Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample19.0ms (0.5%)

Algorithm

1×

intervals

Results

6.0ms	71×	body	512	valid
4.0ms	133×	body	128	valid
2.0ms	34×	body	256	valid
2.0ms	18×	body	1024	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify176.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	76	16
1	76	16

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 16.7b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
3.2b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

rewrite68.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64_2124`
95×	`add-sqr-sqrt_binary64_2146`
90×	`times-frac_binary64_2130`
43×	`add-cube-cbrt_binary64_2159`
30×	`distribute-lft-out--_binary64_2076`
27×	`cancel-sign-sub-inv_binary64_2090`
23×	`difference-of-squares_binary64_2093`
11×	`associate-/r*_binary64_2068` `add-exp-log_binary64_2162`
10×	`distribute-lft-out_binary64_2075`
8×	`associate-/r/_binary64_2070`
7×	`difference-of-sqr-1_binary64_2094` `div-inv_binary64_2121` `add-cbrt-cube_binary64_2160`
6×	`associate-/l*_binary64_2069`
5×	`pow1_binary64_2185` `add-log-exp_binary64_2163`
4×	`flip--_binary64_2099` `div-exp_binary64_2175`
3×	`flip3--_binary64_2128`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `pow-flip_binary64_2198` `flip-+_binary64_2098` `1-exp_binary64_2168` `inv-pow_binary64_2209` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`
1×	`diff-log_binary64_2216` `sub-neg_binary64_2117` `frac-sub_binary64_2133` `flip3-+_binary64_2127`

Counts

3 → 151

Calls

3 calls:

41.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
7.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))

series108.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

71.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
18.0ms	(/.f64 1 (-.f64 x 1))
18.0ms	(/.f64 1 (+.f64 x 1))

simplify81.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5421	2407

prune169.0ms (4.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	2	161

Merged error: 0.6b

Counts

161 → 2

Compiler

Compiled 2697 to 2204 computations (18.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 (/.f64 1 (-.f64 (.f64 x x) (*.f64 1 1))) -2)
0.6b	(/.f64 1 (-.f64 (.f64 x x) (.f64 1 1)))

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_2146`
26×	`times-frac_binary64_2130`
21×	`*-un-lft-identity_binary64_2124`
20×	`add-cube-cbrt_binary64_2159`
18×	`associate-l_binary64_2065`
15×	`add-exp-log_binary64_2162`
9×	`add-cbrt-cube_binary64_2160`
7×	`difference-of-squares_binary64_2093`
5×	`pow1_binary64_2185`
4×	`associate-/r/_binary64_2070` `associate-/r*_binary64_2068` `prod-exp_binary64_2173` `div-exp_binary64_2175`
3×	`unswap-sqr_binary64_2092` `associate-/l_binary64_2069` `associate-r*_binary64_2064`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `add-log-exp_binary64_2163` `1-exp_binary64_2168` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157` `rec-exp_binary64_2174`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `-commutative_binary64_2055` `associate-l/_binary64_2067` `pow-flip_binary64_2198` `inv-pow_binary64_2209` `frac-2neg_binary64_2135`

Counts

2 → 77

Calls

2 calls:

14.0ms	(.f64 (/.f64 1 (-.f64 (.f64 x x) (*.f64 1 1))) -2)
7.0ms	(/.f64 1 (-.f64 (.f64 x x) (.f64 1 1)))

series78.0ms (2.1%)

Counts

2 → 6

Calls

2 calls:

40.0ms	(.f64 (/.f64 1 (-.f64 (.f64 x x) (*.f64 1 1))) -2)
38.0ms	(/.f64 1 (-.f64 (.f64 x x) (.f64 1 1)))

simplify61.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5075	1208

prune90.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	79	6	85

Merged error: 0.0b

Counts

85 → 6

Compiler

Compiled 1384 to 1005 computations (27.4% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (/.f64 (/.f64 1 (+.f64 1 x)) (-.f64 x 1)) -2)
0.0b	(/.f64 1 (+.f64 1 x))
0.1b	(/.f64 (/.f64 1 (+.f64 1 x)) (-.f64 x 1))

