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)

sample73.0ms (0.6%)

Algorithm

1×

intervals

Results

57.0ms	256×	body	128	valid
3.0ms	261×	pre	128	true
1.0ms	5×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify169.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5512	47

prune8.0ms (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: 2.7b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))
0.4b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
1.0b	(sqrt.f64 PI.f64)
2.4b	(exp.f64 (*.f64 x x))

rewrite98.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

263×	`times-frac_binary64_2130`
157×	`add-sqr-sqrt_binary64_2146`
148×	`*-un-lft-identity_binary64_2124`
143×	`add-cube-cbrt_binary64_2159`
70×	`associate-l_binary64_2065`
67×	`sqrt-prod_binary64_2140`
22×	`associate-/l*_binary64_2069`
18×	`add-cbrt-cube_binary64_2160`
16×	`add-exp-log_binary64_2162`
9×	`div-inv_binary64_2121`
7×	`pow1_binary64_2185`
6×	`cbrt-undiv_binary64_2158` `add-log-exp_binary64_2163` `div-exp_binary64_2175`
5×	`associate-r_binary64_2064`
4×	`unswap-sqr_binary64_2092`
3×	`distribute-lft-out_binary64_2075` `associate-/r*_binary64_2068` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
2×	`associate-*r/_binary64_2066` `flip3-+_binary64_2127` `frac-times_binary64_2134` `flip-+_binary64_2098`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `-commutative_binary64_2055` `exp-to-pow_binary64_2186` `rem-sqrt-square_binary64_2137` `associate-l/_binary64_2067` `rem-exp-log_binary64_2164` `pow1/2_binary64_2204` `distribute-rgt-in_binary64_2074` `exp-prod_binary64_2176` `associate-/l/_binary64_2071` `distribute-lft-in_binary64_2073` `frac-2neg_binary64_2135`

Counts

4 → 230

Calls

4 calls:

49.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.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)

series176.0ms (1.4%)

Counts

4 → 10

Calls

4 calls:

97.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
70.0ms	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))
8.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify119.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5037	9372

prune533.0ms (4.1%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	211	29	240
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	213	29	242

Merged error: 0.3b

Counts

242 → 29

Compiler

Compiled 11805 to 4959 computations (58% saved)

localize25.0ms (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))
0.4b	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
0.5b	(*.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)))
1.0b	(pow.f64 (exp.f64 x) x)

rewrite95.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64_2146`
54×	`times-frac_binary64_2130`
45×	`*-un-lft-identity_binary64_2124`
33×	`add-exp-log_binary64_2162`
32×	`add-cube-cbrt_binary64_2159`
30×	`associate-r_binary64_2064`
25×	`sqrt-prod_binary64_2140`
23×	`add-cbrt-cube_binary64_2160`
17×	`associate-l_binary64_2065`
16×	`unswap-sqr_binary64_2092` `unpow-prod-down_binary64_2203`
14×	`prod-exp_binary64_2173`
12×	`pow1_binary64_2185`
10×	`frac-times_binary64_2134`
8×	`sqrt-div_binary64_2141` `sqr-pow_binary64_2096` `div-exp_binary64_2175` `cbrt-unprod_binary64_2157`
7×	`associate-*l/_binary64_2067`
6×	`associate-*r/_binary64_2066`
5×	`distribute-lft-out_binary64_2075` `flip3-+_binary64_2127` `flip-+_binary64_2098`
4×	`pow-prod-down_binary64_2195` `cbrt-undiv_binary64_2158` `pow-pow_binary64_2196` `associate-/l*_binary64_2069` `add-log-exp_binary64_2163`
3×	`pow-unpow_binary64_2201` `pow-exp_binary64_2192` `exp-prod_binary64_2176` `pow-to-exp_binary64_2193` `div-inv_binary64_2121`
2×	`*-commutative_binary64_2055` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `associate-/r*_binary64_2068` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `frac-2neg_binary64_2135`

Counts

4 → 157

Calls

4 calls:

37.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
19.0ms	(*.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)))
10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
3.0ms	(pow.f64 (exp.f64 x) x)

series269.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
83.0ms	(*.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)))
51.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
20.0ms	(pow.f64 (exp.f64 x) x)

simplify128.0ms (1%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4938	5291
1	4938	5291

prune425.0ms (3.3%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	152	17	169
Fresh	15	13	28
Picked	1	0	1
Done	0	0	0
Total	168	30	198

Merged error: 0.2b

Counts

198 → 30

Compiler

Compiled 8467 to 4740 computations (44% saved)

localize23.0ms (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))
0.4b	(.f64 (.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 1 (fabs.f64 x))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
0.5b	(.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 1 (fabs.f64 x)))
1.0b	(pow.f64 (exp.f64 x) x)

