Details

analyze43.0ms (0.1%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 7 to 7 computations (0% saved)

sample38.0ms (0.1%)

Algorithm

1×

intervals

Results

17.0ms	59×	body	2048	valid
7.0ms	62×	body	1024	valid
2.0ms	90×	body	128	valid
2.0ms	25×	body	512	valid
1.0ms	20×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify162.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4875	9
1	4875	9

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

29.3b

Counts

2 → 1

Compiler

Compiled 6 to 6 computations (0% saved)

localize4.0ms (0%)

Local error

Found 4 expressions with local error:

4.2b	(-.f64 (exp.f64 (*.f64 a x)) 1)
0.0b	(exp.f64 (*.f64 a x))
0.0b	(exp.f64 (*.f64 a x))
4.2b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64_1464`
6×	`add-log-exp_binary64_1481` `*-un-lft-identity_binary64_1442`
3×	`cancel-sign-sub-inv_binary64_1408` `add-cube-cbrt_binary64_1477`
2×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503` `difference-of-squares_binary64_1411`
1×	`sub-neg_binary64_1435` `rem-exp-log_binary64_1482` `flip3--_binary64_1446` `difference-of-sqr-1_binary64_1412` `exp-prod_binary64_1494` `flip--_binary64_1417` `diff-log_binary64_1534` `exp-to-pow_binary64_1504` `distribute-lft-out--_binary64_1394`

Counts

2 → 28

Calls

4 calls:

4.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
2.0ms	(exp.f64 (*.f64 a x))
0.0ms	(exp.f64 (*.f64 a x))
0.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)

series78.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

48.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
30.0ms	(exp.f64 (*.f64 a x))

Compiler

Compiled 348 to 316 computations (9.2% saved)

simplify65.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4917	652
1	4917	652

prune100.0ms (0.2%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	31	21	52
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	31	22	53

Error

0.1b

Counts

53 → 22

Compiler

Compiled 593 to 365 computations (38.4% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (*.f64 a x) 3)
0.1b	(.f64 1/6 (pow.f64 (.f64 a x) 3))
0.0b	(.f64 1/2 (.f64 a (*.f64 x x)))
0.0b	(+.f64 x (.f64 1/2 (.f64 a (*.f64 x x))))
0.2b	(pow.f64 (*.f64 a x) 3)
1.9b	(.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))
5.1b	(.f64 a (.f64 x x))
11.6b	(+.f64 (.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x))))) (.f64 1/6 (pow.f64 (.f64 a x) 3)))

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
11×	`add-sqr-sqrt_binary64_1464`
8×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`associate-l_binary64_1383` `add-log-exp_binary64_1481`
5×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491`
4×	`associate-r_binary64_1382`
3×	`pow-unpow_binary64_1519`
2×	`associate-r/_binary64_1384` `pow-exp_binary64_1510` `associate-+l+_binary64_1375` `-commutative_binary64_1373` `rem-cube-cbrt_binary64_1465` `distribute-lft-in_binary64_1391` `flip3-+_binary64_1445` `distribute-rgt-in_binary64_1392` `flip-+_binary64_1416` `unswap-sqr_binary64_1410` `pow-pow_binary64_1514`
1×	`cube-mult_binary64_1472` `sum-log_binary64_1533` `+-commutative_binary64_1372` `cube-prod_binary64_1470` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `unpow-prod-down_binary64_1521` `pow-to-exp_binary64_1511`

Counts

4 → 76

Calls

8 calls:

8.0ms	(+.f64 (.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x))))) (.f64 1/6 (pow.f64 (.f64 a x) 3)))
6.0ms	(.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))
6.0ms	(.f64 a (.f64 x x))
4.0ms	(pow.f64 (*.f64 a x) 3)
0.0ms	(+.f64 x (.f64 1/2 (.f64 a (*.f64 x x))))

series594.0ms (1.3%)

Counts

4 → 42

Calls

4 calls:

315.0ms	(+.f64 (.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x))))) (.f64 1/6 (pow.f64 (.f64 a x) 3)))
145.0ms	(.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))
76.0ms	(pow.f64 (*.f64 a x) 3)
58.0ms	(.f64 a (.f64 x x))

