Details

analyze9.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 106 to 71 computations (33% saved)

sample72.0ms (0.8%)

Algorithm

1×

intervals

Results

56.0ms	256×	body	128	valid
4.0ms	261×	pre	128	true
1.0ms	5×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify167.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5512	47

prune9.0ms (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: 2.5b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.5b	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)
2.3b	(exp.f64 (*.f64 x x))

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`times-frac_binary64_1789`
86×	`*-un-lft-identity_binary64_1783`
83×	`add-sqr-sqrt_binary64_1805`
82×	`add-cube-cbrt_binary64_1818`
39×	`sqrt-prod_binary64_1799`
26×	`associate-/l*_binary64_1728`
14×	`add-cbrt-cube_binary64_1819`
13×	`add-exp-log_binary64_1821`
6×	`div-inv_binary64_1780` `add-log-exp_binary64_1822`
5×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `pow1_binary64_1844`
4×	`associate-/r*_binary64_1727`
3×	`associate-/l/_binary64_1730`
2×	`distribute-lft-out_binary64_1734` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`rem-exp-log_binary64_1823` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `pow1/2_binary64_1863` `exp-to-pow_binary64_1845` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `exp-prod_binary64_1835`

Counts

4 → 154

Calls

4 calls:

10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
10.0ms	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

series137.0ms (1.5%)

Counts

4 → 10

Calls

4 calls:

76.0ms	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))
52.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
8.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify95.0ms (1%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4979	4396
1	4979	4396

prune371.0ms (4%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	136	28	164
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	138	28	166

Merged error: 0.3b

Counts

166 → 28

Compiler

Compiled 7821 to 3462 computations (55.7% saved)

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 PI.f64)
1.0b	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
1.0b	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
1.0b	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1805`
28×	`pow1_binary64_1844`
22×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
19×	`cbrt-prod_binary64_1814` `pow1/3_binary64_1865`
18×	`sqrt-pow1_binary64_1801`
12×	`times-frac_binary64_1789`
11×	`pow-flip_binary64_1857`
10×	`add-exp-log_binary64_1821`
6×	`add-cbrt-cube_binary64_1819` `swap-sqr_binary64_1750` `pow-prod-up_binary64_1853` `associate-l_binary64_1724` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854` `associate-r_binary64_1723`
5×	`sqrt-prod_binary64_1799`
4×	`associate-/r*_binary64_1727` `unswap-sqr_binary64_1751` `add-log-exp_binary64_1822`
3×	`associate-/l*_binary64_1728` `pow-plus_binary64_1846` `pow2_binary64_1864`
2×	`pow1/2_binary64_1863` `div-exp_binary64_1834`
1×	`inv-pow_binary64_1868` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `1-exp_binary64_1827` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `rec-exp_binary64_1833`

Counts

4 → 115

Calls

4 calls:

8.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
7.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
4.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
1.0ms	(cbrt.f64 PI.f64)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
0.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
0.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
0.0ms	(cbrt.f64 PI.f64)

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4949	1284
1	4949	1284

prune248.0ms (2.7%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	7	20	27
Picked	1	0	1
Done	0	0	0
Total	124	23	147

Merged error: 0.2b

Counts

147 → 23

Compiler

Compiled 6057 to 2878 computations (52.5% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (pow.f64 (exp.f64 x) x) (/.f64 (/.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))) (fabs.f64 (cbrt.f64 PI.f64))) (.f64 (sqrt.f64 (cbrt.f64 PI.f64)) (fabs.f64 x))))
1.0b	(pow.f64 (exp.f64 x) x)
1.0b	(cbrt.f64 PI.f64)
1.0b	(cbrt.f64 PI.f64)

