Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	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 10 computations (16.7% saved)

sample12.0ms (0.4%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify158.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	16
1	14	16

prune3.0ms (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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.0b	(/.f64 1 (-.f64 x 1))

rewrite46.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64_2143`
30×	`add-sqr-sqrt_binary64_2165`
29×	`times-frac_binary64_2149`
14×	`add-cube-cbrt_binary64_2178`
8×	`distribute-lft-out_binary64_2094` `difference-of-squares_binary64_2112`
7×	`associate-/r*_binary64_2087`
6×	`distribute-lft-out--_binary64_2095` `add-exp-log_binary64_2181`
4×	`add-log-exp_binary64_2182` `difference-of-sqr-1_binary64_2113` `add-cbrt-cube_binary64_2179`
3×	`pow1_binary64_2204` `associate-/l*_binary64_2088`
2×	`associate-/r/_binary64_2089` `div-inv_binary64_2140` `div-exp_binary64_2194`
1×	`cbrt-undiv_binary64_2177` `+-commutative_binary64_2073` `clear-num_binary64_2142` `flip--_binary64_2118` `1-exp_binary64_2187` `rec-exp_binary64_2193` `sum-log_binary64_2234` `flip3--_binary64_2147` `pow-flip_binary64_2217` `flip3-+_binary64_2146` `flip-+_binary64_2117` `inv-pow_binary64_2228` `frac-2neg_binary64_2154` `frac-add_binary64_2151`

Counts

2 → 67

Calls

2 calls:

33.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
7.0ms	(/.f64 1 (-.f64 x 1))

series81.0ms (2.4%)

Counts

2 → 6

Calls

2 calls:

62.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
19.0ms	(/.f64 1 (-.f64 x 1))

simplify77.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4942	1114
1	4942	1114

prune90.0ms (2.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	4	74

Merged error: 0b

Counts

74 → 4

Compiler

Compiled 1615 to 1227 computations (24% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.3b	(/.f64 1 (+.f64 -1 (*.f64 x x)))
14.1b	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))

rewrite44.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_2165`
22×	`*-un-lft-identity_binary64_2143`
20×	`times-frac_binary64_2149`
19×	`add-cube-cbrt_binary64_2178`
16×	`add-exp-log_binary64_2181`
15×	`associate-l_binary64_2084`
10×	`add-cbrt-cube_binary64_2179`
7×	`flip3-+_binary64_2146` `flip-+_binary64_2117`
6×	`pow1_binary64_2204`
5×	`add-log-exp_binary64_2182` `frac-add_binary64_2151`
4×	`associate-/r/_binary64_2089` `frac-times_binary64_2153` `associate-r_binary64_2083` `prod-exp_binary64_2192` `associate-*r/_binary64_2085` `div-exp_binary64_2194`
3×	`associate-/r_binary64_2087` `associate-/l_binary64_2088` `unswap-sqr_binary64_2111`
2×	`cbrt-undiv_binary64_2177` `distribute-rgt-in_binary64_2093` `1-exp_binary64_2187` `div-inv_binary64_2140` `cbrt-unprod_binary64_2176` `rec-exp_binary64_2193` `associate-+l+_binary64_2076` `associate-*l/_binary64_2086` `distribute-lft-in_binary64_2092`
1×	`+-commutative_binary64_2073` `clear-num_binary64_2142` `sum-log_binary64_2234` `pow-prod-down_binary64_2214` `pow-flip_binary64_2217` `distribute-lft-out_binary64_2094` `*-commutative_binary64_2074` `inv-pow_binary64_2228` `frac-2neg_binary64_2154`

Counts

3 → 95

Calls

3 calls:

17.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
13.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))
5.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))

series160.0ms (4.8%)

Counts

3 → 9

Calls

3 calls:

95.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
35.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))
29.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))

simplify76.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	6211	1770

prune115.0ms (3.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	104	4	108

Merged error: 0b

Counts

108 → 4

Compiler

Compiled 2338 to 1596 computations (31.7% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))
0.0b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3))
0.0b	(/.f64 1 (+.f64 -1 x))
0.0b	(pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3)

rewrite104.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`*-un-lft-identity_binary64_2143`
54×	`distribute-lft-out_binary64_2094`
52×	`times-frac_binary64_2149`
24×	`cbrt-prod_binary64_2174`
19×	`add-sqr-sqrt_binary64_2165` `add-cube-cbrt_binary64_2178`
18×	`unpow-prod-down_binary64_2222` `cube-prod_binary64_2171`
9×	`add-exp-log_binary64_2181`
7×	`add-cbrt-cube_binary64_2179`
6×	`pow1_binary64_2204` `add-log-exp_binary64_2182` `div-inv_binary64_2140` `cube-div_binary64_2172`
4×	`associate-/r*_binary64_2087` `flip3-+_binary64_2146` `flip-+_binary64_2117`
3×	`pow-unpow_binary64_2220` `associate-/l*_binary64_2088` `cbrt-div_binary64_2175` `frac-add_binary64_2151`
2×	`associate-/r/_binary64_2089` `cube-mult_binary64_2173` `unpow3_binary64_2209` `sqr-pow_binary64_2115` `div-exp_binary64_2194`
1×	`cbrt-undiv_binary64_2177` `+-commutative_binary64_2073` `clear-num_binary64_2142` `1-exp_binary64_2187` `rem-cbrt-cube_binary64_2167` `pow-to-exp_binary64_2212` `rec-exp_binary64_2193` `sum-log_binary64_2234` `pow-flip_binary64_2217` `pow-pow_binary64_2215` `inv-pow_binary64_2228` `rem-cube-cbrt_binary64_2166` `frac-2neg_binary64_2154` `pow-exp_binary64_2211` `pow1/3_binary64_2225`