Compiler

Compiled 1242 to 1000 computations (19.5% saved)

simplify71.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5104	1721

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

4.2b	(-.f64 (log.f64 (exp.f64 (exp.f64 (*.f64 a x)))) 1)
0.0b	(exp.f64 (*.f64 a x))
0.0b	(log.f64 (exp.f64 (exp.f64 (*.f64 a x))))
0.0b	(exp.f64 (exp.f64 (*.f64 a x)))
0.0b	(exp.f64 (exp.f64 (*.f64 a x)))
0.0b	(log.f64 (exp.f64 (exp.f64 (*.f64 a x))))
0.0b	(exp.f64 (*.f64 a x))
4.2b	(-.f64 (log.f64 (exp.f64 (exp.f64 (*.f64 a x)))) 1)

rewrite16.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
9×	`add-cube-cbrt_binary64_1477`
8×	`add-log-exp_binary64_1481`
7×	`exp-prod_binary64_1494`
6×	`log-prod_binary64_1528` `pow1_binary64_1503`
5×	`log-pow_binary64_1531`
4×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
3×	`associate--l+_binary64_1379` `cancel-sign-sub-inv_binary64_1408`
2×	`rem-exp-log_binary64_1482` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
1×	`sub-neg_binary64_1435` `rem-log-exp_binary64_1483` `flip3--_binary64_1446` `difference-of-sqr-1_binary64_1412` `flip--_binary64_1417` `diff-log_binary64_1534` `exp-to-pow_binary64_1504`

Counts

4 → 58

Calls

8 calls:

6.0ms	(-.f64 (log.f64 (exp.f64 (exp.f64 (*.f64 a x)))) 1)
2.0ms	(log.f64 (exp.f64 (exp.f64 (*.f64 a x))))
2.0ms	(exp.f64 (exp.f64 (*.f64 a x)))
2.0ms	(exp.f64 (*.f64 a x))
0.0ms	(exp.f64 (exp.f64 (*.f64 a x)))

series361.0ms (0.8%)

Counts

4 → 48

Calls

4 calls:

153.0ms	(-.f64 (log.f64 (exp.f64 (exp.f64 (*.f64 a x)))) 1)
128.0ms	(log.f64 (exp.f64 (exp.f64 (*.f64 a x))))
47.0ms	(exp.f64 (exp.f64 (*.f64 a x)))
32.0ms	(exp.f64 (*.f64 a x))

Compiler

Compiled 764 to 704 computations (7.9% saved)

simplify70.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4945	1272
1	4945	1272

localize8.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(sqrt.f64 (exp.f64 (*.f64 a x)))
0.0b	(exp.f64 (*.f64 a x))
0.0b	(exp.f64 (*.f64 a x))
0.0b	(.f64 (sqrt.f64 (exp.f64 (.f64 a x))) (sqrt.f64 (exp.f64 (*.f64 a x))))
0.0b	(exp.f64 (*.f64 a x))
0.2b	(sqrt.f64 (exp.f64 (*.f64 a x)))
0.2b	(sqrt.f64 (exp.f64 (*.f64 a x)))
4.2b	(-.f64 (.f64 (sqrt.f64 (exp.f64 (.f64 a x))) (sqrt.f64 (exp.f64 (*.f64 a x)))) 1)

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64_1481` `add-sqr-sqrt_binary64_1464`
8×	`*-un-lft-identity_binary64_1442`
7×	`add-cube-cbrt_binary64_1477`
6×	`sqrt-pow1_binary64_1460` `sqrt-prod_binary64_1458` `pow1_binary64_1503`
4×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
3×	`cancel-sign-sub-inv_binary64_1408` `exp-prod_binary64_1494` `exp-to-pow_binary64_1504`
2×	`rem-sqrt-square_binary64_1455` `pow1/2_binary64_1522` `difference-of-squares_binary64_1411`
1×	`sub-neg_binary64_1435` `rem-exp-log_binary64_1482` `flip3--_binary64_1446` `difference-of-sqr-1_binary64_1412` `flip--_binary64_1417` `diff-log_binary64_1534`

Counts

4 → 57

Calls

8 calls:

9.0ms	(-.f64 (.f64 (sqrt.f64 (exp.f64 (.f64 a x))) (sqrt.f64 (exp.f64 (*.f64 a x)))) 1)
2.0ms	(sqrt.f64 (exp.f64 (*.f64 a x)))
2.0ms	(sqrt.f64 (exp.f64 (*.f64 a x)))
2.0ms	(exp.f64 (*.f64 a x))
0.0ms	(.f64 (sqrt.f64 (exp.f64 (.f64 a x))) (sqrt.f64 (exp.f64 (*.f64 a x))))

series191.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

55.0ms	(sqrt.f64 (exp.f64 (*.f64 a x)))
52.0ms	(sqrt.f64 (exp.f64 (*.f64 a x)))
48.0ms	(-.f64 (.f64 (sqrt.f64 (exp.f64 (.f64 a x))) (sqrt.f64 (exp.f64 (*.f64 a x)))) 1)
35.0ms	(exp.f64 (*.f64 a x))

