Details

analyze571.0ms (6.6%)

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)

sample49.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	38×	body	2048	valid
11.0ms	166×	body	128	valid
4.0ms	12×	body	4096	valid
4.0ms	18×	body	1024	valid
2.0ms	10×	body	512	valid
2.0ms	12×	body	256	valid
1.0ms	16×	body	128	nan
1.0ms	15×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify296.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

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: 33.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
21.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite45.0ms (0.5%)

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-/l*_binary64_1387`
3×	`associate-/r*_binary64_1386` `sqrt-prod_binary64_1458`
2×	`associate-/l/_binary64_1389` `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:

13.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
10.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
10.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series635.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

237.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
163.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
144.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
90.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify84.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5101	2019

prune213.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	76	8	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	8	85

Merged error: 6.3b

Counts

85 → 8

Compiler

Compiled 2147 to 1169 computations (45.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.2b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
21.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite52.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1464`
18×	`*-un-lft-identity_binary64_1442`
13×	`associate-r_binary64_1382` `add-exp-log_binary64_1480` `add-cube-cbrt_binary64_1477`
11×	`times-frac_binary64_1448`
9×	`add-cbrt-cube_binary64_1478`
8×	`add-log-exp_binary64_1481`
7×	`pow1_binary64_1503`
4×	`associate-l_binary64_1383` `prod-exp_binary64_1491`
3×	`sqrt-prod_binary64_1458` `flip3-+_binary64_1445` `flip-+_binary64_1416` `unswap-sqr_binary64_1410`
2×	`cbrt-unprod_binary64_1475` `flip3--_binary64_1446` `sqrt-div_binary64_1459` `distribute-lft-out_binary64_1393` `flip--_binary64_1417` `frac-times_binary64_1452` `associate-*l/_binary64_1385` `div-exp_binary64_1493`
1×	`sqrt-pow1_binary64_1460` `associate-r/_binary64_1384` `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` `1-exp_binary64_1486` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `rec-exp_binary64_1492` `diff-log_binary64_1534` `un-div-inv_binary64_1440` `pow1/2_binary64_1522`

Counts

4 → 80

Calls

4 calls:

21.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
12.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series632.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

187.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
186.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
163.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
96.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify136.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4920	2059
1	4920	2059

prune146.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	94	6	100

Merged error: 6.3b

Counts

100 → 6

Compiler

Compiled 2330 to 1336 computations (42.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
21.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite55.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64_1448`
82×	`*-un-lft-identity_binary64_1442`
57×	`add-sqr-sqrt_binary64_1464`
56×	`add-cube-cbrt_binary64_1477`
18×	`associate-/r*_binary64_1386`
15×	`add-exp-log_binary64_1480`
13×	`distribute-lft-out_binary64_1393`
9×	`add-cbrt-cube_binary64_1478` `associate-/r/_binary64_1388`
8×	`add-log-exp_binary64_1481`
7×	`div-exp_binary64_1493`
6×	`pow1_binary64_1503`
5×	`div-inv_binary64_1439` `flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`cbrt-undiv_binary64_1476` `associate-/l*_binary64_1387` `sqrt-prod_binary64_1458`
2×	`1-exp_binary64_1486` `flip3--_binary64_1446` `rec-exp_binary64_1492` `sqrt-div_binary64_1459` `flip--_binary64_1417`
1×	`sqrt-pow1_binary64_1460` `inv-pow_binary64_1527` `cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `sub-neg_binary64_1435` `clear-num_binary64_1441` `+-commutative_binary64_1372` `pow-flip_binary64_1516` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `pow1/2_binary64_1522`

Counts

4 → 135

Calls

4 calls:

15.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
10.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series561.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

208.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
155.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
129.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
68.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify122.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4908	4499
1	4908	4499

prune264.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	146	7	153

Merged error: 6.2b

Counts

153 → 7

Compiler

Compiled 4229 to 2347 computations (44.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
21.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
21.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1442`
8×	`add-log-exp_binary64_1481` `add-sqr-sqrt_binary64_1464`
6×	`sqrt-prod_binary64_1458` `pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
4×	`add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459` `add-exp-log_binary64_1480`
2×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `flip3--_binary64_1446` `+-commutative_binary64_1372` `distribute-lft-out_binary64_1393` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522`

Counts

4 → 54

Calls

4 calls:

14.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
10.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series636.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

176.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
173.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
147.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
140.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify49.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4928	1354
1	4928	1354

prune122.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	66	7	73

Merged error: 6.2b

Counts

73 → 7

Compiler

Compiled 2450 to 1310 computations (46.5% saved)

regimes941.0ms (10.9%)

Compiler: Compiled 3828 to 2854 computations (25.4% saved)

bsearch221.0ms (2.6%)

Steps

Iters	Range		Point
8	3.9671678271281564e+138	1.124243621054002e+142	3.685989243441257e+139
11	-1.1882864963932584e-67	-3.3444877014751962e-90	-3.559620564434074e-74
8	-976339708351.8907	-943974737.4200811	-7524134179.167663
8	-1.8658211839353844e+66	-4.1022764590776905e+63	-2.7823652310513766e+65

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	97	111
1	97	111

end0.0ms (0%)

sample2.7s (30.9%)

Algorithm

1×

intervals

Results

376.0ms	1125×	body	2048	valid
358.0ms	5209×	body	128	valid
180.0ms	702×	body	1024	valid
167.0ms	405×	body	4096	valid
75.0ms	359×	body	512	valid
42.0ms	648×	body	128	nan
28.0ms	383×	body	128	invalid
26.0ms	200×	body	256	valid

Compiler

Compiled 1082 to 797 computations (26.3% saved)

Details

analyze571.0ms (6.6%)

sample49.0ms (0.6%)

simplify296.0ms (3.4%)

prune4.0ms (0%)

localize23.0ms (0.3%)

rewrite45.0ms (0.5%)

series635.0ms (7.4%)

simplify84.0ms (1%)

prune213.0ms (2.5%)

localize13.0ms (0.2%)

rewrite52.0ms (0.6%)

series632.0ms (7.3%)

simplify136.0ms (1.6%)

prune146.0ms (1.7%)

localize13.0ms (0.1%)

rewrite55.0ms (0.6%)

series561.0ms (6.5%)

simplify122.0ms (1.4%)

prune264.0ms (3.1%)

localize14.0ms (0.2%)

rewrite44.0ms (0.5%)

series636.0ms (7.4%)

simplify49.0ms (0.6%)

prune122.0ms (1.4%)

regimes941.0ms (10.9%)

bsearch221.0ms (2.6%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample2.7s (30.9%)

Profiling