Details

analyze45.0ms (1.4%)

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%	74.9%	25.1%	4
18.7%	56.2%	25.1%	5
28.1%	34.3%	37.6%	6
34.3%	28.1%	37.6%	7
39%	17.2%	43.8%	8
41%	13.7%	45.4%	9
43.1%	8.4%	48.5%	10
44%	6.7%	49.3%	11
45%	4.1%	50.8%	12
45.4%	3.3%	51.2%	13
45.9%	2.1%	52%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample19.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
0.0ms	4×	body	128	nan
0.0ms	3×	body	128	invalid

Compiler

Compiled 17 to 17 computations (0% saved)

simplify166.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	188	12
1	188	12

prune2.0ms (0.1%)

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

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
0.2b	(*.f64 y (sqrt.f64 x))

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1821`
7×	`add-log-exp_binary64_1838`
6×	`add-cube-cbrt_binary64_1834` `-un-lft-identity_binary64_1799` `associate-r*_binary64_1739`
4×	`pow1_binary64_1860` `sqrt-prod_binary64_1815` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837` `associate-+l+_binary64_1732`
3×	`associate-l_binary64_1740` `cancel-sign-sub-inv_binary64_1765`
2×	`sum-log_binary64_1890` `unswap-sqr_binary64_1767`
1×	`sub-neg_binary64_1792` `+-commutative_binary64_1729` `prod-exp_binary64_1848` `diff-log_binary64_1891` `cbrt-unprod_binary64_1832` `*-commutative_binary64_1730` `pow-prod-down_binary64_1870` `flip3-+_binary64_1802` `associate-+l-_binary64_1734` `flip-+_binary64_1773`

Counts

2 → 39

Calls

2 calls:

11.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
6.0ms	(*.f64 y (sqrt.f64 x))

series99.0ms (3.1%)

Counts

2 → 6

Calls

2 calls:

56.0ms	(*.f64 y (sqrt.f64 x))
43.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

simplify52.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5082	594

prune82.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	5	46

Merged error: 0.0b

Counts

46 → 5

Compiler

Compiled 1293 to 757 computations (41.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 x))
0.1b	(sqrt.f64 (sqrt.f64 x))
0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

rewrite30.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod_binary64_1815`
25×	`add-sqr-sqrt_binary64_1821`
18×	`associate-r_binary64_1739`
15×	`pow1_binary64_1860` `add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
11×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
8×	`sqrt-pow1_binary64_1817`
4×	`add-log-exp_binary64_1838` `prod-exp_binary64_1848` `associate-l_binary64_1740` `pow1/2_binary64_1879` `cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870` `rem-sqrt-square_binary64_1812`
3×	`unswap-sqr_binary64_1767`
2×	`*-commutative_binary64_1730`

Counts

4 → 88

Calls

4 calls:

11.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
7.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
2.0ms	(sqrt.f64 (sqrt.f64 x))
2.0ms	(sqrt.f64 (sqrt.f64 x))

series343.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(sqrt.f64 (sqrt.f64 x))
96.0ms	(sqrt.f64 (sqrt.f64 x))
86.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
59.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

simplify66.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5316	1029

prune103.0ms (3.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	99	6	105

Merged error: 0b

Counts

105 → 6

Compiler

Compiled 2058 to 884 computations (57% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (*.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 x)))
0.3b	(.f64 (.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x))))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite38.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-prod_binary64_1815`
21×	`associate-r_binary64_1739`
18×	`pow1_binary64_1860` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
13×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
9×	`prod-exp_binary64_1848` `cbrt-prod_binary64_1830` `cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870`
4×	`add-log-exp_binary64_1838`
2×	`pow1/3_binary64_1881` `associate-l_binary64_1740` `*-commutative_binary64_1730`

Counts

4 → 76

Calls

4 calls:

15.0ms	(.f64 (.f64 (*.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 x)))
12.0ms	(.f64 (.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x))))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series746.0ms (23.3%)

Counts

4 → 12

Calls

4 calls:

243.0ms	(.f64 (.f64 (*.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 x)))
191.0ms	(.f64 (.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x))))
162.0ms	(cbrt.f64 x)
150.0ms	(cbrt.f64 x)

simplify71.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5097	1631

prune88.0ms (2.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	88	6	94

Merged error: 0b

Counts

94 → 6

Compiler

Compiled 2121 to 681 computations (67.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 y (fabs.f64 (cbrt.f64 x)))
0.3b	(.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1821`
12×	`associate-r_binary64_1739`
11×	`pow1_binary64_1860` `add-cube-cbrt_binary64_1834` `add-cbrt-cube_binary64_1835` `*-un-lft-identity_binary64_1799` `add-exp-log_binary64_1837`
9×	`cbrt-prod_binary64_1830`
6×	`sqrt-prod_binary64_1815`
4×	`add-log-exp_binary64_1838` `prod-exp_binary64_1848` `associate-l_binary64_1740` `cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870`
2×	`pow1/3_binary64_1881` `*-commutative_binary64_1730`
1×	`unswap-sqr_binary64_1767`

Counts

4 → 64

Calls

4 calls:

8.0ms	(.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
4.0ms	(*.f64 y (fabs.f64 (cbrt.f64 x)))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series475.0ms (14.9%)

Counts

4 → 12

Calls

4 calls:

150.0ms	(.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
150.0ms	(cbrt.f64 x)
147.0ms	(cbrt.f64 x)
27.0ms	(*.f64 y (fabs.f64 (cbrt.f64 x)))

simplify59.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4961	847
1	4961	847

prune59.0ms (1.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	76	6	82

Merged error: 0b

Counts

82 → 6

Compiler

Compiled 1276 to 482 computations (62.2% saved)

regimes46.0ms (1.5%)

Compiler: Compiled 317 to 229 computations (27.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms (0%)

sample531.0ms (16.6%)

Algorithm

1×

intervals

Results

247.0ms	7998×	body	128	valid
4.0ms	145×	body	128	nan
2.0ms	64×	body	128	invalid
0.0ms	2×	body	1024	valid

Compiler

Compiled 116 to 86 computations (25.9% saved)

Details

analyze45.0ms (1.4%)

sample19.0ms (0.6%)

simplify166.0ms (5.2%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite20.0ms (0.6%)

series99.0ms (3.1%)

simplify52.0ms (1.6%)

prune82.0ms (2.6%)

localize8.0ms (0.2%)

rewrite30.0ms (0.9%)

series343.0ms (10.7%)

simplify66.0ms (2.1%)

prune103.0ms (3.2%)

localize14.0ms (0.4%)

rewrite38.0ms (1.2%)

series746.0ms (23.3%)

simplify71.0ms (2.2%)

prune88.0ms (2.7%)

localize9.0ms (0.3%)

rewrite19.0ms (0.6%)

series475.0ms (14.9%)

simplify59.0ms (1.8%)

prune59.0ms (1.8%)

regimes46.0ms (1.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample531.0ms (16.6%)

Profiling