Compiler

Compiled 1004 to 770 computations (23.3% saved)

simplify49.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5428	1251

prune2.3s (5.3%)

Pruning

107 alts after pruning (101 fresh and 6 done)

	Pruned	Kept	Total
New	240	89	329
Fresh	4	12	16
Picked	0	0	0
Done	0	6	6
Total	244	107	351

Error

0.0b

Counts

351 → 107

Compiler

Compiled 5147 to 2809 computations (45.4% saved)

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (*.f64 a x) 3)
0.2b	(pow.f64 (*.f64 a x) 2)
0.1b	(.f64 1/6 (pow.f64 (.f64 a x) 3))
0.0b	(.f64 1/2 (pow.f64 (.f64 a x) 2))
0.2b	(pow.f64 (*.f64 a x) 2)
0.2b	(pow.f64 (*.f64 a x) 3)
4.4b	(+.f64 (.f64 a x) (.f64 1/2 (pow.f64 (*.f64 a x) 2)))
11.6b	(+.f64 (+.f64 (.f64 a x) (.f64 1/2 (pow.f64 (.f64 a x) 2))) (.f64 1/6 (pow.f64 (*.f64 a x) 3)))

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-log-exp_binary64_1481`
10×	`add-exp-log_binary64_1480` `pow1_binary64_1503`
7×	`add-cbrt-cube_binary64_1478`
6×	`pow-unpow_binary64_1519` `add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`sum-log_binary64_1533` `pow-exp_binary64_1510` `pow-pow_binary64_1514`
2×	`+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `rem-cube-cbrt_binary64_1465` `sqr-pow_binary64_1414` `flip3-+_binary64_1445` `flip-+_binary64_1416` `prod-exp_binary64_1491` `unpow-prod-down_binary64_1521` `pow-to-exp_binary64_1511`
1×	`cube-mult_binary64_1472` `cbrt-unprod_binary64_1475` `associate-+l+_binary64_1375` `unpow2_binary64_1507` `cube-prod_binary64_1470` `unpow3_binary64_1508`

Counts

4 → 64

Calls

8 calls:

8.0ms	(+.f64 (+.f64 (.f64 a x) (.f64 1/2 (pow.f64 (.f64 a x) 2))) (.f64 1/6 (pow.f64 (*.f64 a x) 3)))
4.0ms	(+.f64 (.f64 a x) (.f64 1/2 (pow.f64 (*.f64 a x) 2)))
4.0ms	(pow.f64 (*.f64 a x) 2)
4.0ms	(pow.f64 (*.f64 a x) 3)
0.0ms	(.f64 1/2 (pow.f64 (.f64 a x) 2))

series621.0ms (1.4%)

Counts

4 → 42

Calls

4 calls:

332.0ms	(+.f64 (+.f64 (.f64 a x) (.f64 1/2 (pow.f64 (.f64 a x) 2))) (.f64 1/6 (pow.f64 (*.f64 a x) 3)))
147.0ms	(+.f64 (.f64 a x) (.f64 1/2 (pow.f64 (*.f64 a x) 2)))
82.0ms	(pow.f64 (*.f64 a x) 3)
60.0ms	(pow.f64 (*.f64 a x) 2)

Compiler

Compiled 1266 to 1012 computations (20.1% saved)

simplify92.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4926	1531
1	4926	1531

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

4.2b	(-.f64 (+.f64 (*.f64 a x) 1) 1)
0.0b	(+.f64 (*.f64 a x) 1)
0.0b	(+.f64 (*.f64 a x) 1)
4.2b	(-.f64 (+.f64 (*.f64 a x) 1) 1)

rewrite14.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64_1481`
7×	`add-sqr-sqrt_binary64_1464`
6×	`*-un-lft-identity_binary64_1442`
3×	`cancel-sign-sub-inv_binary64_1408` `add-cube-cbrt_binary64_1477`
2×	`add-cbrt-cube_binary64_1478` `sum-log_binary64_1533` `add-exp-log_binary64_1480` `diff-log_binary64_1534` `pow1_binary64_1503` `difference-of-squares_binary64_1411`
1×	`associate--l+_binary64_1379` `sub-neg_binary64_1435` `flip3--_binary64_1446` `+-commutative_binary64_1372` `difference-of-sqr-1_binary64_1412` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `distribute-lft-out--_binary64_1394`

Counts

2 → 31

Calls

4 calls:

8.0ms	(-.f64 (+.f64 (*.f64 a x) 1) 1)
4.0ms	(+.f64 (*.f64 a x) 1)
0.0ms	(+.f64 (*.f64 a x) 1)
0.0ms	(-.f64 (+.f64 (*.f64 a x) 1) 1)

series85.0ms (0.2%)

