Details

analyze476.0ms (6.3%)

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)

sample41.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	39×	body	2048	valid
9.0ms	162×	body	128	valid
5.0ms	25×	body	1024	valid
4.0ms	12×	body	4096	valid
2.0ms	15×	body	512	valid
1.0ms	18×	body	128	nan
1.0ms	11×	body	128	invalid
0.0ms	3×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify236.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (0%)

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: 32.6b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1464`
14×	`*-un-lft-identity_binary64_1442`
9×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
8×	`add-log-exp_binary64_1481` `add-cube-cbrt_binary64_1477`
6×	`times-frac_binary64_1448` `associate-/l*_binary64_1387` `sqrt-prod_binary64_1458` `difference-of-squares_binary64_1411`
5×	`pow1_binary64_1503`
4×	`cancel-sign-sub-inv_binary64_1408` `flip3--_binary64_1446` `flip--_binary64_1417`
3×	`distribute-lft-out--_binary64_1394`
2×	`cbrt-undiv_binary64_1476` `associate-/l/_binary64_1389` `sub-neg_binary64_1435` `sqrt-div_binary64_1459` `diff-log_binary64_1534` `div-exp_binary64_1493`
1×	`sqrt-pow1_binary64_1460` `associate-/r*_binary64_1386` `rem-sqrt-square_binary64_1455` `cbrt-unprod_binary64_1475` `div-inv_binary64_1439` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `pow1/2_binary64_1522` `prod-exp_binary64_1491` `div-sub_binary64_1447`

Counts

4 → 74

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series553.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
149.0ms	(-.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)))
67.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5031	1979

prune126.0ms (1.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	77	9	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	10	87

Merged error: 4.4b

Counts

87 → 10

Compiler

Compiled 2160 to 1297 computations (40% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
3.7b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
8.5b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite54.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
22×	`times-frac_binary64_1448`
19×	`*-un-lft-identity_binary64_1442`
17×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
13×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
12×	`add-sqr-sqrt_binary64_1464`
11×	`associate-/l*_binary64_1387` `add-cube-cbrt_binary64_1477`
6×	`associate-/r/_binary64_1388` `add-log-exp_binary64_1481`
5×	`associate-/r*_binary64_1386` `pow1_binary64_1503`
4×	`div-inv_binary64_1439` `distribute-lft-out_binary64_1393`
3×	`sqrt-prod_binary64_1458` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`clear-num_binary64_1441` `flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417` `frac-2neg_binary64_1453`
1×	`sqrt-pow1_binary64_1460` `cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `associate-/l/_binary64_1389` `sub-neg_binary64_1435` `diff-log_binary64_1534` `pow1/2_binary64_1522`

Counts

4 → 102

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series902.0ms (12%)

Counts

4 → 12

Calls

4 calls:

399.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
314.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4953	3059
1	4953	3059

prune150.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	115	9	124

Merged error: 4.4b

Counts

124 → 9

Compiler

Compiled 3241 to 1999 computations (38.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1442`
15×	`add-sqr-sqrt_binary64_1464`
14×	`add-cube-cbrt_binary64_1477`
12×	`times-frac_binary64_1448`
8×	`add-log-exp_binary64_1481`
6×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
5×	`distribute-lft-out_binary64_1393` `pow1_binary64_1503`
4×	`associate-/r*_binary64_1386`
3×	`associate-/l*_binary64_1387` `sqrt-prod_binary64_1458`
2×	`associate-/r/_binary64_1388` `flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`sqrt-pow1_binary64_1460` `cbrt-undiv_binary64_1476` `cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `pow1/2_binary64_1522` `div-exp_binary64_1493`

Counts

4 → 72

Calls

4 calls:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.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)))

series660.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

330.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
140.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
68.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5099	1969

prune101.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	84	9	93

Merged error: 4.4b

Counts

93 → 9

Compiler

Compiled 2240 to 1394 computations (37.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_1442`
18×	`associate-r_binary64_1382`
16×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
14×	`add-sqr-sqrt_binary64_1464`
13×	`add-cube-cbrt_binary64_1477`
12×	`times-frac_binary64_1448`
10×	`pow1_binary64_1503`
8×	`add-log-exp_binary64_1481`
6×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
4×	`distribute-lft-out_binary64_1393`
3×	`pow-prod-down_binary64_1513` `sqrt-prod_binary64_1458`
2×	`cbrt-undiv_binary64_1476` `associate-/r/_binary64_1388` `flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `div-exp_binary64_1493`
1×	`sqrt-pow1_binary64_1460` `associate-r/_binary64_1384` `cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `div-inv_binary64_1439` `sub-neg_binary64_1435` `+-commutative_binary64_1372` `associate-l_binary64_1383` `-commutative_binary64_1373` `diff-log_binary64_1534` `pow1/2_binary64_1522`

Counts

4 → 77

Calls

4 calls:

16.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
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)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series675.0ms (9%)

Counts

4 → 12

Calls

4 calls:

370.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (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))))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
70.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify88.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4891	1915
1	4891	1915

prune99.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	89	9	98

Merged error: 4.4b

Counts

98 → 9

Compiler

Compiled 2185 to 1357 computations (37.9% saved)

regimes682.0ms (9%)

Compiler: Compiled 4688 to 3608 computations (23% saved)

bsearch82.0ms (1.1%)

Steps

Iters	Range	Point
4	2.4118898042567286e+124	4.78029124252191e+124	4.1783942655877156e+124
7	1.1374938612922884e-295	4.026500282123675e-294	1.1570789262807629e-295
10	-3.171065729716075e+141	-2.5266528926358777e+128	-3.2218651897993396e+133

Iters

Range

Point

2.4118898042567286e+124

4.78029124252191e+124

4.1783942655877156e+124

1.1374938612922884e-295

4.026500282123675e-294

1.1570789262807629e-295

-3.171065729716075e+141

-2.5266528926358777e+128

-3.2218651897993396e+133

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	110	88
1	110	88

end0.0ms (0%)

sample2.2s (29.5%)

Algorithm

1×

intervals

Results

292.0ms	1099×	body	2048	valid
292.0ms	5254×	body	128	valid
147.0ms	708×	body	1024	valid
123.0ms	387×	body	4096	valid
60.0ms	365×	body	512	valid
37.0ms	711×	body	128	nan
19.0ms	187×	body	256	valid
19.0ms	345×	body	128	invalid

Compiler

Compiled 1268 to 963 computations (24.1% saved)

Details

analyze476.0ms (6.3%)

sample41.0ms (0.5%)

simplify236.0ms (3.1%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite39.0ms (0.5%)

series553.0ms (7.3%)

simplify73.0ms (1%)

prune126.0ms (1.7%)

localize15.0ms (0.2%)

rewrite54.0ms (0.7%)

series902.0ms (12%)

simplify76.0ms (1%)

prune150.0ms (2%)

localize12.0ms (0.2%)

rewrite33.0ms (0.4%)

series660.0ms (8.7%)

simplify74.0ms (1%)

prune101.0ms (1.3%)

localize16.0ms (0.2%)

rewrite41.0ms (0.5%)

series675.0ms (9%)

simplify88.0ms (1.2%)

prune99.0ms (1.3%)

regimes682.0ms (9%)

bsearch82.0ms (1.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.2s (29.5%)

Profiling