counts

4 → 165

Calls

4 calls:

19.0ms	(/.f64 (/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4))) (*.f64 a 2))
12.0ms	(/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4)))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series1.0s (15.2%)

Counts

4 → 12

Calls

4 calls:

411.0ms	(/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4)))
349.0ms	(/.f64 (/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4))) (*.f64 a 2))
128.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
121.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

simplify103.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5065	6019

prune276.0ms (4.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	175	8	183

Merged error: 7.2b

Counts

183 → 8

Compiler

Compiled 5937 to 3573 computations (39.8% saved)

regimes142.0ms (2.1%)

Compiler: Compiled 402 to 345 computations (14.2% saved)

bsearch104.0ms (1.6%)

Steps

Iters	Range	Point
8	6.787489049073195e+118	7.133955408180205e+122	5.525835260688754e+121
9	2.173626231849138e-227	1.6620553427918547e-219	7.131198222427231e-227
8	-1.6407368404235515e+56	-3.3624292403433257e+53	-1.6236541306877014e+56

Iters

Range

Point

6.787489049073195e+118

7.133955408180205e+122

5.525835260688754e+121

2.173626231849138e-227

1.6620553427918547e-219

7.131198222427231e-227

-1.6407368404235515e+56

-3.3624292403433257e+53

-1.6236541306877014e+56

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	122	104
1	122	104

end0.0ms (0%)

sample1.4s (20.6%)

Algorithm

1×

intervals

Results

278.0ms	5258×	body	128	valid
275.0ms	1104×	body	2048	valid
137.0ms	682×	body	1024	valid
123.0ms	398×	body	4096	valid
53.0ms	372×	body	512	valid
34.0ms	662×	body	128	nan
18.0ms	360×	body	128	invalid
18.0ms	186×	body	256	valid

Compiler

Compiled 262 to 200 computations (23.7% saved)

Details

analyze462.0ms (6.9%)

sample38.0ms (0.6%)

simplify241.0ms (3.6%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

rewrite29.0ms (0.4%)

series356.0ms (5.3%)

simplify80.0ms (1.2%)

prune265.0ms (4%)

localize14.0ms (0.2%)

rewrite51.0ms (0.8%)

series953.0ms (14.3%)

simplify76.0ms (1.1%)

prune430.0ms (6.5%)

localize15.0ms (0.2%)

rewrite27.0ms (0.4%)

series330.0ms (5%)

simplify82.0ms (1.2%)

prune108.0ms (1.6%)

localize15.0ms (0.2%)

rewrite64.0ms (1%)

series1.0s (15.2%)

simplify103.0ms (1.5%)

prune276.0ms (4.1%)

regimes142.0ms (2.1%)

bsearch104.0ms (1.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (20.6%)

Profiling