Counts

2 → 18

Calls

2 calls:

50.0ms	(+.f64 (*.f64 a x) 1)
35.0ms	(-.f64 (+.f64 (*.f64 a x) 1) 1)

Compiler

Compiled 146 to 150 computations (-2.7% saved)

simplify88.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4855	410
1	4855	410

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b	(log.f64 (exp.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x))))))))
0.0b	(exp.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))))
0.0b	(.f64 1/2 (.f64 a (*.f64 x x)))
0.0b	(+.f64 x (.f64 1/2 (.f64 a (*.f64 x x))))
0.5b	(log.f64 (exp.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x))))))))
1.9b	(.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))
4.3b	(-.f64 (log.f64 (exp.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))))) 1)
5.1b	(.f64 a (.f64 x x))

rewrite33.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1464`
15×	`*-un-lft-identity_binary64_1442`
13×	`pow1_binary64_1503`
11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `add-cube-cbrt_binary64_1477`
8×	`log-prod_binary64_1528`
6×	`associate-l_binary64_1383`
5×	`log-pow_binary64_1531` `add-log-exp_binary64_1481`
4×	`associate--l+_binary64_1379` `associate-r_binary64_1382` `cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491`
3×	`cancel-sign-sub-inv_binary64_1408` `exp-prod_binary64_1494`
2×	`associate-r/_binary64_1384` `-commutative_binary64_1373` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `exp-sum_binary64_1488` `unswap-sqr_binary64_1410`
1×	`sub-neg_binary64_1435` `rem-log-exp_binary64_1483` `flip3--_binary64_1446` `difference-of-sqr-1_binary64_1412` `flip--_binary64_1417` `diff-log_binary64_1534` `distribute-lft-in_binary64_1391` `flip3-+_binary64_1445` `distribute-rgt-in_binary64_1392` `flip-+_binary64_1416`

Counts

4 → 80

Calls

8 calls:

9.0ms	(-.f64 (log.f64 (exp.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))))) 1)
6.0ms	(.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))
6.0ms	(.f64 a (.f64 x x))
4.0ms	(log.f64 (exp.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x))))))))
0.0ms	(+.f64 x (.f64 1/2 (.f64 a (*.f64 x x))))

series850.0ms (1.9%)

Counts

4 → 36

Calls

4 calls:

328.0ms	(-.f64 (log.f64 (exp.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))))) 1)
324.0ms	(log.f64 (exp.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x))))))))
137.0ms	(.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))
61.0ms	(.f64 a (.f64 x x))

Compiler

Compiled 960 to 868 computations (9.6% saved)

simplify127.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4998	1971
1	4998	1971

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 1/6 (pow.f64 (.f64 a x) 3))
0.1b	(.f64 (sqrt.f64 (.f64 a (.f64 x x))) (sqrt.f64 (.f64 a (*.f64 x x))))
0.0b	(.f64 1/2 (.f64 (sqrt.f64 (.f64 a (.f64 x x))) (sqrt.f64 (.f64 a (.f64 x x)))))
0.0b	(+.f64 x (.f64 1/2 (.f64 (sqrt.f64 (.f64 a (.f64 x x))) (sqrt.f64 (.f64 a (.f64 x x))))))
5.1b	(.f64 a (.f64 x x))
7.3b	(+.f64 (.f64 a (+.f64 x (.f64 1/2 (.f64 (sqrt.f64 (.f64 a (.f64 x x))) (sqrt.f64 (.f64 a (.f64 x x))))))) (.f64 1/6 (pow.f64 (*.f64 a x) 3)))
26.2b	(sqrt.f64 (.f64 a (.f64 x x)))
26.2b	(sqrt.f64 (.f64 a (.f64 x x)))

rewrite33.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64_1503`
9×	`add-cbrt-cube_binary64_1478` `pow-prod-down_binary64_1513` `add-exp-log_binary64_1480`
6×	`sqrt-pow1_binary64_1460` `add-log-exp_binary64_1481` `add-sqr-sqrt_binary64_1464`
5×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
3×	`cbrt-unprod_binary64_1475` `associate-l_binary64_1383` `prod-exp_binary64_1491`
2×	`associate-+l+_binary64_1375` `sqrt-prod_binary64_1458` `pow1/2_binary64_1522`
1×	`associate-r_binary64_1382` `sum-log_binary64_1533` `+-commutative_binary64_1372` `*-commutative_binary64_1373` `distribute-lft-in_binary64_1391` `flip3-+_binary64_1445` `distribute-rgt-in_binary64_1392` `flip-+_binary64_1416` `unswap-sqr_binary64_1410`

