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)

sample17.0ms (0.7%)

Algorithm

1×

intervals

Results

5.0ms	60×	body	512	valid
4.0ms	144×	body	128	valid
2.0ms	40×	body	256	valid
1.0ms	12×	body	1024	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify105.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

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: 12.8b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
2.1b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

rewrite57.0ms (2.2%)

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:

33.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
6.0ms	(/.f64 1 (-.f64 x 1))
5.0ms	(/.f64 1 (+.f64 x 1))

series54.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

36.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
10.0ms	(/.f64 1 (-.f64 x 1))
9.0ms	(/.f64 1 (+.f64 x 1))

simplify109.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4814	2407
1	4814	2407

prune166.0ms (6.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.1b

Counts

161 → 1

Compiler

Compiled 2679 to 2187 computations (18.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `times-frac_binary64_2130` `*-un-lft-identity_binary64_2124`
3×	`associate-/l_binary64_2069` `associate-/r_binary64_2068` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
2×	`associate-/r/_binary64_2070`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `pow1_binary64_2185` `add-log-exp_binary64_2163` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

1 → 29

Calls

1 calls:

5.0ms

(/.f64 -2 (+.f64 -1 (*.f64 x x)))

series21.0ms (0.8%)

Counts

1 → 3

Calls

1 calls:

21.0ms

(/.f64 -2 (+.f64 -1 (*.f64 x x)))

simplify82.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5511	557

prune34.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	3	33

Merged error: 0.1b

Counts

33 → 3

Compiler

Compiled 493 to 336 computations (31.8% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.1b	(/.f64 -2 (-.f64 1 (pow.f64 x 4)))
24.7b	(.f64 (/.f64 -2 (-.f64 1 (pow.f64 x 4))) (-.f64 -1 (.f64 x x)))

rewrite38.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`add-sqr-sqrt_binary64_2146`
67×	`*-un-lft-identity_binary64_2124`
61×	`times-frac_binary64_2130`
43×	`difference-of-squares_binary64_2093`
36×	`associate-l_binary64_2065`
32×	`add-cube-cbrt_binary64_2159`
14×	`unpow-prod-down_binary64_2203` `sqr-pow_binary64_2096`
10×	`associate-/r*_binary64_2068`
9×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
7×	`distribute-lft-out--_binary64_2076`
4×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `pow1_binary64_2185` `associate-r_binary64_2064`
3×	`associate-/l*_binary64_2069`
2×	`cbrt-undiv_binary64_2158` `cancel-sign-sub-inv_binary64_2090` `unswap-sqr_binary64_2092` `add-log-exp_binary64_2163` `prod-exp_binary64_2173` `distribute-rgt-in_binary64_2074` `sub-neg_binary64_2117` `associate-*r/_binary64_2066` `frac-times_binary64_2134` `div-inv_binary64_2121` `div-exp_binary64_2175` `distribute-lft-in_binary64_2073` `cbrt-unprod_binary64_2157`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `-commutative_binary64_2055` `associate-l/_binary64_2067` `frac-2neg_binary64_2135`

Counts

2 → 121

Calls

2 calls:

18.0ms	(.f64 (/.f64 -2 (-.f64 1 (pow.f64 x 4))) (-.f64 -1 (.f64 x x)))
8.0ms	(/.f64 -2 (-.f64 1 (pow.f64 x 4)))

series86.0ms (3.3%)

Counts

2 → 6

Calls

2 calls:

53.0ms	(/.f64 -2 (-.f64 1 (pow.f64 x 4)))
33.0ms	(.f64 (/.f64 -2 (-.f64 1 (pow.f64 x 4))) (-.f64 -1 (.f64 x x)))

simplify76.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4900	2590
1	4900	2590

prune155.0ms (5.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	127	3	130

Merged error: 0.1b

Counts

130 → 3

Compiler

Compiled 2775 to 2053 computations (26% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 -2 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
0.1b	(/.f64 (/.f64 -2 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (sqrt.f64 (+.f64 -1 (.f64 x x))))
16.8b	(sqrt.f64 (+.f64 -1 (*.f64 x x)))
16.8b	(sqrt.f64 (+.f64 -1 (*.f64 x x)))

rewrite63.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64_2130`
164×	`add-sqr-sqrt_binary64_2146`
162×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
156×	`sqrt-prod_binary64_2140`
27×	`associate-/l*_binary64_2069`
22×	`sqrt-div_binary64_2141`
18×	`associate-/r/_binary64_2070`
12×	`associate-/r*_binary64_2068`
11×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`div-inv_binary64_2121`
6×	`pow1_binary64_2185`
4×	`cbrt-undiv_binary64_2158` `add-log-exp_binary64_2163` `div-exp_binary64_2175`
2×	`clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `frac-2neg_binary64_2135`
1×	`associate-/l/_binary64_2071`

Counts

4 → 262

Calls

4 calls:

19.0ms	(/.f64 (/.f64 -2 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (sqrt.f64 (+.f64 -1 (.f64 x x))))
6.0ms	(/.f64 -2 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
3.0ms	(sqrt.f64 (+.f64 -1 (*.f64 x x)))
3.0ms	(sqrt.f64 (+.f64 -1 (*.f64 x x)))

series98.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(/.f64 -2 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
22.0ms	(sqrt.f64 (+.f64 -1 (*.f64 x x)))
21.0ms	(/.f64 (/.f64 -2 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (sqrt.f64 (+.f64 -1 (.f64 x x))))
21.0ms	(sqrt.f64 (+.f64 -1 (*.f64 x x)))

simplify159.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5558	8590

prune462.0ms (17.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	273	1	274
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	273	4	277

Merged error: 0.1b

Counts

277 → 4

Compiler

Compiled 6886 to 4702 computations (31.7% saved)

regimes48.0ms (1.8%)

Compiler: Compiled 510 to 400 computations (21.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	10
1	8	10

end0.0ms (0%)

sample757.0ms (28.8%)

Algorithm

1×

intervals

Results

162.0ms	1964×	body	512	valid
133.0ms	4614×	body	128	valid
61.0ms	1049×	body	256	valid
39.0ms	373×	body	1024	valid

Compiler

Compiled 262 to 207 computations (21% saved)

Details

analyze4.0ms (0.1%)

sample17.0ms (0.7%)

simplify105.0ms (4%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

rewrite57.0ms (2.2%)

series54.0ms (2.1%)

simplify109.0ms (4.1%)

prune166.0ms (6.3%)

localize4.0ms (0.2%)

rewrite6.0ms (0.2%)

series21.0ms (0.8%)

simplify82.0ms (3.1%)

prune34.0ms (1.3%)

localize8.0ms (0.3%)

rewrite38.0ms (1.5%)

series86.0ms (3.3%)

simplify76.0ms (2.9%)

prune155.0ms (5.9%)

localize7.0ms (0.3%)

rewrite63.0ms (2.4%)

series98.0ms (3.7%)

simplify159.0ms (6.1%)

prune462.0ms (17.6%)

regimes48.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample757.0ms (28.8%)

Profiling