Details

analyze9.0ms (0%)

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)

sample65.0ms (0%)

Algorithm

1×

intervals

Results

51.0ms	256×	body	128	valid
3.0ms	257×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify175.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5512	47

prune4.0ms (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

2.3b

Counts

2 → 2

Compiler

Compiled 30 to 21 computations (30% saved)

localize34.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 2) (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (.f64 (/.f64 3 4) (.f64 (.f64 (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))
0.3b	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (exp.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))
0.3b	(.f64 (/.f64 15 8) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))
0.3b	(+.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 2) (.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))
0.5b	(*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))
0.5b	(*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)
2.3b	(exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))

rewrite97.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`add-sqr-sqrt_binary64_2146`
96×	`times-frac_binary64_2130`
84×	`add-exp-log_binary64_2162`
77×	`*-un-lft-identity_binary64_2124`
61×	`add-cube-cbrt_binary64_2159`
35×	`pow1_binary64_2185`
32×	`prod-exp_binary64_2173` `div-exp_binary64_2175`
30×	`swap-sqr_binary64_2091`
28×	`add-cbrt-cube_binary64_2160`
26×	`associate-l_binary64_2065` `associate-r_binary64_2064`
18×	`unswap-sqr_binary64_2092`
16×	`pow-flip_binary64_2198` `1-exp_binary64_2168` `inv-pow_binary64_2209` `rec-exp_binary64_2174`
12×	`div-inv_binary64_2121`
10×	`pow-prod-up_binary64_2194`
8×	`cbrt-undiv_binary64_2158` `cbrt-unprod_binary64_2157`
6×	`pow-prod-down_binary64_2195` `add-log-exp_binary64_2163` `pow-sqr_binary64_2097`
3×	`sqrt-prod_binary64_2140`
2×	`un-div-inv_binary64_2122` `-commutative_binary64_2055` `associate-l/_binary64_2067` `pow-plus_binary64_2187` `associate-*r/_binary64_2066` `pow2_binary64_2205` `frac-times_binary64_2134`
1×	`sqrt-pow1_binary64_2142` `exp-to-pow_binary64_2186` `rem-sqrt-square_binary64_2137` `rem-exp-log_binary64_2164` `pow1/2_binary64_2204` `exp-prod_binary64_2176`

Counts

4 → 213

Calls

8 calls:

16.0ms	(*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))
13.0ms	(*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))
2.0ms	(exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(+.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 2) (.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))

series179.0ms (0.1%)

Counts

4 → 9

Calls

4 calls:

68.0ms	(*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))
66.0ms	(*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))
45.0ms	(exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1812 to 1236 computations (31.8% saved)

simplify102.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4903	1913
1	4903	1913

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))
0.2b	(/.f64 3/4 (*.f64 x x))
0.1b	(+.f64 1/2 (/.f64 3/4 (*.f64 x x)))
0.0b	(+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x 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)))))
0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
1.0b	(sqrt.f64 PI.f64)
2.3b	(exp.f64 (*.f64 x x))

rewrite84.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

129×	`times-frac_binary64_2130`
84×	`add-sqr-sqrt_binary64_2146`
79×	`*-un-lft-identity_binary64_2124`
70×	`add-cube-cbrt_binary64_2159` `associate-l_binary64_2065`
31×	`sqrt-prod_binary64_2140`
18×	`add-cbrt-cube_binary64_2160`
17×	`add-exp-log_binary64_2162`
7×	`pow1_binary64_2185`
6×	`add-log-exp_binary64_2163`
5×	`cbrt-undiv_binary64_2158` `distribute-lft-out_binary64_2075` `associate-r_binary64_2064` `div-inv_binary64_2121` `div-exp_binary64_2175`
4×	`unswap-sqr_binary64_2092` `associate-/l*_binary64_2069` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`associate-*r/_binary64_2066` `frac-times_binary64_2134` `associate-/l/_binary64_2071`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `-commutative_binary64_2055` `exp-to-pow_binary64_2186` `associate-/r_binary64_2068` `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` `distribute-lft-in_binary64_2073` `frac-2neg_binary64_2135`

Counts

4 → 149

Calls

8 calls:

50.0ms	(.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)))))
9.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))))

series304.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

204.0ms	(.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)))))
77.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
22.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1010 to 815 computations (19.3% saved)

simplify142.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4943	6637
1	4943	6637

prune3.8s (2.4%)

Pruning

183 alts after pruning (181 fresh and 2 done)

	Pruned	Kept	Total
New	214	181	395
Fresh	0	0	0
Picked	0	0	0
Done	0	2	2
Total	214	183	397