Counts

4 → 56

Calls

8 calls:

8.0ms	(+.f64 (.f64 a (+.f64 x (.f64 1/2 (.f64 (sqrt.f64 (.f64 a (.f64 x x))) (sqrt.f64 (.f64 a (.f64 x x))))))) (.f64 1/6 (pow.f64 (*.f64 a x) 3)))
6.0ms	(.f64 a (.f64 x x))
5.0ms	(sqrt.f64 (.f64 a (.f64 x x)))
5.0ms	(sqrt.f64 (.f64 a (.f64 x x)))
0.0ms	(+.f64 x (.f64 1/2 (.f64 (sqrt.f64 (.f64 a (.f64 x x))) (sqrt.f64 (.f64 a (.f64 x x))))))

series465.0ms (1.1%)

Counts

4 → 34

Calls

4 calls:

288.0ms	(+.f64 (.f64 a (+.f64 x (.f64 1/2 (.f64 (sqrt.f64 (.f64 a (.f64 x x))) (sqrt.f64 (.f64 a (.f64 x x))))))) (.f64 1/6 (pow.f64 (*.f64 a x) 3)))
62.0ms	(.f64 a (.f64 x x))
58.0ms	(sqrt.f64 (.f64 a (.f64 x x)))
56.0ms	(sqrt.f64 (.f64 a (.f64 x x)))

Compiler

Compiled 1372 to 1056 computations (23% saved)

simplify71.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4940	1243
1	4940	1243

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

2.8b	(-.f64 (.f64 (sqrt.f64 (exp.f64 (.f64 a x))) (sqrt.f64 (pow.f64 (exp.f64 a) x))) 1)
1.2b	(pow.f64 (exp.f64 a) x)
0.2b	(sqrt.f64 (exp.f64 (*.f64 a x)))
0.0b	(exp.f64 (*.f64 a x))
0.0b	(exp.f64 (*.f64 a x))
0.2b	(sqrt.f64 (exp.f64 (*.f64 a x)))
1.2b	(pow.f64 (exp.f64 a) x)
2.8b	(-.f64 (.f64 (sqrt.f64 (exp.f64 (.f64 a x))) (sqrt.f64 (pow.f64 (exp.f64 a) x))) 1)

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1464`
9×	`add-log-exp_binary64_1481` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`pow1_binary64_1503`
5×	`exp-prod_binary64_1494`
4×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow-pow_binary64_1514`
3×	`sqrt-pow1_binary64_1460` `cancel-sign-sub-inv_binary64_1408` `pow-unpow_binary64_1519` `sqrt-prod_binary64_1458` `unpow-prod-down_binary64_1521`
2×	`exp-to-pow_binary64_1504`
1×	`rem-sqrt-square_binary64_1455` `pow-exp_binary64_1510` `sub-neg_binary64_1435` `rem-exp-log_binary64_1482` `flip3--_binary64_1446` `flip--_binary64_1417` `diff-log_binary64_1534` `sqr-pow_binary64_1414` `pow1/2_binary64_1522` `pow-to-exp_binary64_1511`

Counts

4 → 59

Calls

8 calls:

9.0ms	(-.f64 (.f64 (sqrt.f64 (exp.f64 (.f64 a x))) (sqrt.f64 (pow.f64 (exp.f64 a) x))) 1)
3.0ms	(pow.f64 (exp.f64 a) x)
2.0ms	(sqrt.f64 (exp.f64 (*.f64 a x)))
2.0ms	(exp.f64 (*.f64 a x))
0.0ms	(exp.f64 (*.f64 a x))

series334.0ms (0.8%)

Counts

4 → 38

Calls

4 calls:

167.0ms	(-.f64 (.f64 (sqrt.f64 (exp.f64 (.f64 a x))) (sqrt.f64 (pow.f64 (exp.f64 a) x))) 1)
84.0ms	(pow.f64 (exp.f64 a) x)
44.0ms	(sqrt.f64 (exp.f64 (*.f64 a x)))
38.0ms	(exp.f64 (*.f64 a x))

Compiler

Compiled 908 to 765 computations (15.7% saved)

simplify77.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5013	943

prune7.9s (17.8%)

Pruning

222 alts after pruning (212 fresh and 10 done)

	Pruned	Kept	Total
New	331	127	458
Fresh	11	85	96
Picked	0	0	0
Done	1	10	11
Total	343	222	565

Error

Counts

565 → 222

Compiler

Compiled 10519 to 6068 computations (42.3% saved)