rewrite91.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`add-exp-log_binary64_2162`
74×	`prod-exp_binary64_2173`
39×	`add-cbrt-cube_binary64_2160`
26×	`*-un-lft-identity_binary64_2124`
18×	`associate-r_binary64_2064` `div-exp_binary64_2175` `cbrt-unprod_binary64_2157`
17×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
14×	`associate-*r/_binary64_2066`
13×	`times-frac_binary64_2130`
12×	`pow1_binary64_2185` `frac-times_binary64_2134`
9×	`pow-exp_binary64_2192` `pow-to-exp_binary64_2193`
8×	`sqrt-div_binary64_2141` `associate-*l/_binary64_2067` `1-exp_binary64_2168` `rec-exp_binary64_2174`
6×	`cbrt-undiv_binary64_2158` `flip3-+_binary64_2127` `flip-+_binary64_2098`
5×	`distribute-lft-out_binary64_2075`
4×	`pow-prod-down_binary64_2195` `un-div-inv_binary64_2122` `pow-pow_binary64_2196` `associate-/l*_binary64_2069` `add-log-exp_binary64_2163`
3×	`pow-unpow_binary64_2201` `unpow-prod-down_binary64_2203` `exp-prod_binary64_2176`
2×	`-commutative_binary64_2055` `associate-l*_binary64_2065` `div-inv_binary64_2121` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `associate-/r*_binary64_2068` `sqr-pow_binary64_2096` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `frac-2neg_binary64_2135`

Counts

4 → 146

Calls

4 calls:

38.0ms	(.f64 (.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 1 (fabs.f64 x))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
21.0ms	(.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 1 (fabs.f64 x)))
9.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
3.0ms	(pow.f64 (exp.f64 x) x)

series264.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(.f64 (.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 1 (fabs.f64 x))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
82.0ms	(.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 1 (fabs.f64 x)))
53.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
19.0ms	(pow.f64 (exp.f64 x) x)

simplify101.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4992	5091
1	4992	5091

prune369.0ms (2.9%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	3	26	29
Picked	1	0	1
Done	0	0	0
Total	159	29	188

Merged error: 0.1b

Counts

188 → 29

Compiler

Compiled 7717 to 4672 computations (39.5% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))))
0.5b	(*.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)))
1.0b	(pow.f64 (exp.f64 x) x)
3.4b	(log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))))

rewrite95.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-sqr-sqrt_binary64_2146`
54×	`times-frac_binary64_2130`
46×	`*-un-lft-identity_binary64_2124`
33×	`add-cube-cbrt_binary64_2159`
31×	`associate-r_binary64_2064`
28×	`add-exp-log_binary64_2162`
25×	`sqrt-prod_binary64_2140`
18×	`add-cbrt-cube_binary64_2160`
17×	`associate-l_binary64_2065`
16×	`unswap-sqr_binary64_2092` `unpow-prod-down_binary64_2203`
14×	`pow1_binary64_2185`
13×	`prod-exp_binary64_2173`
11×	`exp-prod_binary64_2176`
10×	`log-pow_binary64_2213` `frac-times_binary64_2134`
8×	`sqrt-div_binary64_2141` `sqr-pow_binary64_2096`
7×	`associate-*l/_binary64_2067` `cbrt-unprod_binary64_2157`
6×	`distribute-lft-out_binary64_2075` `associate-*r/_binary64_2066` `div-exp_binary64_2175`
4×	`pow-prod-down_binary64_2195` `pow-pow_binary64_2196` `add-log-exp_binary64_2163` `flip3-+_binary64_2127` `flip-+_binary64_2098`
3×	`pow-unpow_binary64_2201` `pow-exp_binary64_2192` `log-prod_binary64_2210` `pow-to-exp_binary64_2193` `div-inv_binary64_2121`
2×	`cbrt-undiv_binary64_2158` `*-commutative_binary64_2055`
1×	`rem-log-exp_binary64_2165` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`

Counts

4 → 153

Calls

4 calls:

41.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))))
21.0ms	(*.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)))
8.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))))
3.0ms	(pow.f64 (exp.f64 x) x)

series467.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))))
125.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))))
74.0ms	(*.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)))
18.0ms	(pow.f64 (exp.f64 x) x)

simplify95.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4954	5202
1	4954	5202

prune351.0ms (2.7%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	161	4	165
Fresh	4	24	28
Picked	1	0	1
Done	0	0	0
Total	166	28	194

Merged error: 0.1b

Counts

194 → 28

Compiler

Compiled 7103 to 3951 computations (44.4% saved)

regimes1.5s (11.9%)

Compiler: Compiled 23750 to 15309 computations (35.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	53
1	32	53

end0.0ms (0%)

sample7.3s (56.8%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
104.0ms	8128×	pre	128	true
26.0ms	128×	body	128	invalid

Compiler

Compiled 7986 to 5153 computations (35.5% saved)

Details

analyze9.0ms (0.1%)

sample73.0ms (0.6%)

simplify169.0ms (1.3%)

prune8.0ms (0.1%)

localize19.0ms (0.1%)

rewrite98.0ms (0.8%)

series176.0ms (1.4%)

simplify119.0ms (0.9%)

prune533.0ms (4.1%)

localize25.0ms (0.2%)

rewrite95.0ms (0.7%)

series269.0ms (2.1%)

simplify128.0ms (1%)

prune425.0ms (3.3%)

localize23.0ms (0.2%)

rewrite91.0ms (0.7%)

series264.0ms (2.1%)

simplify101.0ms (0.8%)

prune369.0ms (2.9%)

localize25.0ms (0.2%)

rewrite95.0ms (0.7%)

series467.0ms (3.6%)

simplify95.0ms (0.7%)

prune351.0ms (2.7%)

regimes1.5s (11.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample7.3s (56.8%)

Profiling