rewrite60.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-exp-log_binary64_1821`
36×	`*-un-lft-identity_binary64_1783`
34×	`times-frac_binary64_1789`
26×	`add-sqr-sqrt_binary64_1805`
23×	`associate-r_binary64_1723`
22×	`add-cbrt-cube_binary64_1819`
21×	`add-cube-cbrt_binary64_1818` `prod-exp_binary64_1832`
18×	`div-exp_binary64_1834`
9×	`distribute-lft-out_binary64_1734`
7×	`cbrt-unprod_binary64_1816` `unpow-prod-down_binary64_1862` `associate-l_binary64_1724`
6×	`cbrt-prod_binary64_1814` `cbrt-undiv_binary64_1817` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
5×	`pow1_binary64_1844`
4×	`pow-pow_binary64_1855` `add-log-exp_binary64_1822`
3×	`sqr-pow_binary64_1755` `pow-unpow_binary64_1860` `unswap-sqr_binary64_1751` `exp-prod_binary64_1835`
2×	`div-inv_binary64_1780` `pow1/3_binary64_1865`
1×	`associate-r/_binary64_1725` `-commutative_binary64_1714`

Counts

4 → 104

Calls

4 calls:

40.0ms	(.f64 (pow.f64 (exp.f64 x) x) (/.f64 (/.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))) (fabs.f64 (cbrt.f64 PI.f64))) (.f64 (sqrt.f64 (cbrt.f64 PI.f64)) (fabs.f64 x))))
3.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(cbrt.f64 PI.f64)
1.0ms	(cbrt.f64 PI.f64)

series200.0ms (2.2%)

Counts

4 → 8

Calls

4 calls:

177.0ms	(.f64 (pow.f64 (exp.f64 x) x) (/.f64 (/.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))) (fabs.f64 (cbrt.f64 PI.f64))) (.f64 (sqrt.f64 (cbrt.f64 PI.f64)) (fabs.f64 x))))
22.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(cbrt.f64 PI.f64)
0.0ms	(cbrt.f64 PI.f64)

simplify88.0ms (1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5036	4242

prune270.0ms (2.9%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	104	8	112
Fresh	6	16	22
Picked	1	0	1
Done	0	0	0
Total	111	24	135

Merged error: 0.1b

Counts

135 → 24

Compiler

Compiled 6265 to 3081 computations (50.8% saved)

localize37.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 PI.f64)
1.0b	(cbrt.f64 PI.f64)
1.0b	(cbrt.f64 PI.f64)
1.0b	(cbrt.f64 PI.f64)

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64_1814`
8×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `pow1/3_binary64_1865` `add-log-exp_binary64_1822` `pow1_binary64_1844`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt.f64 PI.f64)
1.0ms	(cbrt.f64 PI.f64)
1.0ms	(cbrt.f64 PI.f64)
1.0ms	(cbrt.f64 PI.f64)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(cbrt.f64 PI.f64)
0.0ms	(cbrt.f64 PI.f64)
0.0ms	(cbrt.f64 PI.f64)
0.0ms	(cbrt.f64 PI.f64)

simplify88.0ms (1%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4814	828
1	4814	828

prune150.0ms (1.6%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	23	23
Picked	0	1	1
Done	0	0	0
Total	48	24	72

Merged error: 0.1b

Counts

72 → 24

Compiler

Compiled 3852 to 1973 computations (48.8% saved)

regimes1.1s (11.8%)

Compiler: Compiled 16403 to 10395 computations (36.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	136
1	44	136

end0.0ms (0%)

sample5.9s (63.8%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
113.0ms	8120×	pre	128	true
24.0ms	120×	body	128	invalid

Compiler

Compiled 5585 to 3539 computations (36.6% saved)

Details

analyze9.0ms (0.1%)

sample72.0ms (0.8%)

simplify167.0ms (1.8%)

prune9.0ms (0.1%)

localize19.0ms (0.2%)

rewrite43.0ms (0.5%)

series137.0ms (1.5%)

simplify95.0ms (1%)

prune371.0ms (4%)

localize34.0ms (0.4%)

rewrite35.0ms (0.4%)

series0.0ms (0%)

simplify64.0ms (0.7%)

prune248.0ms (2.7%)

localize29.0ms (0.3%)

rewrite60.0ms (0.7%)

series200.0ms (2.2%)

simplify88.0ms (1%)

prune270.0ms (2.9%)

localize37.0ms (0.4%)

rewrite13.0ms (0.1%)

series0.0ms (0%)

simplify88.0ms (1%)

prune150.0ms (1.6%)

regimes1.1s (11.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.9s (63.8%)

Profiling