rewrite107.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

449×	`times-frac_binary64_2130`
381×	`*-un-lft-identity_binary64_2124`
331×	`add-sqr-sqrt_binary64_2146`
171×	`add-cube-cbrt_binary64_2159`
132×	`associate-l_binary64_2065`
74×	`difference-of-squares_binary64_2093`
49×	`distribute-lft-out_binary64_2075`
37×	`distribute-lft-out--_binary64_2076` `difference-of-sqr-1_binary64_2094`
36×	`associate-/r/_binary64_2070`
31×	`add-exp-log_binary64_2162`
21×	`associate-/l*_binary64_2069`
19×	`add-cbrt-cube_binary64_2160`
18×	`div-inv_binary64_2121`
16×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
14×	`div-exp_binary64_2175`
11×	`associate-/r*_binary64_2068`
7×	`cbrt-undiv_binary64_2158`
6×	`pow1_binary64_2185`
5×	`prod-exp_binary64_2173`
4×	`unswap-sqr_binary64_2092`
3×	`add-log-exp_binary64_2163` `associate-r_binary64_2064` `1-exp_binary64_2168` `cbrt-unprod_binary64_2157` `rec-exp_binary64_2174`
2×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `frac-2neg_binary64_2135`
1×	`pow-prod-down_binary64_2195` `-commutative_binary64_2055` `associate-l/_binary64_2067` `pow-flip_binary64_2198` `associate-/l/_binary64_2071` `inv-pow_binary64_2209`

Counts

3 → 364

Calls

3 calls:

39.0ms	(*.f64 (/.f64 (/.f64 1 (+.f64 1 x)) (-.f64 x 1)) -2)
15.0ms	(/.f64 (/.f64 1 (+.f64 1 x)) (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 1 x))

series122.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

53.0ms	(*.f64 (/.f64 (/.f64 1 (+.f64 1 x)) (-.f64 x 1)) -2)
52.0ms	(/.f64 (/.f64 1 (+.f64 1 x)) (-.f64 x 1))
16.0ms	(/.f64 1 (+.f64 1 x))

simplify114.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

373 → 373

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4943	7646
1	4943	7646

prune594.0ms (16%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	371	2	373
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	373	6	379

Merged error: 0.0b

Counts

379 → 6

Compiler

Compiled 7947 to 6277 computations (21% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 -2 (+.f64 1 x))
0.1b	(/.f64 (/.f64 -2 (+.f64 1 x)) (-.f64 x 1))

rewrite43.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64_2130`
207×	`*-un-lft-identity_binary64_2124`
170×	`add-sqr-sqrt_binary64_2146`
94×	`add-cube-cbrt_binary64_2159`
38×	`difference-of-squares_binary64_2093`
28×	`distribute-lft-out_binary64_2075`
21×	`associate-/l*_binary64_2069`
20×	`associate-/r/_binary64_2070`
19×	`distribute-lft-out--_binary64_2076` `difference-of-sqr-1_binary64_2094`
11×	`associate-/r*_binary64_2068`
10×	`div-inv_binary64_2121`
9×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
4×	`cbrt-undiv_binary64_2158` `div-exp_binary64_2175`
2×	`clear-num_binary64_2123` `pow1_binary64_2185` `add-log-exp_binary64_2163` `frac-2neg_binary64_2135`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/l/_binary64_2071`

Counts

2 → 201

Calls

2 calls:

14.0ms	(/.f64 (/.f64 -2 (+.f64 1 x)) (-.f64 x 1))
5.0ms	(/.f64 -2 (+.f64 1 x))

series76.0ms (2%)

Counts

2 → 6

Calls

2 calls:

53.0ms	(/.f64 (/.f64 -2 (+.f64 1 x)) (-.f64 x 1))
22.0ms	(/.f64 -2 (+.f64 1 x))

simplify99.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4928	5115
1	4928	5115

prune248.0ms (6.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	207	6	213

Merged error: 0.0b

Counts

213 → 6

Compiler

Compiled 3931 to 3051 computations (22.4% saved)

regimes292.0ms (7.8%)

Compiler: Compiled 1144 to 974 computations (14.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	13
1	19	13

end0.0ms (0%)

sample1.1s (29.9%)

Algorithm

1×

intervals

Results

169.0ms	2052×	body	512	valid
143.0ms	4516×	body	128	valid
58.0ms	998×	body	256	valid
47.0ms	434×	body	1024	valid

Compiler

Compiled 581 to 496 computations (14.6% saved)

Details

analyze4.0ms (0.1%)

sample19.0ms (0.5%)

simplify176.0ms (4.7%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

rewrite68.0ms (1.8%)

series108.0ms (2.9%)

simplify81.0ms (2.2%)

prune169.0ms (4.5%)

localize6.0ms (0.2%)

rewrite27.0ms (0.7%)

series78.0ms (2.1%)

simplify61.0ms (1.6%)

prune90.0ms (2.4%)

localize6.0ms (0.2%)

rewrite107.0ms (2.9%)

series122.0ms (3.3%)

simplify114.0ms (3.1%)

prune594.0ms (16%)

localize5.0ms (0.1%)

rewrite43.0ms (1.1%)

series76.0ms (2%)

simplify99.0ms (2.7%)

prune248.0ms (6.7%)

regimes292.0ms (7.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (29.9%)

Profiling