Error

0.3b

Counts

397 → 183

Compiler

Compiled 27530 to 16636 computations (39.6% saved)

localize31.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))
0.2b	(/.f64 3/4 (*.f64 x x))
0.1b	(+.f64 1/2 (/.f64 3/4 (*.f64 x x)))
0.0b	(+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))
0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite41.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_2124`
13×	`add-sqr-sqrt_binary64_2146`
11×	`add-cube-cbrt_binary64_2159`
9×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
7×	`pow1_binary64_2185`
6×	`sqrt-prod_binary64_2140`
4×	`pow-pow_binary64_2196` `associate-/l*_binary64_2069` `add-log-exp_binary64_2163` `times-frac_binary64_2130`
3×	`pow-unpow_binary64_2201` `unpow-prod-down_binary64_2203` `exp-prod_binary64_2176`
2×	`cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142` `distribute-lft-out_binary64_2075` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `associate-/l/_binary64_2071` `div-exp_binary64_2175`
1×	`clear-num_binary64_2123` `pow-exp_binary64_2192` `associate-/r*_binary64_2068` `prod-exp_binary64_2173` `sqr-pow_binary64_2096` `pow-to-exp_binary64_2193` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

4 → 71

Calls

8 calls:

18.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
5.0ms	(pow.f64 (exp.f64 x) x)
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)
0.0ms	(+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))

series137.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
54.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 687 to 532 computations (22.6% saved)

simplify68.0ms (0%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5015	956

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 15/8 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (pow.f64 (fabs.f64 x) 7)))
0.2b	(/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (pow.f64 (fabs.f64 x) 7))
0.2b	(/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (pow.f64 (fabs.f64 x) 7))
0.3b	(*.f64 15/8 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (pow.f64 (fabs.f64 x) 7)))

rewrite82.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

377×	`times-frac_binary64_2130`
227×	`add-sqr-sqrt_binary64_2146`
204×	`sqrt-prod_binary64_2140`
193×	`*-un-lft-identity_binary64_2124`
190×	`add-cube-cbrt_binary64_2159`
116×	`associate-r_binary64_2064`
103×	`unpow-prod-down_binary64_2203`
37×	`sqr-pow_binary64_2096`
17×	`add-exp-log_binary64_2162` `div-inv_binary64_2121`
16×	`associate-/l*_binary64_2069`
13×	`unswap-sqr_binary64_2092`
9×	`add-cbrt-cube_binary64_2160`
7×	`associate-/r*_binary64_2068`
6×	`div-exp_binary64_2175`
4×	`pow1_binary64_2185` `prod-exp_binary64_2173`
3×	`associate-l_binary64_2065`
2×	`cbrt-undiv_binary64_2158` `pow-exp_binary64_2192` `add-log-exp_binary64_2163` `pow-to-exp_binary64_2193` `cbrt-unprod_binary64_2157`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `-commutative_binary64_2055` `sqrt-div_binary64_2141` `associate-r/_binary64_2066` `associate-/l/_binary64_2071` `frac-2neg_binary64_2135`

Counts

2 → 298

Calls

4 calls:

33.0ms	(*.f64 15/8 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (pow.f64 (fabs.f64 x) 7)))
14.0ms	(/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (pow.f64 (fabs.f64 x) 7))
0.0ms	(/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (pow.f64 (fabs.f64 x) 7))
0.0ms	(*.f64 15/8 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (pow.f64 (fabs.f64 x) 7)))

series323.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

175.0ms	(*.f64 15/8 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (pow.f64 (fabs.f64 x) 7)))
147.0ms	(/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (pow.f64 (fabs.f64 x) 7))

Compiler

Compiled 156 to 156 computations (0% saved)

simplify134.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4954	7934
1	4954	7934

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b	(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 3))
0.3b	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
0.2b	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (.f64 1/2 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 3)))))
0.2b	(+.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 3))))
0.3b	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
0.4b	(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 3))
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite48.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`times-frac_binary64_2130`
81×	`unpow-prod-down_binary64_2203`
76×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
27×	`sqr-pow_binary64_2096`
24×	`cube-prod_binary64_2152`
17×	`add-exp-log_binary64_2162`
15×	`associate-/r*_binary64_2068`
14×	`associate-/l*_binary64_2069`
12×	`div-exp_binary64_2175`
9×	`pow-exp_binary64_2192` `pow-to-exp_binary64_2193`
8×	`unpow3_binary64_2190` `cube-mult_binary64_2154` `pow-pow_binary64_2196` `add-cbrt-cube_binary64_2160`
6×	`pow-unpow_binary64_2201` `pow1_binary64_2185` `exp-prod_binary64_2176`
4×	`add-log-exp_binary64_2163`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

