Details

analyze5.0ms (0.2%)

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)

sample13.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify99.0ms (4.1%)

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)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite50.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_2124`
41×	`times-frac_binary64_2130`
40×	`add-sqr-sqrt_binary64_2146`
24×	`add-cube-cbrt_binary64_2159`
12×	`distribute-lft-out_binary64_2075`
11×	`associate-/r*_binary64_2068`
9×	`add-exp-log_binary64_2162`
8×	`difference-of-squares_binary64_2093`
7×	`add-cbrt-cube_binary64_2160`
6×	`distribute-lft-out--_binary64_2076` `associate-/l*_binary64_2069`
5×	`add-log-exp_binary64_2163`
4×	`associate-/r/_binary64_2070` `pow1_binary64_2185` `difference-of-sqr-1_binary64_2094`
3×	`div-inv_binary64_2121` `div-exp_binary64_2175`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `flip3-+_binary64_2127` `flip-+_binary64_2098` `frac-2neg_binary64_2135`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `sum-log_binary64_2215` `+-commutative_binary64_2054` `pow-flip_binary64_2198` `1-exp_binary64_2168` `inv-pow_binary64_2209` `frac-add_binary64_2132` `rec-exp_binary64_2174`

Counts

3 → 100

Calls

3 calls:

31.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
6.0ms	(/.f64 1 (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series58.0ms (2.4%)

Counts

3 → 9

Calls

3 calls:

30.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
14.0ms	(/.f64 1 (-.f64 x 1))
14.0ms	(/.f64 x (+.f64 x 1))

simplify74.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5162	1579

prune113.0ms (4.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	4	110

Merged error: 0b

Counts

110 → 4

Compiler

Compiled 1931 to 1421 computations (26.4% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cbrt.f64 (+.f64 -1 x)) (cbrt.f64 (+.f64 -1 x)))
0.3b	(cbrt.f64 (-.f64 x 1))
0.3b	(cbrt.f64 (+.f64 -1 x))
0.3b	(cbrt.f64 (+.f64 -1 x))

rewrite34.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`cbrt-prod_binary64_2155`
36×	`*-un-lft-identity_binary64_2124`
27×	`add-sqr-sqrt_binary64_2146`
18×	`cbrt-div_binary64_2156`
15×	`add-cube-cbrt_binary64_2159`
11×	`pow1_binary64_2185`
9×	`swap-sqr_binary64_2091` `pow1/3_binary64_2206`
8×	`distribute-lft-out_binary64_2075` `flip3-+_binary64_2127` `flip-+_binary64_2098`
7×	`associate-l_binary64_2065` `associate-r_binary64_2064`
6×	`add-exp-log_binary64_2162`
4×	`unswap-sqr_binary64_2092` `add-log-exp_binary64_2163` `frac-times_binary64_2134` `add-cbrt-cube_binary64_2160`
2×	`difference-of-squares_binary64_2093` `pow-prod-down_binary64_2195` `pow-prod-up_binary64_2194` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `pow-sqr_binary64_2097`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `*-commutative_binary64_2055` `prod-exp_binary64_2173` `pow-plus_binary64_2187` `pow2_binary64_2205` `difference-of-sqr-1_binary64_2094` `cbrt-unprod_binary64_2157`

Counts

4 → 98

Calls

4 calls:

16.0ms	(*.f64 (cbrt.f64 (+.f64 -1 x)) (cbrt.f64 (+.f64 -1 x)))
3.0ms	(cbrt.f64 (-.f64 x 1))
3.0ms	(cbrt.f64 (+.f64 -1 x))
3.0ms	(cbrt.f64 (+.f64 -1 x))

series131.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

39.0ms	(*.f64 (cbrt.f64 (+.f64 -1 x)) (cbrt.f64 (+.f64 -1 x)))
32.0ms	(cbrt.f64 (-.f64 x 1))
31.0ms	(cbrt.f64 (+.f64 -1 x))
30.0ms	(cbrt.f64 (+.f64 -1 x))

simplify77.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5099	1633

prune171.0ms (7.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	111	3	114

Merged error: 0b

Counts

114 → 3

Compiler

Compiled 3096 to 2418 computations (21.9% saved)

localize18.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (cbrt.f64 (+.f64 -1 x)) 6)
0.3b	(cbrt.f64 (+.f64 -1 x))
0.3b	(cbrt.f64 (-.f64 x 1))
19.1b	(pow.f64 (pow.f64 (cbrt.f64 (+.f64 -1 x)) 6) 1/3)

rewrite25.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`unpow-prod-down_binary64_2203`
22×	`*-un-lft-identity_binary64_2124`
19×	`cbrt-prod_binary64_2155`
17×	`add-sqr-sqrt_binary64_2146`
13×	`add-cube-cbrt_binary64_2159`
7×	`add-exp-log_binary64_2162`
6×	`pow-unpow_binary64_2201`
5×	`pow-exp_binary64_2192` `pow1_binary64_2185`
4×	`cbrt-div_binary64_2156` `add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
3×	`pow-pow_binary64_2196` `distribute-lft-out_binary64_2075` `pow1/3_binary64_2206` `sqr-pow_binary64_2096` `pow-to-exp_binary64_2193`
2×	`difference-of-squares_binary64_2093`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `unpow1/3_binary64_2191` `distribute-lft-out--_binary64_2076` `flip3-+_binary64_2127` `difference-of-sqr-1_binary64_2094` `flip-+_binary64_2098`