Counts

4 → 129

Calls

4 calls:

33.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3))
27.0ms	(pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3)
25.0ms	(+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))
6.0ms	(/.f64 1 (+.f64 -1 x))

series220.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3)
69.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3))
56.0ms	(+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))
16.0ms	(/.f64 1 (+.f64 -1 x))

simplify92.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4957	2805
1	4957	2805

prune160.0ms (4.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	141	4	145

Merged error: 0b

Counts

145 → 4

Compiler

Compiled 2792 to 2202 computations (21.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))) (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))))) (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))))
0.0b	(/.f64 1 (+.f64 -1 x))
0.0b	(/.f64 1 (+.f64 -1 x))
0.0b	(/.f64 1 (+.f64 -1 x))

rewrite151.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`cbrt-div_binary64_2175`
81×	`frac-times_binary64_2153`
80×	`*-un-lft-identity_binary64_2143`
51×	`flip3-+_binary64_2146` `flip-+_binary64_2117`
48×	`frac-add_binary64_2151`
44×	`times-frac_binary64_2149`
35×	`add-sqr-sqrt_binary64_2165`
33×	`add-cube-cbrt_binary64_2178`
27×	`associate-*l/_binary64_2086`
26×	`pow1_binary64_2204`
22×	`distribute-lft-out_binary64_2094`
21×	`add-exp-log_binary64_2181`
15×	`associate-*r/_binary64_2085`
12×	`associate-/r_binary64_2087` `associate-r*_binary64_2083`
11×	`add-cbrt-cube_binary64_2179`
10×	`cbrt-prod_binary64_2174`
9×	`associate-/l*_binary64_2088` `pow-prod-up_binary64_2213` `pow1/3_binary64_2225`
6×	`associate-/r/_binary64_2089` `pow-plus_binary64_2206` `div-exp_binary64_2194`
5×	`pow-prod-down_binary64_2214`
4×	`add-log-exp_binary64_2182` `div-inv_binary64_2140`
3×	`cbrt-undiv_binary64_2177` `clear-num_binary64_2142` `pow-sqr_binary64_2116` `1-exp_binary64_2187` `cbrt-unprod_binary64_2176` `rec-exp_binary64_2193` `prod-exp_binary64_2192` `pow-flip_binary64_2217` `inv-pow_binary64_2228` `frac-2neg_binary64_2154`
2×	`pow2_binary64_2224` `unswap-sqr_binary64_2111`
1×	`rem-3cbrt-lft_binary64_2168` `pow3_binary64_2226` `associate-l_binary64_2084` `*-commutative_binary64_2074`

Counts

4 → 216

Calls

4 calls:

93.0ms	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))) (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))))) (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))))
6.0ms	(/.f64 1 (+.f64 -1 x))
6.0ms	(/.f64 1 (+.f64 -1 x))
6.0ms	(/.f64 1 (+.f64 -1 x))

series161.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))) (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))))) (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))))
16.0ms	(/.f64 1 (+.f64 -1 x))
16.0ms	(/.f64 1 (+.f64 -1 x))
15.0ms	(/.f64 1 (+.f64 -1 x))

simplify109.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5022	9294

prune948.0ms (28.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	228	0	228
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	228	4	232

Merged error: 0b

Counts

232 → 4

Compiler

Compiled 11415 to 8663 computations (24.1% saved)

regimes22.0ms (0.7%)

Compiler: Compiled 184 to 148 computations (19.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	16
1	20	16

end0.0ms (0%)

sample455.0ms (13.7%)

Algorithm

1×

intervals

Results

239.0ms

8000×

body

128

valid

Compiler

Compiled 103 to 84 computations (18.4% saved)

Details

analyze4.0ms (0.1%)

sample12.0ms (0.4%)

simplify158.0ms (4.8%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

rewrite46.0ms (1.4%)

series81.0ms (2.4%)

simplify77.0ms (2.3%)

prune90.0ms (2.7%)

localize11.0ms (0.3%)

rewrite44.0ms (1.3%)

series160.0ms (4.8%)

simplify76.0ms (2.3%)

prune115.0ms (3.5%)

localize9.0ms (0.3%)

rewrite104.0ms (3.1%)

series220.0ms (6.6%)

simplify92.0ms (2.8%)

prune160.0ms (4.8%)

localize10.0ms (0.3%)

rewrite151.0ms (4.5%)

series161.0ms (4.8%)

simplify109.0ms (3.3%)

prune948.0ms (28.5%)

regimes22.0ms (0.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample455.0ms (13.7%)

Profiling