4 → 208

Calls

8 calls:

8.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 3))
5.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
3.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(+.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 3))))

series168.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 3))
47.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
21.0ms	(pow.f64 (exp.f64 x) x)
18.0ms	(pow.f64 (exp.f64 x) x)

Compiler

Compiled 576 to 408 computations (29.2% saved)

simplify69.0ms (0%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5188	4371

localize41.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (pow.f64 (exp.f64 x) x))
0.1b	(sqrt.f64 (exp.f64 (*.f64 x x)))
0.1b	(+.f64 1/2 (/.f64 3/4 (*.f64 x x)))
0.0b	(+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))
0.6b	(cbrt.f64 (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 x) x)
2.3b	(exp.f64 (*.f64 x x))

rewrite15.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2146`
9×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
6×	`pow1_binary64_2185` `add-log-exp_binary64_2163`
4×	`pow-pow_binary64_2196` `exp-prod_binary64_2176` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`pow-unpow_binary64_2201` `unpow-prod-down_binary64_2203` `sqrt-prod_binary64_2140` `cbrt-prod_binary64_2155`
1×	`sqrt-pow1_binary64_2142` `pow-exp_binary64_2192` `exp-to-pow_binary64_2186` `rem-sqrt-square_binary64_2137` `pow1/3_binary64_2206` `rem-exp-log_binary64_2164` `sqr-pow_binary64_2096` `pow1/2_binary64_2204` `pow-to-exp_binary64_2193`

Counts

4 → 54

Calls

8 calls:

3.0ms	(pow.f64 (exp.f64 x) x)
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(cbrt.f64 (fabs.f64 x))
0.0ms	(+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))

series165.0ms (0.1%)

Counts

4 → 15

Calls

4 calls:

89.0ms	(cbrt.f64 (fabs.f64 x))
48.0ms	(pow.f64 (exp.f64 x) x)
28.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1120 to 768 computations (31.4% saved)

simplify101.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4887	545
1	4887	545

localize41.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 2) (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (.f64 (/.f64 3 4) (.f64 (.f64 (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))
0.3b	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (exp.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))
0.3b	(.f64 (/.f64 15 8) (.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 6))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))
0.3b	(+.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 2) (.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))
0.5b	(*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))
0.7b	(cbrt.f64 (/.f64 1 (pow.f64 x 6)))
1.0b	(sqrt.f64 PI.f64)
2.3b	(exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))

rewrite61.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_2146`
69×	`times-frac_binary64_2130`
55×	`*-un-lft-identity_binary64_2124`
47×	`add-cube-cbrt_binary64_2159`
44×	`add-exp-log_binary64_2162`
25×	`cbrt-prod_binary64_2155`
20×	`pow1_binary64_2185`
16×	`prod-exp_binary64_2173` `add-cbrt-cube_binary64_2160` `div-exp_binary64_2175`
15×	`swap-sqr_binary64_2091`
13×	`associate-l_binary64_2065` `associate-r_binary64_2064`
9×	`unswap-sqr_binary64_2092` `unpow-prod-down_binary64_2203`
8×	`pow-flip_binary64_2198` `1-exp_binary64_2168` `inv-pow_binary64_2209` `rec-exp_binary64_2174`
7×	`div-inv_binary64_2121`
6×	`add-log-exp_binary64_2163`
5×	`pow-prod-up_binary64_2194`
4×	`cbrt-undiv_binary64_2158` `cbrt-unprod_binary64_2157`
3×	`pow-prod-down_binary64_2195` `sqrt-prod_binary64_2140` `sqr-pow_binary64_2096` `pow-sqr_binary64_2097`
1×	`cbrt-div_binary64_2156` `un-div-inv_binary64_2122` `sqrt-pow1_binary64_2142` `-commutative_binary64_2055` `exp-to-pow_binary64_2186` `rem-sqrt-square_binary64_2137` `associate-l/_binary64_2067` `pow1/3_binary64_2206` `rem-exp-log_binary64_2164` `pow-plus_binary64_2187` `pow1/2_binary64_2204` `exp-prod_binary64_2176` `associate-*r/_binary64_2066` `pow2_binary64_2205` `frac-times_binary64_2134`

Counts

4 → 152

Calls

8 calls:

12.0ms	(*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))
4.0ms	(cbrt.f64 (/.f64 1 (pow.f64 x 6)))
4.0ms	(sqrt.f64 PI.f64)
2.0ms	(exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))
0.0ms	(+.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 2) (.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))

series157.0ms (0.1%)