Counts

4 → 81

Calls

4 calls:

7.0ms	(pow.f64 (pow.f64 (cbrt.f64 (+.f64 -1 x)) 6) 1/3)
5.0ms	(pow.f64 (cbrt.f64 (+.f64 -1 x)) 6)
3.0ms	(cbrt.f64 (-.f64 x 1))
3.0ms	(cbrt.f64 (+.f64 -1 x))

series218.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(pow.f64 (pow.f64 (cbrt.f64 (+.f64 -1 x)) 6) 1/3)
64.0ms	(pow.f64 (cbrt.f64 (+.f64 -1 x)) 6)
35.0ms	(cbrt.f64 (+.f64 -1 x))
31.0ms	(cbrt.f64 (-.f64 x 1))

simplify74.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4879	1116
1	4879	1116

prune133.0ms (5.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	93	3	96

Merged error: 0b

Counts

96 → 3

Compiler

Compiled 2346 to 1886 computations (19.6% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.0b	(/.f64 x (+.f64 x 1))
0.1b	(/.f64 1 (+.f64 -1 (*.f64 x x)))
17.5b	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))

rewrite50.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64_2124`
36×	`add-sqr-sqrt_binary64_2146`
32×	`times-frac_binary64_2130`
29×	`add-cube-cbrt_binary64_2159`
19×	`add-exp-log_binary64_2162`
15×	`associate-l_binary64_2065`
13×	`add-cbrt-cube_binary64_2160`
8×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
7×	`pow1_binary64_2185` `associate-/r*_binary64_2068`
6×	`associate-/r/_binary64_2070` `associate-/l*_binary64_2069` `add-log-exp_binary64_2163`
5×	`distribute-lft-out_binary64_2075` `div-exp_binary64_2175` `frac-add_binary64_2132`
4×	`prod-exp_binary64_2173` `associate-r/_binary64_2066` `associate-r*_binary64_2064` `frac-times_binary64_2134`
3×	`cbrt-undiv_binary64_2158` `unswap-sqr_binary64_2092` `div-inv_binary64_2121`
2×	`clear-num_binary64_2123` `associate-*l/_binary64_2067` `distribute-rgt-in_binary64_2074` `associate-+l+_binary64_2057` `1-exp_binary64_2168` `distribute-lft-in_binary64_2073` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`
1×	`pow-prod-down_binary64_2195` `sum-log_binary64_2215` `*-commutative_binary64_2055` `+-commutative_binary64_2054` `pow-flip_binary64_2198` `inv-pow_binary64_2209`

Counts

4 → 128

Calls

4 calls:

15.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
14.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))
5.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))

series92.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
17.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))
16.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))
13.0ms	(/.f64 x (+.f64 x 1))

simplify100.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4975	2244
1	4975	2244

prune155.0ms (6.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	140	3	143

Merged error: 0b

Counts

143 → 3

Compiler

Compiled 3117 to 2095 computations (32.8% saved)

regimes48.0ms (2%)

Compiler: Compiled 488 to 404 computations (17.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	30
1	20	30

end0.0ms (0%)

sample633.0ms (26.3%)

Algorithm

1×

intervals

Results

242.0ms

8000×

body

128

valid

Compiler

Compiled 264 to 220 computations (16.7% saved)

Details

analyze5.0ms (0.2%)

sample13.0ms (0.5%)

simplify99.0ms (4.1%)

prune3.0ms (0.1%)

localize6.0ms (0.3%)

rewrite50.0ms (2.1%)

series58.0ms (2.4%)

simplify74.0ms (3.1%)

prune113.0ms (4.7%)

localize13.0ms (0.5%)

rewrite34.0ms (1.4%)

series131.0ms (5.5%)

simplify77.0ms (3.2%)

prune171.0ms (7.1%)

localize18.0ms (0.7%)

rewrite25.0ms (1%)

series218.0ms (9.1%)

simplify74.0ms (3.1%)

prune133.0ms (5.5%)

localize9.0ms (0.4%)

rewrite50.0ms (2.1%)

series92.0ms (3.8%)

simplify100.0ms (4.1%)

prune155.0ms (6.4%)

regimes48.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample633.0ms (26.3%)

Profiling