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

4.2b	(-.f64 (+.f64 (*.f64 a x) 1) 1)
0.0b	(+.f64 (*.f64 a x) 1)
0.0b	(+.f64 (*.f64 a x) 1)
4.2b	(-.f64 (+.f64 (*.f64 a x) 1) 1)

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64_1481`
7×	`add-sqr-sqrt_binary64_1464`
6×	`*-un-lft-identity_binary64_1442`
3×	`cancel-sign-sub-inv_binary64_1408` `add-cube-cbrt_binary64_1477`
2×	`add-cbrt-cube_binary64_1478` `sum-log_binary64_1533` `add-exp-log_binary64_1480` `diff-log_binary64_1534` `pow1_binary64_1503` `difference-of-squares_binary64_1411`
1×	`associate--l+_binary64_1379` `sub-neg_binary64_1435` `flip3--_binary64_1446` `+-commutative_binary64_1372` `difference-of-sqr-1_binary64_1412` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `distribute-lft-out--_binary64_1394`

Counts

2 → 31

Calls

4 calls:

7.0ms	(-.f64 (+.f64 (*.f64 a x) 1) 1)
4.0ms	(+.f64 (*.f64 a x) 1)
0.0ms	(+.f64 (*.f64 a x) 1)
0.0ms	(-.f64 (+.f64 (*.f64 a x) 1) 1)

series84.0ms (0.2%)

Counts

2 → 18

Calls

2 calls:

49.0ms	(+.f64 (*.f64 a x) 1)
35.0ms	(-.f64 (+.f64 (*.f64 a x) 1) 1)

Compiler

Compiled 206 to 210 computations (-1.9% saved)

simplify82.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4855	410
1	4855	410

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

1.9b	(.f64 a (+.f64 x (.f64 (.f64 a (.f64 x x)) 1/2)))
0.8b	(exp.f64 (log.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 (.f64 a (.f64 x x)) 1/2))))))
0.0b	(+.f64 x (.f64 (.f64 a (*.f64 x x)) 1/2))
0.0b	(.f64 (.f64 a (*.f64 x x)) 1/2)
1.9b	(.f64 a (+.f64 x (.f64 (.f64 a (.f64 x x)) 1/2)))
4.3b	(-.f64 (exp.f64 (log.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 (.f64 a (.f64 x x)) 1/2)))))) 1)
5.1b	(.f64 a (.f64 x x))
15.4b	(log.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 (.f64 a (.f64 x x)) 1/2)))))

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1464`
13×	`*-un-lft-identity_binary64_1442`
12×	`add-exp-log_binary64_1480` `pow1_binary64_1503`
11×	`add-cbrt-cube_binary64_1478`
9×	`add-cube-cbrt_binary64_1477`
6×	`log-prod_binary64_1528` `associate-l_binary64_1383` `add-log-exp_binary64_1481`
4×	`associate-r_binary64_1382` `cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `difference-of-squares_binary64_1411`
3×	`cancel-sign-sub-inv_binary64_1408` `exp-sum_binary64_1488`
2×	`associate-r/_binary64_1384` `-commutative_binary64_1373` `difference-of-sqr-1_binary64_1412` `flip3-+_binary64_1445` `flip-+_binary64_1416` `log-div_binary64_1529` `unswap-sqr_binary64_1410`
1×	`sub-neg_binary64_1435` `rem-log-exp_binary64_1483` `log-pow_binary64_1531` `flip3--_binary64_1446` `flip--_binary64_1417` `diff-log_binary64_1534` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `distribute-lft-out--_binary64_1394`

Counts

4 → 76

Calls

8 calls:

8.0ms	(-.f64 (exp.f64 (log.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 (.f64 a (.f64 x x)) 1/2)))))) 1)
6.0ms	(.f64 a (+.f64 x (.f64 (.f64 a (.f64 x x)) 1/2)))
6.0ms	(.f64 a (.f64 x x))
3.0ms	(log.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 (.f64 a (.f64 x x)) 1/2)))))
0.0ms	(.f64 (.f64 a (*.f64 x x)) 1/2)

series681.0ms (1.5%)

Counts

4 → 38

Calls

4 calls:

393.0ms	(-.f64 (exp.f64 (log.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 (.f64 a (.f64 x x)) 1/2)))))) 1)
150.0ms	(.f64 a (+.f64 x (.f64 (.f64 a (.f64 x x)) 1/2)))
84.0ms	(log.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 (.f64 a (.f64 x x)) 1/2)))))
54.0ms	(.f64 a (.f64 x x))