Counts

4 → 9

Calls

4 calls:

69.0ms	(*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))
52.0ms	(exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))
35.0ms	(cbrt.f64 (/.f64 1 (pow.f64 x 6)))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1770 to 1236 computations (30.2% saved)

simplify84.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4920	1682
1	4920	1682

prune21.3s (13.4%)

Pruning

536 alts after pruning (529 fresh and 7 done)

	Pruned	Kept	Total
New	483	354	837
Fresh	1	175	176
Picked	0	0	0
Done	0	7	7
Total	484	536	1020

Error

0.2b

Counts

1020 → 536

Compiler

Compiled 48919 to 30866 computations (36.9% saved)

localize34.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 3/4 (*.f64 x x))
0.2b	(exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))
0.1b	(+.f64 1/2 (/.f64 3/4 (*.f64 x x)))
0.0b	(+.f64 1 (+.f64 (log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))) (/.f64 15/8 (pow.f64 x 6))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 x) x)
3.2b	(log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))))

rewrite22.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
12×	`add-cube-cbrt_binary64_2159`
11×	`exp-prod_binary64_2176`
9×	`log-pow_binary64_2213`
8×	`pow1_binary64_2185`
6×	`sqrt-prod_binary64_2140`
4×	`pow-pow_binary64_2196` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `times-frac_binary64_2130` `add-cbrt-cube_binary64_2160`
3×	`pow-unpow_binary64_2201` `unpow-prod-down_binary64_2203` `log-prod_binary64_2210`
2×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204`
1×	`rem-log-exp_binary64_2165` `pow-exp_binary64_2192` `distribute-lft-out_binary64_2075` `sqr-pow_binary64_2096` `pow-to-exp_binary64_2193` `div-inv_binary64_2121`

Counts

4 → 66

Calls

8 calls:

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)
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(+.f64 1 (+.f64 (log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))) (/.f64 15/8 (pow.f64 x 6))))

series254.0ms (0.2%)

Counts

4 → 11

Calls

4 calls:

212.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))))
42.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 670 to 522 computations (22.1% saved)

simplify81.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4921	851
1	4921	851

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

0.4b	(/.f64 (*.f64 15/8 (sqrt.f64 (/.f64 1 PI.f64))) (pow.f64 (fabs.f64 x) 7))
0.4b	(/.f64 (*.f64 15/8 (sqrt.f64 (/.f64 1 PI.f64))) (pow.f64 (fabs.f64 x) 7))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64_2162`
7×	`associate-/r*_binary64_2068` `times-frac_binary64_2130`
6×	`unpow-prod-down_binary64_2203` `add-cbrt-cube_binary64_2160` `div-exp_binary64_2175`
5×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
3×	`prod-exp_binary64_2173`
2×	`cbrt-undiv_binary64_2158` `pow-exp_binary64_2192` `sqr-pow_binary64_2096` `pow-to-exp_binary64_2193`
1×	`clear-num_binary64_2123` `associate-/l_binary64_2069` `sqrt-div_binary64_2141` `pow1_binary64_2185` `add-log-exp_binary64_2163` `associate-r/_binary64_2066` `div-inv_binary64_2121` `associate-/l/_binary64_2071` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

1 → 34

Calls

2 calls:

8.0ms	(/.f64 (*.f64 15/8 (sqrt.f64 (/.f64 1 PI.f64))) (pow.f64 (fabs.f64 x) 7))
0.0ms	(/.f64 (*.f64 15/8 (sqrt.f64 (/.f64 1 PI.f64))) (pow.f64 (fabs.f64 x) 7))

series168.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

168.0ms

(/.f64 (*.f64 15/8 (sqrt.f64 (/.f64 1 PI.f64))) (pow.f64 (fabs.f64 x) 7))

Compiler

Compiled 78 to 78 computations (0% saved)

simplify81.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4923	771
1	4923	771

