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)

sample20.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms	72×	body	512	valid
5.0ms	139×	body	128	valid
2.0ms	35×	body	256	valid
1.0ms	10×	body	1024	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify102.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	76	16
1	76	16

prune2.0ms (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

Error

15.3b

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))
3.9b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

rewrite64.0ms (2.1%)

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:

39.0ms	(-.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))

series50.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
9.0ms	(/.f64 1 (-.f64 x 1))
9.0ms	(/.f64 1 (+.f64 x 1))

simplify104.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4814	2407
1	4814	2407

prune162.0ms (5.3%)

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

Error

0.4b

Counts

161 → 2

Compiler

Compiled 2698 to 2202 computations (18.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.4b	(/.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)))

series22.0ms (0.7%)

Counts

1 → 3

Calls

1 calls:

22.0ms

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

simplify75.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5511	557

prune31.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	31	3	34

Error

0.4b

Counts

34 → 3

Compiler

Compiled 505 to 342 computations (32.3% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 -1 (*.f64 x x)))
0.0b	(/.f64 -2 (+.f64 -1 (pow.f64 x 6)))
0.1b	(.f64 (.f64 x x) (*.f64 x x))
26.4b	(.f64 (/.f64 -2 (+.f64 -1 (pow.f64 x 6))) (+.f64 (.f64 -1 -1) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 -1 (*.f64 x x)))))

rewrite68.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

117×	`pow1_binary64_2185`
36×	`pow-prod-up_binary64_2194` `*-un-lft-identity_binary64_2124`
27×	`add-sqr-sqrt_binary64_2146`
25×	`times-frac_binary64_2130`
24×	`pow-prod-down_binary64_2195`
23×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
22×	`add-cube-cbrt_binary64_2159` `pow-sqr_binary64_2097`
19×	`associate-l_binary64_2065`
18×	`pow-plus_binary64_2187`
13×	`pow2_binary64_2205`
10×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
7×	`distribute-lft-out_binary64_2075`
6×	`add-log-exp_binary64_2163`
4×	`associate-/r/_binary64_2070` `associate-/r_binary64_2068` `flip3-+_binary64_2127` `associate-r*_binary64_2064` `flip-+_binary64_2098`
3×	`unswap-sqr_binary64_2092` `associate-/l*_binary64_2069`
2×	`cbrt-undiv_binary64_2158` `-commutative_binary64_2055` `associate-r/_binary64_2066` `frac-times_binary64_2134` `div-inv_binary64_2121` `div-exp_binary64_2175`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `swap-sqr_binary64_2091` `diff-log_binary64_2216` `associate-*l/_binary64_2067` `distribute-rgt-out--_binary64_2078` `distribute-rgt-in_binary64_2074` `sub-neg_binary64_2117` `distribute-lft-in_binary64_2073` `frac-2neg_binary64_2135`

Counts

4 → 152

Calls

4 calls:

25.0ms	(.f64 (/.f64 -2 (+.f64 -1 (pow.f64 x 6))) (+.f64 (.f64 -1 -1) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 -1 (*.f64 x x)))))
10.0ms	(-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 -1 (*.f64 x x)))
9.0ms	(.f64 (.f64 x x) (*.f64 x x))
7.0ms	(/.f64 -2 (+.f64 -1 (pow.f64 x 6)))

series234.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(/.f64 -2 (+.f64 -1 (pow.f64 x 6)))
53.0ms	(-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 -1 (*.f64 x x)))
42.0ms	(.f64 (/.f64 -2 (+.f64 -1 (pow.f64 x 6))) (+.f64 (.f64 -1 -1) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 -1 (*.f64 x x)))))
26.0ms	(.f64 (.f64 x x) (*.f64 x x))

simplify84.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5067	2353

prune235.0ms (7.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	164	3	167

Error

0.4b

Counts

167 → 3

Compiler

Compiled 4368 to 3040 computations (30.4% saved)

localize6.0ms (0.2%)

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))))
15.9b	(sqrt.f64 (+.f64 -1 (*.f64 x x)))
15.9b	(sqrt.f64 (+.f64 -1 (*.f64 x x)))

rewrite62.0ms (2%)

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:

15.0ms	(/.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 (3.2%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(/.f64 -2 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
22.0ms	(/.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)))
21.0ms	(sqrt.f64 (+.f64 -1 (*.f64 x x)))

simplify148.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5558	8590

prune614.0ms (20%)

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

Error

0.4b

Counts

277 → 4

Compiler

Compiled 6886 to 4702 computations (31.7% saved)

regimes53.0ms (1.7%)

Accuracy

Total 0.1b remaining (14.9%)

Threshold costs 0.1b (14.9%)

Compiler

Compiled 628 to 494 computations (21.3% 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%)

sample805.0ms (26.2%)

Algorithm

1×

intervals

Results

162.0ms	2002×	body	512	valid
135.0ms	4598×	body	128	valid
54.0ms	989×	body	256	valid
44.0ms	411×	body	1024	valid

Compiler

Compiled 321 to 254 computations (20.9% saved)

Details

analyze4.0ms (0.1%)

sample20.0ms (0.6%)

simplify102.0ms (3.3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite64.0ms (2.1%)

series50.0ms (1.6%)

simplify104.0ms (3.4%)

prune162.0ms (5.3%)

localize4.0ms (0.1%)

rewrite6.0ms (0.2%)

series22.0ms (0.7%)

simplify75.0ms (2.5%)

prune31.0ms (1%)

localize12.0ms (0.4%)

rewrite68.0ms (2.2%)

series234.0ms (7.6%)

simplify84.0ms (2.7%)

prune235.0ms (7.6%)

localize6.0ms (0.2%)

rewrite62.0ms (2%)

series98.0ms (3.2%)

simplify148.0ms (4.8%)

prune614.0ms (20%)

regimes53.0ms (1.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample805.0ms (26.2%)

Profiling