Details

analyze70.0ms (1.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	43.7%	12.6%	6
53.1%	31.2%	15.7%	7
59.3%	18.7%	22%	8
62.4%	14%	23.5%	9
64.8%	8.6%	26.6%	10
66%	6.6%	27.4%	11
66.9%	4.1%	29%	12
67.4%	3.2%	29.4%	13
67.9%	2%	30.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample26.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	232×	body	128	valid
5.0ms	10×	body	1024	valid
2.0ms	8×	body	512	valid
1.0ms	6×	body	256	valid
0.0ms	2×	body	128	overflowed
0.0ms	1×	body	128	invalid

Compiler

Compiled 19 to 19 computations (0% saved)

simplify170.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	96	14
1	96	14

prune3.0ms (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: 0.3b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (exp.f64 x))
0.0b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
0.3b	(log.f64 (+.f64 1 (exp.f64 x)))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_2143`
8×	`log-prod_binary64_2229`
6×	`add-log-exp_binary64_2182`
5×	`add-sqr-sqrt_binary64_2165` `add-cube-cbrt_binary64_2178`
4×	`pow1_binary64_2204` `log-div_binary64_2230` `add-exp-log_binary64_2181` `associate--l+_binary64_2080`
3×	`distribute-lft-out_binary64_2094` `flip3-+_binary64_2146` `flip-+_binary64_2117` `add-cbrt-cube_binary64_2179`
2×	`associate--l-_binary64_2081`
1×	`+-commutative_binary64_2073` `diff-log_binary64_2235` `flip--_binary64_2118` `rem-log-exp_binary64_2184` `sub-neg_binary64_2136` `sum-log_binary64_2234` `flip3--_binary64_2147` `log-pow_binary64_2232` `cancel-sign-sub-inv_binary64_2109`

Counts

3 → 45

Calls

3 calls:

7.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
4.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
4.0ms	(+.f64 1 (exp.f64 x))

series163.0ms (4.4%)

Counts

3 → 9

Calls

3 calls:

79.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
74.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
10.0ms	(+.f64 1 (exp.f64 x))

simplify70.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5066	767

prune87.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	49	5	54
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	6	55

Merged error: 0.2b

Counts

55 → 6

Compiler

Compiled 1459 to 938 computations (35.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (exp.f64 x))
0.0b	(-.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (*.f64 x y))
1.0b	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
1.0b	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))

rewrite39.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`log-prod_binary64_2229` `*-un-lft-identity_binary64_2143`
9×	`add-log-exp_binary64_2182`
8×	`sqrt-div_binary64_2160` `pow1_binary64_2204` `add-sqr-sqrt_binary64_2165` `log-div_binary64_2230` `sqrt-prod_binary64_2159` `add-cube-cbrt_binary64_2178`
6×	`add-exp-log_binary64_2181` `log-pow_binary64_2232`
5×	`flip3-+_binary64_2146` `flip-+_binary64_2117`
4×	`associate--l-_binary64_2081` `add-cbrt-cube_binary64_2179`
3×	`distribute-lft-out_binary64_2094`
2×	`pow1/2_binary64_2223` `diff-log_binary64_2235` `rem-log-exp_binary64_2184` `associate-+l-_binary64_2078` `sum-log_binary64_2234` `associate-+r-_binary64_2077` `sqrt-pow1_binary64_2161`
1×	`+-commutative_binary64_2073` `flip--_binary64_2118` `sub-neg_binary64_2136` `flip3--_binary64_2147` `associate--l+_binary64_2080` `cancel-sign-sub-inv_binary64_2109`

Counts

4 → 70

Calls

4 calls:

17.0ms	(-.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (*.f64 x y))
7.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
5.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
4.0ms	(+.f64 1 (exp.f64 x))

series386.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

145.0ms	(-.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (*.f64 x y))
116.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
115.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
10.0ms	(+.f64 1 (exp.f64 x))

simplify50.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4921	1290
1	4921	1290

prune92.0ms (2.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	82	6	88

Merged error: 0.2b

Counts

88 → 6

Compiler

Compiled 1838 to 1152 computations (37.3% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (*.f64 x y) 3)
0.6b	(.f64 (log.f64 (+.f64 1 (exp.f64 x))) (+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 x y)))
0.7b	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)
12.2b	(/.f64 (-.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (log.f64 (+.f64 1 (exp.f64 x))) (+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 x y)))))