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
0.3b	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
0.2b	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (.f64 1/2 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (*.f64 (fabs.f64 x) (fabs.f64 x))))))
0.2b	(+.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (.f64 1/2 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (.f64 (fabs.f64 x) (fabs.f64 x)))))
0.3b	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
0.3b	(/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (*.f64 (fabs.f64 x) (fabs.f64 x)))
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite43.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`times-frac_binary64_2130`
54×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
36×	`unpow-prod-down_binary64_2203`
32×	`associate-/l*_binary64_2069`
30×	`add-exp-log_binary64_2162`
18×	`add-cbrt-cube_binary64_2160`
17×	`div-exp_binary64_2175`
12×	`sqr-pow_binary64_2096`
8×	`pow-pow_binary64_2196`
7×	`cbrt-undiv_binary64_2158`
6×	`pow-unpow_binary64_2201` `pow1_binary64_2185` `exp-prod_binary64_2176`
5×	`pow-exp_binary64_2192` `pow-to-exp_binary64_2193`
4×	`associate-/r*_binary64_2068` `add-log-exp_binary64_2163` `prod-exp_binary64_2173` `div-inv_binary64_2121`
2×	`clear-num_binary64_2123` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`
1×	`associate-/l/_binary64_2071`

Counts

4 → 159

Calls

8 calls:

13.0ms	(/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (*.f64 (fabs.f64 x) (fabs.f64 x)))
5.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
3.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(+.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (.f64 1/2 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (.f64 (fabs.f64 x) (fabs.f64 x)))))

series158.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (*.f64 (fabs.f64 x) (fabs.f64 x)))
41.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
18.0ms	(pow.f64 (exp.f64 x) x)
17.0ms	(pow.f64 (exp.f64 x) x)

Compiler

Compiled 648 to 396 computations (38.9% saved)

simplify73.0ms (0%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5008	3117

localize34.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (pow.f64 (exp.f64 x) x))
0.1b	(sqrt.f64 (pow.f64 (exp.f64 x) x))
0.1b	(+.f64 1/2 (/.f64 3/4 (*.f64 x x)))
0.0b	(+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2146`
12×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
8×	`pow-pow_binary64_2196` `pow1_binary64_2185`
6×	`pow-unpow_binary64_2201` `unpow-prod-down_binary64_2203` `sqrt-prod_binary64_2140` `exp-prod_binary64_2176`
4×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
2×	`sqrt-pow1_binary64_2142` `pow-exp_binary64_2192` `rem-sqrt-square_binary64_2137` `sqr-pow_binary64_2096` `pow1/2_binary64_2204` `pow-to-exp_binary64_2193`

Counts

4 → 66

Calls

8 calls:

4.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))

series85.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(pow.f64 (exp.f64 x) x)
39.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 772 to 544 computations (29.5% saved)

simplify48.0ms (0%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5200	632

localize49.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (pow.f64 (pow.f64 (exp.f64 x) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
0.1b	(sqrt.f64 (exp.f64 (*.f64 x x)))
0.1b	(+.f64 1/2 (/.f64 3/4 (*.f64 x x)))
0.0b	(+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))
1.0b	(sqrt.f64 PI.f64)
2.0b	(pow.f64 (exp.f64 x) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
2.3b	(exp.f64 (*.f64 x x))
2.4b	(pow.f64 (pow.f64 (exp.f64 x) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))

rewrite22.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`unpow-prod-down_binary64_2203`
12×	`add-sqr-sqrt_binary64_2146`
11×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
7×	`pow-unpow_binary64_2201`
6×	`pow1_binary64_2185` `add-log-exp_binary64_2163`
5×	`pow-pow_binary64_2196` `pow-exp_binary64_2192` `add-exp-log_binary64_2162`
4×	`exp-prod_binary64_2176` `add-cbrt-cube_binary64_2160`
3×	`sqrt-prod_binary64_2140` `sqr-pow_binary64_2096` `cbrt-prod_binary64_2155` `pow-to-exp_binary64_2193`
1×	`sqrt-pow1_binary64_2142` `exp-to-pow_binary64_2186` `rem-sqrt-square_binary64_2137` `rem-exp-log_binary64_2164` `pow1/2_binary64_2204`

Counts

4 → 67

Calls

8 calls:

5.0ms	(pow.f64 (pow.f64 (exp.f64 x) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
3.0ms	(pow.f64 (exp.f64 x) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))

series544.0ms (0.3%)

Counts

4 → 18

Calls

4 calls:

348.0ms	(pow.f64 (pow.f64 (exp.f64 x) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
164.0ms	(pow.f64 (exp.f64 x) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
31.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1410 to 976 computations (30.8% saved)

simplify95.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4919	901
1	4919	901

prune25.3s (15.8%)

Pruning

724 alts after pruning (713 fresh and 11 done)

	Pruned	Kept	Total
New	250	198	448
Fresh	9	515	524
Picked	0	0	0
Done	1	11	12
Total	260	724	984