Compiler

Compiled 1304 to 1180 computations (9.5% saved)

simplify88.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4934	2292
1	4934	2292

localize27.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 1/2 (.f64 a (*.f64 x x)))
0.0b	(.f64 1/2 (.f64 a (*.f64 x x)))
0.0b	(.f64 1/2 (.f64 a (*.f64 x x)))
0.0b	(.f64 1/2 (.f64 a (*.f64 x x)))
5.1b	(.f64 a (.f64 x x))
11.5b	(+.f64 (pow.f64 x 3) (pow.f64 (.f64 1/2 (.f64 a (*.f64 x x))) 3))
11.6b	(+.f64 (/.f64 (.f64 a (+.f64 (pow.f64 x 3) (pow.f64 (.f64 1/2 (.f64 a (.f64 x x))) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 1/2 (.f64 a (.f64 x x))) (.f64 1/2 (.f64 a (.f64 x x)))) (.f64 x (.f64 1/2 (.f64 a (.f64 x x))))))) (.f64 1/6 (pow.f64 (.f64 a x) 3)))
39.7b	(/.f64 (.f64 a (+.f64 (pow.f64 x 3) (pow.f64 (.f64 1/2 (.f64 a (.f64 x x))) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 1/2 (.f64 a (.f64 x x))) (.f64 1/2 (.f64 a (.f64 x x)))) (.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))))

rewrite100.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
9×	`pow1_binary64_1503` `*-un-lft-identity_binary64_1442`
8×	`add-log-exp_binary64_1481` `add-sqr-sqrt_binary64_1464`
7×	`add-cube-cbrt_binary64_1477`
4×	`cbrt-unprod_binary64_1475` `flip3-+_binary64_1445` `flip-+_binary64_1416` `prod-exp_binary64_1491`
3×	`associate-/r_binary64_1386` `times-frac_binary64_1448` `associate-l*_binary64_1383` `pow-prod-down_binary64_1513`
2×	`associate-*r/_binary64_1384` `cbrt-undiv_binary64_1476` `sum-log_binary64_1533` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `+-commutative_binary64_1372` `div-exp_binary64_1493`
1×	`associate-r_binary64_1382` `div-inv_binary64_1439` `clear-num_binary64_1441` `associate-/l_binary64_1387` `-commutative_binary64_1373` `distribute-lft-out_binary64_1393` `frac-2neg_binary64_1453` `sum-cubes_binary64_1443` `unswap-sqr_binary64_1410`

Counts

4 → 68

Calls

8 calls:

36.0ms	(+.f64 (/.f64 (.f64 a (+.f64 (pow.f64 x 3) (pow.f64 (.f64 1/2 (.f64 a (.f64 x x))) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 1/2 (.f64 a (.f64 x x))) (.f64 1/2 (.f64 a (.f64 x x)))) (.f64 x (.f64 1/2 (.f64 a (.f64 x x))))))) (.f64 1/6 (pow.f64 (.f64 a x) 3)))
32.0ms	(/.f64 (.f64 a (+.f64 (pow.f64 x 3) (pow.f64 (.f64 1/2 (.f64 a (.f64 x x))) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 1/2 (.f64 a (.f64 x x))) (.f64 1/2 (.f64 a (.f64 x x)))) (.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))))
14.0ms	(+.f64 (pow.f64 x 3) (pow.f64 (.f64 1/2 (.f64 a (*.f64 x x))) 3))
6.0ms	(.f64 a (.f64 x x))
0.0ms	(.f64 1/2 (.f64 a (*.f64 x x)))

series1.8s (4%)

Counts

4 → 48

Calls

4 calls:

887.0ms	(+.f64 (/.f64 (.f64 a (+.f64 (pow.f64 x 3) (pow.f64 (.f64 1/2 (.f64 a (.f64 x x))) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 1/2 (.f64 a (.f64 x x))) (.f64 1/2 (.f64 a (.f64 x x)))) (.f64 x (.f64 1/2 (.f64 a (.f64 x x))))))) (.f64 1/6 (pow.f64 (.f64 a x) 3)))
527.0ms	(/.f64 (.f64 a (+.f64 (pow.f64 x 3) (pow.f64 (.f64 1/2 (.f64 a (.f64 x x))) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 1/2 (.f64 a (.f64 x x))) (.f64 1/2 (.f64 a (.f64 x x)))) (.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))))
294.0ms	(+.f64 (pow.f64 x 3) (pow.f64 (.f64 1/2 (.f64 a (*.f64 x x))) 3))
68.0ms	(.f64 a (.f64 x x))

Compiler

Compiled 2316 to 1560 computations (32.6% saved)

simplify108.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4960	3949
1	4960	3949

