Details

analyze276.0ms (5.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample66.0ms (1.3%)

Algorithm

1×

intervals

Results

29.0ms	86×	body	1024	valid
13.0ms	40×	body	2048	valid
9.0ms	44×	body	512	valid
3.0ms	68×	body	128	valid
2.0ms	4×	body	4096	valid
2.0ms	14×	body	256	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify96.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune2.0ms (0%)

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

Error

53.3b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.1%)

Local error

Found 6 expressions with local error:

14.4b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
1.1b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
0.5b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.5b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
1.1b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.4b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_2124`
6×	`add-sqr-sqrt_binary64_2146`
5×	`pow1_binary64_2185` `add-log-exp_binary64_2163` `add-cube-cbrt_binary64_2159`
4×	`log-prod_binary64_2210` `add-exp-log_binary64_2162`
3×	`sqrt-prod_binary64_2140` `flip3-+_binary64_2127` `flip-+_binary64_2098` `add-cbrt-cube_binary64_2160`
2×	`distribute-lft-out_binary64_2075` `sqrt-div_binary64_2141` `log-div_binary64_2211`
1×	`rem-log-exp_binary64_2165` `sum-log_binary64_2215` `sqrt-pow1_binary64_2142` `log-pow_binary64_2213` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `pow1/2_binary64_2204`

Counts

3 → 42

Calls

6 calls:

8.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))

series204.0ms (4.1%)

Counts

3 → 33

Calls

3 calls:

105.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
56.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
42.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 523 to 465 computations (11.1% saved)

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5201	1166

prune121.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	6	76

Error

0.0b

Counts

76 → 6

Compiler

Compiled 1065 to 713 computations (33.1% saved)

localize9.0ms (0.2%)

Local error

Found 8 expressions with local error:

21.2b	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 (pow.f64 x 5) 3/40))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
0.1b	(*.f64 (pow.f64 x 5) 3/40)
0.0b	(-.f64 x (*.f64 (pow.f64 x 3) 1/6))
0.0b	(-.f64 x (*.f64 (pow.f64 x 3) 1/6))
0.1b	(*.f64 (pow.f64 x 5) 3/40)
0.1b	(*.f64 (pow.f64 x 3) 1/6)
21.2b	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 (pow.f64 x 5) 3/40))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2146`
19×	`associate-l_binary64_2065`
14×	`add-exp-log_binary64_2162`
11×	`add-log-exp_binary64_2163` `add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
8×	`unpow-prod-down_binary64_2203` `add-cbrt-cube_binary64_2160`
7×	`unswap-sqr_binary64_2092`
6×	`prod-exp_binary64_2173` `associate-r_binary64_2064`
4×	`pow1_binary64_2185` `sqr-pow_binary64_2096` `cube-prod_binary64_2152`
2×	`cancel-sign-sub-inv_binary64_2090` `sum-log_binary64_2215` `pow-exp_binary64_2192` `*-commutative_binary64_2055` `diff-log_binary64_2216` `sub-neg_binary64_2117` `pow-to-exp_binary64_2193` `associate-+l+_binary64_2057` `cbrt-unprod_binary64_2157`
1×	`flip--_binary64_2099` `unpow3_binary64_2190` `flip3--_binary64_2128` `cube-mult_binary64_2154` `associate-+l-_binary64_2059` `+-commutative_binary64_2054` `flip3-+_binary64_2127` `flip-+_binary64_2098`

Counts

4 → 83

Calls

8 calls:

9.0ms	(*.f64 (pow.f64 x 3) 1/6)
7.0ms	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 (pow.f64 x 5) 3/40))
5.0ms	(*.f64 (pow.f64 x 5) 3/40)
3.0ms	(-.f64 x (*.f64 (pow.f64 x 3) 1/6))
0.0ms	(-.f64 x (*.f64 (pow.f64 x 3) 1/6))

series177.0ms (3.6%)

Counts

4 → 17

Calls

4 calls:

65.0ms	(-.f64 x (*.f64 (pow.f64 x 3) 1/6))
42.0ms	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 (pow.f64 x 5) 3/40))
39.0ms	(*.f64 (pow.f64 x 5) 3/40)
31.0ms	(*.f64 (pow.f64 x 3) 1/6)

Compiler

Compiled 329 to 283 computations (14% saved)

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4898	1252
1	4898	1252

prune107.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	100	6	106

Error

0.0b

Counts

106 → 6

Compiler

Compiled 1775 to 1376 computations (22.5% saved)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune4.0ms (0.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	1	1
Total	6	6

Error

0.0b

Counts

6 → 6

Compiler

Compiled 51 to 39 computations (23.5% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
0.0b	(+.f64 x (+.f64 x (/.f64 1/2 x)))
0.0b	(+.f64 x (+.f64 x (/.f64 1/2 x)))
0.0b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_2124`
7×	`add-log-exp_binary64_2163`
6×	`distribute-lft-out_binary64_2075`
5×	`log-prod_binary64_2210`
3×	`sum-log_binary64_2215` `pow1_binary64_2185` `add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `add-exp-log_binary64_2162`
2×	`flip3-+_binary64_2127` `log-div_binary64_2211` `flip-+_binary64_2098` `add-cbrt-cube_binary64_2160`
1×	`rem-log-exp_binary64_2165` `log-pow_binary64_2213` `associate-+r+_binary64_2056` `+-commutative_binary64_2054`

Counts

2 → 31

Calls

4 calls:

9.0ms	(+.f64 x (+.f64 x (/.f64 1/2 x)))
8.0ms	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
0.0ms	(+.f64 x (+.f64 x (/.f64 1/2 x)))
0.0ms	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))

series92.0ms (1.8%)

Counts

2 → 11

Calls

2 calls:

50.0ms	(+.f64 x (+.f64 x (/.f64 1/2 x)))
42.0ms	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))

Compiler

Compiled 172 to 159 computations (7.6% saved)

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4821	573
1	4821	573

prune31.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	43	5	48

Error

0.0b

Counts

48 → 5

Compiler

Compiled 487 to 329 computations (32.4% saved)

simplify21.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	436	520
1	436	520

regimes210.0ms (4.2%)

Compiler: Compiled 1219 to 957 computations (21.5% saved)

bsearch38.0ms (0.8%)

Steps

Iters	Range		Point
11	1.4915888139300387e-20	196.81541420403747	1.0253859810357775
7	-1.4434663788830187	-0.025454405799417566	-1.3299041834197318

Compiler

Compiled 1 to 1 computations (0% saved)

regimes31.0ms (0.6%)

Compiler: Compiled 45 to 42 computations (6.7% saved)

bsearch35.0ms (0.7%)

Steps

Iters	Range		Point
11	1.4915888139300387e-20	196.81541420403747	0.9589061090684858
7	-1.4434663788830187	-0.025454405799417566	-1.284479305234417

Compiler

Compiled 1 to 1 computations (0% saved)

regimes30.0ms (0.6%)

Compiler: Compiled 33 to 32 computations (3% saved)

bsearch34.0ms (0.7%)

Steps

Iters	Range		Point
11	1.4915888139300387e-20	196.81541420403747	0.9589061090684858
7	-1.4434663788830187	-0.025454405799417566	-1.284479305234417

Compiler

Compiled 1 to 1 computations (0% saved)

regimes27.0ms (0.5%)

Compiler: Compiled 25 to 26 computations (-4% saved)

bsearch33.0ms (0.7%)

Steps

Iters	Range		Point
11	1.4915888139300387e-20	196.81541420403747	1.2763914277996573
7	-1.4434663788830187	-0.025454405799417566	-1.284479305234417

Compiler

Compiled 1 to 1 computations (0% saved)

regimes26.0ms (0.5%)

Compiler: Compiled 18 to 20 computations (-11.1% saved)

bsearch33.0ms (0.7%)

Steps

Iters	Range		Point
11	1.4915888139300387e-20	196.81541420403747	1.2763914277996573
7	-1.4434663788830187	-0.025454405799417566	-1.2390544270491022

Compiler

Compiled 1 to 1 computations (0% saved)

regimes20.0ms (0.4%)

Compiler: Compiled 10 to 12 computations (-20% saved)

bsearch32.0ms (0.6%)

Steps

Iters	Range		Point
11	1.4915888139300387e-20	196.81541420403747	1.2763914277996573
7	-1.4434663788830187	-0.025454405799417566	-1.0119300361225283

Compiler

Compiled 1 to 1 computations (0% saved)

regimes18.0ms (0.4%)

Compiler: Compiled 6 to 9 computations (-50% saved)

bsearch32.0ms (0.6%)

Steps

Iters	Range		Point
11	1.4915888139300387e-20	196.81541420403747	0.9947640300347544
7	-1.4434663788830187	-0.025454405799417566	-1.0119300361225283

Compiler

Compiled 1 to 1 computations (0% saved)

regimes12.0ms (0.2%)

Compiler: Compiled 5 to 8 computations (-60% saved)

bsearch109.0ms (2.2%)

Steps

Iters	Range		Point
10	-4.255752956047238e-303	5.099660751536309e-297	-4.74488972669753e-310

Compiler

Compiled 1 to 1 computations (0% saved)

regimes13.0ms (0.3%)

Accuracy

Total 0.3b remaining (97.7%)

Threshold costs 0.3b (97.7%)

Compiler

Compiled 4 to 6 computations (-50% saved)

bsearch81.0ms (1.6%)

Steps

Iters	Range		Point
11	5.3451513721510883e-163	6.002843225207223e-138	1.1080017980008641e-154

Compiler

Compiled 176 to 135 computations (23.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	142	255
1	142	255

end0.0ms (0%)

sample2.7s (53.5%)

Algorithm

1×

intervals

Results

924.0ms	2538×	body	1024	valid
398.0ms	1233×	body	2048	valid
275.0ms	1296×	body	512	valid
111.0ms	2313×	body	128	valid
69.0ms	577×	body	256	valid
19.0ms	43×	body	4096	valid

Compiler

Compiled 544 to 423 computations (22.2% saved)

Pareto

0.4721674100812592

Details

analyze276.0ms (5.5%)

sample66.0ms (1.3%)

simplify96.0ms (1.9%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite23.0ms (0.5%)

series204.0ms (4.1%)

simplify70.0ms (1.4%)

prune121.0ms (2.4%)

localize9.0ms (0.2%)

rewrite31.0ms (0.6%)

series177.0ms (3.6%)

simplify54.0ms (1.1%)

prune107.0ms (2.1%)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.1%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

rewrite19.0ms (0.4%)

series92.0ms (1.8%)

simplify70.0ms (1.4%)

prune31.0ms (0.6%)

simplify21.0ms (0.4%)

regimes210.0ms (4.2%)

bsearch38.0ms (0.8%)

regimes31.0ms (0.6%)

bsearch35.0ms (0.7%)

regimes30.0ms (0.6%)

bsearch34.0ms (0.7%)

regimes27.0ms (0.5%)

bsearch33.0ms (0.7%)

regimes26.0ms (0.5%)

bsearch33.0ms (0.7%)

regimes20.0ms (0.4%)

bsearch32.0ms (0.6%)

regimes18.0ms (0.4%)

bsearch32.0ms (0.6%)

regimes12.0ms (0.2%)

bsearch109.0ms (2.2%)

regimes13.0ms (0.3%)

bsearch81.0ms (1.6%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.7s (53.5%)

Profiling