Error

0.1b

Counts

984 → 724

Compiler

Compiled 49963 to 30102 computations (39.8% saved)

localize35.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 3/4 (*.f64 x x))
0.2b	(exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))
0.1b	(+.f64 1/2 (/.f64 3/4 (*.f64 x x)))
0.0b	(+.f64 1 (+.f64 (.f64 1 (log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))) (/.f64 15/8 (pow.f64 x 6))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 x) x)
3.2b	(log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))))

rewrite22.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
12×	`add-cube-cbrt_binary64_2159`
11×	`exp-prod_binary64_2176`
9×	`log-pow_binary64_2213`
8×	`pow1_binary64_2185`
6×	`sqrt-prod_binary64_2140`
4×	`pow-pow_binary64_2196` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `times-frac_binary64_2130` `add-cbrt-cube_binary64_2160`
3×	`pow-unpow_binary64_2201` `unpow-prod-down_binary64_2203` `log-prod_binary64_2210`
2×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204`
1×	`rem-log-exp_binary64_2165` `pow-exp_binary64_2192` `distribute-lft-out_binary64_2075` `sqr-pow_binary64_2096` `pow-to-exp_binary64_2193` `div-inv_binary64_2121`

Counts

4 → 66

Calls

8 calls:

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)
2.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(+.f64 1 (+.f64 (.f64 1 (log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))) (/.f64 15/8 (pow.f64 x 6))))

series246.0ms (0.2%)

Counts

4 → 11

Calls

4 calls:

203.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))))
42.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 702 to 554 computations (21.1% saved)

simplify82.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4921	851
1	4921	851

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (pow.f64 (fabs.f64 x) 7) (sqrt.f64 (/.f64 1 PI.f64)))
0.3b	(/.f64 15/8 (/.f64 (pow.f64 (fabs.f64 x) 7) (sqrt.f64 (/.f64 1 PI.f64))))
0.3b	(/.f64 15/8 (/.f64 (pow.f64 (fabs.f64 x) 7) (sqrt.f64 (/.f64 1 PI.f64))))
0.3b	(/.f64 (pow.f64 (fabs.f64 x) 7) (sqrt.f64 (/.f64 1 PI.f64)))

rewrite140.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1235×	`times-frac_binary64_2130`
574×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
468×	`sqrt-prod_binary64_2140`
243×	`unpow-prod-down_binary64_2203`
133×	`associate-/r*_binary64_2068`
81×	`sqr-pow_binary64_2096`
42×	`div-inv_binary64_2121`
17×	`add-exp-log_binary64_2162`
10×	`associate-/l*_binary64_2069` `div-exp_binary64_2175`
9×	`add-cbrt-cube_binary64_2160`
6×	`associate-/r/_binary64_2070`
5×	`sqrt-div_binary64_2141`
4×	`cbrt-undiv_binary64_2158`
2×	`clear-num_binary64_2123` `pow-exp_binary64_2192` `pow1_binary64_2185` `add-log-exp_binary64_2163` `pow-to-exp_binary64_2193` `frac-2neg_binary64_2135`

Counts

2 → 638

Calls

4 calls:

31.0ms	(/.f64 15/8 (/.f64 (pow.f64 (fabs.f64 x) 7) (sqrt.f64 (/.f64 1 PI.f64))))
9.0ms	(/.f64 (pow.f64 (fabs.f64 x) 7) (sqrt.f64 (/.f64 1 PI.f64)))
0.0ms	(/.f64 15/8 (/.f64 (pow.f64 (fabs.f64 x) 7) (sqrt.f64 (/.f64 1 PI.f64))))
0.0ms	(/.f64 (pow.f64 (fabs.f64 x) 7) (sqrt.f64 (/.f64 1 PI.f64)))

series476.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

389.0ms	(/.f64 15/8 (/.f64 (pow.f64 (fabs.f64 x) 7) (sqrt.f64 (/.f64 1 PI.f64))))
88.0ms	(/.f64 (pow.f64 (fabs.f64 x) 7) (sqrt.f64 (/.f64 1 PI.f64)))

Compiler

Compiled 132 to 132 computations (0% saved)

simplify291.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

644 → 644

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4917	22637
1	4917	22637

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b	(.f64 (.f64 15/8 (/.f64 (fabs.f64 (cbrt.f64 1)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7))) (/.f64 (sqrt.f64 (/.f64 (cbrt.f64 1) PI.f64)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7)))
0.3b	(/.f64 (fabs.f64 (cbrt.f64 1)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7))
0.3b	(/.f64 (sqrt.f64 (/.f64 (cbrt.f64 1) PI.f64)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7))
0.2b	(*.f64 15/8 (/.f64 (fabs.f64 (cbrt.f64 1)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7)))
0.3b	(/.f64 (fabs.f64 (cbrt.f64 1)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7))
0.4b	(.f64 (.f64 15/8 (/.f64 (fabs.f64 (cbrt.f64 1)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7))) (/.f64 (sqrt.f64 (/.f64 (cbrt.f64 1) PI.f64)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7)))
1.4b	(pow.f64 (sqrt.f64 (fabs.f64 x)) 7)
1.4b	(pow.f64 (sqrt.f64 (fabs.f64 x)) 7)