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (.f64 (cbrt.f64 (.f64 a (.f64 x x))) (cbrt.f64 (.f64 a (.f64 x x)))) (cbrt.f64 (.f64 a (.f64 x x))))
0.0b	(exp.f64 (+.f64 1 (.f64 a (+.f64 x (.f64 1/2 (.f64 (.f64 (cbrt.f64 (.f64 a (.f64 x x))) (cbrt.f64 (.f64 a (.f64 x x)))) (cbrt.f64 (.f64 a (.f64 x x)))))))))
0.0b	(+.f64 x (.f64 1/2 (.f64 (.f64 (cbrt.f64 (.f64 a (.f64 x x))) (cbrt.f64 (.f64 a (.f64 x x)))) (cbrt.f64 (.f64 a (*.f64 x x))))))
0.0b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (.f64 a (.f64 x x))) (cbrt.f64 (.f64 a (.f64 x x)))) (cbrt.f64 (.f64 a (*.f64 x x)))))
5.1b	(.f64 a (.f64 x x))
34.4b	(cbrt.f64 (.f64 a (.f64 x x)))
34.4b	(cbrt.f64 (.f64 a (.f64 x x)))
34.4b	(cbrt.f64 (.f64 a (.f64 x x)))

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
6×	`add-sqr-sqrt_binary64_1464`
5×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`add-log-exp_binary64_1481`
3×	`cbrt-unprod_binary64_1475` `cbrt-prod_binary64_1473` `associate-l_binary64_1383` `pow-prod-down_binary64_1513` `pow1/3_binary64_1524` `prod-exp_binary64_1491`
1×	`associate-r_binary64_1382` `*-commutative_binary64_1373` `unswap-sqr_binary64_1410`

Counts

4 → 46

Calls

8 calls:

6.0ms	(.f64 a (.f64 x x))
5.0ms	(cbrt.f64 (.f64 a (.f64 x x)))
5.0ms	(cbrt.f64 (.f64 a (.f64 x x)))
5.0ms	(cbrt.f64 (.f64 a (.f64 x x)))
0.0ms	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (.f64 a (.f64 x x))) (cbrt.f64 (.f64 a (.f64 x x)))) (cbrt.f64 (.f64 a (*.f64 x x)))))

series675.0ms (1.5%)

Counts

4 → 24

Calls

4 calls:

207.0ms	(cbrt.f64 (.f64 a (.f64 x x)))
206.0ms	(cbrt.f64 (.f64 a (.f64 x x)))
200.0ms	(cbrt.f64 (.f64 a (.f64 x x)))
62.0ms	(.f64 a (.f64 x x))

Compiler

Compiled 1746 to 1218 computations (30.2% saved)

simplify95.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5036	665

prune8.7s (19.8%)

Pruning

328 alts after pruning (314 fresh and 14 done)

	Pruned	Kept	Total
New	235	114	349
Fresh	7	200	207
Picked	0	0	0
Done	1	14	15
Total	243	328	571

Error

Counts

571 → 328

Compiler

Compiled 7312 to 3476 computations (52.5% saved)

simplify335.0ms (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5188	22895

regimes4.6s (10.3%)

Compiler: Compiled 44858 to 28806 computations (35.8% saved)

bsearch18.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

regimes1.0s (2.3%)

Compiler: Compiled 7879 to 5695 computations (27.7% saved)

bsearch4.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

regimes315.0ms (0.7%)

Compiler: Compiled 1999 to 1475 computations (26.2% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

regimes242.0ms (0.5%)

Compiler: Compiled 1503 to 1075 computations (28.5% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

regimes186.0ms (0.4%)

Compiler: Compiled 1039 to 713 computations (31.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

regimes35.0ms (0.1%)

Compiler: Compiled 10 to 26 computations (-160% saved)

bsearch46.0ms (0.1%)

Steps

Iters	Range		Point
6	2.1920135586149017e-33	2.556511707207216e-32	4.347966906444705e-33
9	-1.1560771998352434e-99	-1.505180468261534e-105	-7.124667420801598e-100

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes15.0ms (0%)

Accuracy

Total 0.4b remaining (91.5%)

Threshold costs 0.4b (91.5%)

Compiler

Compiled 8 to 20 computations (-150% saved)

bsearch7.0ms (0%)

Compiler: Compiled 127 to 83 computations (34.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	186
1	54	186

end0.0ms (0%)

sample9.7s (21.9%)

Algorithm

1×

intervals

Results

441.0ms	1517×	body	2048	valid
258.0ms	1776×	body	1024	valid
87.0ms	1075×	body	512	valid
77.0ms	3040×	body	128	valid
30.0ms	592×	body	256	valid
4.0ms	141×	body	128	invalid

Compiler

Compiled 11462 to 7357 computations (35.8% saved)

Pareto

0.7521602798874752