rewrite63.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`add-sqr-sqrt_binary64_2165`
39×	`times-frac_binary64_2149`
36×	`*-un-lft-identity_binary64_2143`
32×	`difference-of-squares_binary64_2112`
28×	`add-cube-cbrt_binary64_2178`
26×	`sqr-pow_binary64_2115`
13×	`pow1_binary64_2204` `unpow-prod-down_binary64_2222` `cube-prod_binary64_2171` `associate-/l*_binary64_2088`
12×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
6×	`pow-unpow_binary64_2220`
4×	`add-log-exp_binary64_2182` `difference-cubes_binary64_2145` `distribute-lft-out--_binary64_2095` `associate-l_binary64_2084`
3×	`associate-/r_binary64_2087` `associate-r*_binary64_2083` `pow-pow_binary64_2215` `log-pow_binary64_2232` `rem-cube-cbrt_binary64_2166` `pow-exp_binary64_2211`
2×	`associate-/r/_binary64_2089` `cube-mult_binary64_2173` `pow-to-exp_binary64_2212` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `associate-*r/_binary64_2085` `unpow3_binary64_2209` `flip3-+_binary64_2146` `flip-+_binary64_2117` `associate-/l/_binary64_2090`
1×	`cbrt-undiv_binary64_2177` `clear-num_binary64_2142` `flip--_binary64_2118` `distribute-rgt-in_binary64_2093` `div-inv_binary64_2140` `flip3--_binary64_2147` `unswap-sqr_binary64_2111` `*-commutative_binary64_2074` `distribute-lft-in_binary64_2092` `div-exp_binary64_2194` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

4 → 142

Calls

4 calls:

25.0ms	(/.f64 (-.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (log.f64 (+.f64 1 (exp.f64 x))) (+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 x y)))))
7.0ms	(.f64 (log.f64 (+.f64 1 (exp.f64 x))) (+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 x y)))
4.0ms	(pow.f64 (*.f64 x y) 3)
3.0ms	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)

series666.0ms (18%)

Counts

4 → 12

Calls

4 calls:

297.0ms	(/.f64 (-.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (log.f64 (+.f64 1 (exp.f64 x))) (+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 x y)))))
169.0ms	(.f64 (log.f64 (+.f64 1 (exp.f64 x))) (+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 x y)))
129.0ms	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)
70.0ms	(pow.f64 (*.f64 x y) 3)

simplify119.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5095	7792

prune411.0ms (11.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	154	6	160

Merged error: 0.2b

Counts

160 → 6

Compiler

Compiled 8060 to 4495 computations (44.2% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))
0.0b	(-.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))) (*.f64 x y))
6.3b	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_2143`
9×	`add-log-exp_binary64_2182`
8×	`log-prod_binary64_2229`
5×	`add-sqr-sqrt_binary64_2165` `add-cube-cbrt_binary64_2178`
4×	`pow1_binary64_2204` `log-div_binary64_2230` `add-exp-log_binary64_2181` `associate--l+_binary64_2080`
3×	`sum-log_binary64_2234` `distribute-lft-out_binary64_2094` `flip3-+_binary64_2146` `flip-+_binary64_2117` `add-cbrt-cube_binary64_2179`
2×	`associate--l-_binary64_2081`
1×	`+-commutative_binary64_2073` `diff-log_binary64_2235` `flip--_binary64_2118` `rem-log-exp_binary64_2184` `sub-neg_binary64_2136` `flip3--_binary64_2147` `associate-+r+_binary64_2075` `log-pow_binary64_2232` `cancel-sign-sub-inv_binary64_2109`

Counts

3 → 47

Calls

3 calls:

8.0ms	(-.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))) (*.f64 x y))
6.0ms	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))
6.0ms	(+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))

series125.0ms (3.4%)

Counts

3 → 9

Calls

3 calls:

77.0ms	(-.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))) (*.f64 x y))
30.0ms	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))
18.0ms	(+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))

simplify59.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5016	1292

prune68.0ms (1.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	56	6	62

Merged error: 0.2b

Counts

62 → 6

Compiler

Compiled 1398 to 904 computations (35.3% saved)

regimes51.0ms (1.4%)

Compiler: Compiled 433 to 330 computations (23.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	14
1	37	14

end0.0ms (0%)

sample892.0ms (24.1%)

Algorithm

1×

intervals

Results

370.0ms	7376×	body	128	valid
88.0ms	209×	body	1024	valid
57.0ms	248×	body	512	valid
22.0ms	167×	body	256	valid
3.0ms	47×	body	128	invalid
0.0ms	6×	body	128	overflowed

Compiler

Compiled 182 to 141 computations (22.5% saved)

Details

analyze70.0ms (1.9%)

sample26.0ms (0.7%)

simplify170.0ms (4.6%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

rewrite18.0ms (0.5%)

series163.0ms (4.4%)

simplify70.0ms (1.9%)

prune87.0ms (2.4%)

localize10.0ms (0.3%)

rewrite39.0ms (1.1%)

series386.0ms (10.5%)

simplify50.0ms (1.3%)

prune92.0ms (2.5%)

localize16.0ms (0.4%)

rewrite63.0ms (1.7%)

series666.0ms (18%)

simplify119.0ms (3.2%)

prune411.0ms (11.1%)

localize10.0ms (0.3%)

rewrite24.0ms (0.6%)

series125.0ms (3.4%)

simplify59.0ms (1.6%)

prune68.0ms (1.8%)

regimes51.0ms (1.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample892.0ms (24.1%)

Profiling