rewrite142.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

460×	`times-frac_binary64_2130`
313×	`sqrt-prod_binary64_2140`
254×	`associate-r_binary64_2064`
249×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
186×	`unpow-prod-down_binary64_2203`
90×	`cbrt-prod_binary64_2155`
85×	`add-exp-log_binary64_2162`
36×	`prod-exp_binary64_2173`
31×	`sqr-pow_binary64_2096`
30×	`div-exp_binary64_2175`
27×	`add-cbrt-cube_binary64_2160`
13×	`pow1_binary64_2185`
12×	`pow-exp_binary64_2192` `pow-to-exp_binary64_2193` `div-inv_binary64_2121`
10×	`associate-/r*_binary64_2068` `cbrt-unprod_binary64_2157`
6×	`cbrt-undiv_binary64_2158` `pow-unpow_binary64_2201` `pow-pow_binary64_2196`
4×	`add-log-exp_binary64_2163`
3×	`pow-prod-down_binary64_2195` `associate-/l_binary64_2069` `associate-r/_binary64_2066`
2×	`sqrt-pow2_binary64_2143` `sqrt-pow1_binary64_2142` `pow1/2_binary64_2204`
1×	`clear-num_binary64_2123` `-commutative_binary64_2055` `associate-l_binary64_2065` `associate-l/_binary64_2067` `frac-times_binary64_2134` `frac-2neg_binary64_2135`

Counts

4 → 397

Calls

8 calls:

62.0ms	(.f64 (.f64 15/8 (/.f64 (fabs.f64 (cbrt.f64 1)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7))) (/.f64 (sqrt.f64 (/.f64 (cbrt.f64 1) PI.f64)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7)))
5.0ms	(/.f64 (fabs.f64 (cbrt.f64 1)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7))
3.0ms	(pow.f64 (sqrt.f64 (fabs.f64 x)) 7)
3.0ms	(pow.f64 (sqrt.f64 (fabs.f64 x)) 7)
0.0ms	(*.f64 15/8 (/.f64 (fabs.f64 (cbrt.f64 1)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7)))

series482.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(.f64 (.f64 15/8 (/.f64 (fabs.f64 (cbrt.f64 1)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7))) (/.f64 (sqrt.f64 (/.f64 (cbrt.f64 1) PI.f64)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7)))
126.0ms	(/.f64 (fabs.f64 (cbrt.f64 1)) (pow.f64 (sqrt.f64 (fabs.f64 x)) 7))
101.0ms	(pow.f64 (sqrt.f64 (fabs.f64 x)) 7)
85.0ms	(pow.f64 (sqrt.f64 (fabs.f64 x)) 7)

Compiler

Compiled 480 to 444 computations (7.5% saved)

simplify145.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

409 → 409

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5167	14320

localize38.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))
0.2b	(*.f64 x (cbrt.f64 x))
0.1b	(+.f64 1/2 (/.f64 3/4 (*.f64 x x)))
0.0b	(+.f64 1 (+.f64 (log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))) (/.f64 15/8 (pow.f64 x 6))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
2.5b	(pow.f64 (exp.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 x (cbrt.f64 x)))
3.2b	(log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))))

rewrite23.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
10×	`add-cube-cbrt_binary64_2159`
9×	`log-pow_binary64_2213` `exp-prod_binary64_2176`
8×	`pow1_binary64_2185`
6×	`sqrt-prod_binary64_2140`
5×	`add-log-exp_binary64_2163`
4×	`add-exp-log_binary64_2162` `times-frac_binary64_2130` `add-cbrt-cube_binary64_2160`
3×	`unpow-prod-down_binary64_2203` `pow-pow_binary64_2196` `log-prod_binary64_2210`
2×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204`
1×	`rem-log-exp_binary64_2165` `pow-unpow_binary64_2201` `pow-exp_binary64_2192` `exp-to-pow_binary64_2186` `distribute-lft-out_binary64_2075` `sqr-pow_binary64_2096` `pow-to-exp_binary64_2193` `div-inv_binary64_2121`

Counts

4 → 63

Calls

8 calls:

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 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 x (cbrt.f64 x)))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(+.f64 1 (+.f64 (log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))) (/.f64 15/8 (pow.f64 x 6))))

series541.0ms (0.3%)

Counts

4 → 8

Calls

4 calls:

320.0ms	(pow.f64 (exp.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 x (cbrt.f64 x)))
221.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 698 to 538 computations (22.9% saved)

simplify65.0ms (0%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5353	906

localize48.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (pow.f64 (pow.f64 (exp.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) x) (cbrt.f64 x)))
0.1b	(sqrt.f64 (exp.f64 (*.f64 x x)))
0.1b	(+.f64 1/2 (/.f64 3/4 (*.f64 x x)))
0.0b	(+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) x)
2.3b	(exp.f64 (*.f64 x x))
2.4b	(pow.f64 (pow.f64 (exp.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) x) (cbrt.f64 x))

rewrite21.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`unpow-prod-down_binary64_2203`
12×	`add-sqr-sqrt_binary64_2146`
11×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
9×	`pow-unpow_binary64_2201`
7×	`add-log-exp_binary64_2163`
6×	`pow1_binary64_2185`
5×	`pow-exp_binary64_2192` `add-exp-log_binary64_2162`
4×	`pow-pow_binary64_2196` `add-cbrt-cube_binary64_2160`
3×	`sqrt-prod_binary64_2140` `sqr-pow_binary64_2096` `cbrt-prod_binary64_2155` `pow-to-exp_binary64_2193`
2×	`exp-to-pow_binary64_2186` `exp-prod_binary64_2176`
1×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `rem-exp-log_binary64_2164` `pow1/2_binary64_2204`

Counts

4 → 68

Calls

8 calls:

4.0ms	(pow.f64 (pow.f64 (exp.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) x) (cbrt.f64 x))
4.0ms	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) x)
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))

series338.0ms (0.2%)

Counts

4 → 18

Calls

4 calls:

245.0ms	(pow.f64 (pow.f64 (exp.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) x) (cbrt.f64 x))
62.0ms	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) x)
31.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1480 to 1034 computations (30.1% saved)

simplify77.0ms (0%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4922	951
1	4922	951

prune1.2min (45.4%)

Pruning

1213 alts after pruning (1200 fresh and 13 done)

	Pruned	Kept	Total
New	774	513	1287
Fresh	21	687	708
Picked	0	0	0
Done	3	13	16
Total	798	1213	2011

Error

0.1b

Counts

2011 → 1213

Compiler

Compiled 27789 to 17124 computations (38.4% saved)

simplify1.9s (1.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	6030	119174

regimes14.4s (9%)

Compiler: Compiled 159545 to 115264 computations (27.8% saved)

bsearch0.0ms (0%)

regimes2.8s (1.8%)

Compiler: Compiled 28253 to 22736 computations (19.5% saved)

bsearch0.0ms (0%)

regimes1.3s (0.8%)

Compiler: Compiled 14284 to 11862 computations (17% saved)

bsearch0.0ms (0%)

regimes1.3s (0.8%)

Compiler: Compiled 13802 to 11500 computations (16.7% saved)

bsearch0.0ms (0%)

regimes1.3s (0.8%)

Compiler: Compiled 13724 to 11444 computations (16.6% saved)

bsearch0.0ms (0%)

regimes392.0ms (0.2%)

Compiler: Compiled 3543 to 3164 computations (10.7% saved)

bsearch0.0ms (0%)

regimes202.0ms (0.1%)

Compiler: Compiled 1542 to 1469 computations (4.7% saved)

bsearch0.0ms (0%)

regimes193.0ms (0.1%)

Compiler: Compiled 1422 to 1385 computations (2.6% saved)

bsearch0.0ms (0%)

regimes226.0ms (0.1%)

Compiler: Compiled 1374 to 1349 computations (1.8% saved)

bsearch1.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

regimes160.0ms (0.1%)

Compiler: Compiled 1155 to 1134 computations (1.8% saved)

bsearch0.0ms (0%)

regimes155.0ms (0.1%)

Compiler: Compiled 1093 to 1090 computations (0.3% saved)

bsearch0.0ms (0%)

regimes100.0ms (0.1%)

Compiler: Compiled 692 to 698 computations (-0.9% saved)

bsearch18.0ms (0%)

Compiler: Compiled 381 to 276 computations (27.6% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	593
1	102	593

end0.0ms (0%)

sample4.4s (2.8%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
106.0ms	8111×	pre	128	true
22.0ms	111×	body	128	invalid

Compiler

Compiled 68264 to 48449 computations (29% saved)