Details

analyze783.0ms (10.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample42.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	189×	body	128	valid
7.0ms	28×	body	2048	valid
5.0ms	256×	pre	128	true
4.0ms	18×	body	1024	valid
2.0ms	12×	body	512	valid
1.0ms	4×	body	4096	valid
1.0ms	5×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify99.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune3.0ms (0%)

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: 15.7b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
1.4b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
13.3b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite55.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_2124`
21×	`add-sqr-sqrt_binary64_2146`
20×	`add-cube-cbrt_binary64_2159`
18×	`times-frac_binary64_2130`
16×	`sqrt-prod_binary64_2140`
8×	`pow1_binary64_2185`
6×	`sqrt-div_binary64_2141` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
4×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
3×	`sqrt-pow1_binary64_2142` `associate-/l*_binary64_2069`
2×	`associate-/r/_binary64_2070` `pow1/2_binary64_2204` `associate-*r/_binary64_2066`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `sum-log_binary64_2215` `distribute-lft-out_binary64_2075` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 81

Calls

4 calls:

15.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
14.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
10.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
9.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))

series508.0ms (6.9%)

Counts

4 → 51

Calls

4 calls:

172.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
135.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
120.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
81.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))

Compiler

Compiled 1453 to 1349 computations (7.2% saved)

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5051	2997

prune406.0ms (5.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	118	14	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	14	133

Merged error: 15.3b

Counts

133 → 14

Compiler

Compiled 3324 to 2219 computations (33.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
0.2b	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
4.3b	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
13.3b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64_2146`
40×	`times-frac_binary64_2130`
36×	`*-un-lft-identity_binary64_2124`
34×	`add-cube-cbrt_binary64_2159`
26×	`sqrt-prod_binary64_2140`
24×	`associate-r_binary64_2064`
17×	`add-exp-log_binary64_2162`
11×	`add-cbrt-cube_binary64_2160`
9×	`pow1_binary64_2185`
6×	`sqrt-div_binary64_2141` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163`
5×	`unswap-sqr_binary64_2092`
4×	`associate-/r/_binary64_2070` `prod-exp_binary64_2173` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-exp_binary64_2175`
3×	`associate-/l_binary64_2069` `associate-l*_binary64_2065` `pow-flip_binary64_2198`
2×	`cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142` `pow1/2_binary64_2204` `1-exp_binary64_2168` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157` `rec-exp_binary64_2174`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `un-div-inv_binary64_2122` `sum-log_binary64_2215` `-commutative_binary64_2055` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `associate-r/_binary64_2066` `inv-pow_binary64_2209` `frac-2neg_binary64_2135`

Counts

4 → 122

Calls

4 calls:

16.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
3.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))

series429.0ms (5.9%)

Counts

4 → 51

Calls

4 calls:

133.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
125.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
89.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
82.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))

Compiler

Compiled 1436 to 1316 computations (8.4% saved)

simplify100.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4952	3551
1	4952	3551

prune259.0ms (3.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	168	5	173
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	172	15	187

Merged error: 15.3b

Counts

187 → 15

Compiler

Compiled 4662 to 3214 computations (31.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
0.2b	(.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2))
4.3b	(+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2)))
13.6b	(pow.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)) -1/2)

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2146`
10×	`add-exp-log_binary64_2162`
9×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
8×	`add-log-exp_binary64_2163`
7×	`unpow-prod-down_binary64_2203` `associate-r_binary64_2064`
6×	`add-cbrt-cube_binary64_2160`
5×	`pow1_binary64_2185`
3×	`unswap-sqr_binary64_2092` `pow-unpow_binary64_2201` `associate-l_binary64_2065` `prod-exp_binary64_2173` `sqr-pow_binary64_2096`
2×	`sum-log_binary64_2215` `pow-exp_binary64_2192` `+-commutative_binary64_2054` `pow-to-exp_binary64_2193` `flip3-+_binary64_2127` `flip-+_binary64_2098`
1×	`pow-pow_binary64_2196` `*-commutative_binary64_2055` `cbrt-unprod_binary64_2157`

Counts

4 → 64

Calls

4 calls:

10.0ms	(.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2))
7.0ms	(pow.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)) -1/2)
6.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
4.0ms	(+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2)))

series471.0ms (6.4%)

Counts

4 → 44

Calls

4 calls:

156.0ms	(pow.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)) -1/2)
119.0ms	(.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2))
109.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
86.0ms	(+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2)))

Compiler

Compiled 1298 to 1214 computations (6.5% saved)

simplify63.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5312	2011

prune144.0ms (2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Merged error: 15.3b

Counts

123 → 15

Compiler

Compiled 2755 to 1889 computations (31.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(cbrt.f64 (pow.f64 (+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)) -1/2))) 3))
0.2b	(.f64 x (pow.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)) -1/2))
4.3b	(+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)) -1/2)))
13.6b	(pow.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)) -1/2)

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_2146`
12×	`add-cube-cbrt_binary64_2159` `cbrt-prod_binary64_2155` `*-un-lft-identity_binary64_2124`
10×	`unpow-prod-down_binary64_2203` `add-exp-log_binary64_2162`
7×	`associate-r_binary64_2064`
6×	`add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
5×	`pow1_binary64_2185`
4×	`sqr-pow_binary64_2096`
3×	`unswap-sqr_binary64_2092` `pow-unpow_binary64_2201` `associate-l_binary64_2065` `prod-exp_binary64_2173` `cube-prod_binary64_2152`
2×	`cbrt-div_binary64_2156` `pow-exp_binary64_2192` `pow-to-exp_binary64_2193` `flip3-+_binary64_2127` `cube-div_binary64_2153` `flip-+_binary64_2098`
1×	`unpow3_binary64_2190` `cube-mult_binary64_2154` `pow-pow_binary64_2196` `sum-log_binary64_2215` `rem-cbrt-cube_binary64_2148` `*-commutative_binary64_2055` `pow1/3_binary64_2206` `+-commutative_binary64_2054` `cbrt-unprod_binary64_2157`

Counts

4 → 76

Calls

4 calls:

11.0ms	(.f64 x (pow.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)) -1/2))
7.0ms	(pow.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)) -1/2)
4.0ms	(cbrt.f64 (pow.f64 (+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)) -1/2))) 3))
4.0ms	(+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)) -1/2)))

series451.0ms (6.2%)

Counts

4 → 41

Calls

4 calls:

162.0ms	(pow.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)) -1/2)
118.0ms	(.f64 x (pow.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)) -1/2))
85.0ms	(+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)) -1/2)))
85.0ms	(cbrt.f64 (pow.f64 (+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)) -1/2))) 3))

Compiler

Compiled 1324 to 1252 computations (5.4% saved)

simplify63.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5071	2565

prune163.0ms (2.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	112	5	117
Fresh	4	10	14
Picked	0	1	1
Done	0	0	0
Total	116	16	132

Merged error: 15.3b

Counts

132 → 16

Compiler

Compiled 2879 to 2035 computations (29.3% saved)

regimes741.0ms (10.1%)

Compiler: Compiled 10492 to 8184 computations (22% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	29
1	23	29

end0.0ms (0%)

sample2.3s (31.4%)

Algorithm

1×

intervals

Results

313.0ms	6109×	body	128	valid
204.0ms	757×	body	2048	valid
150.0ms	8000×	pre	128	true
106.0ms	519×	body	1024	valid
85.0ms	261×	body	4096	valid
37.0ms	232×	body	512	valid
12.0ms	122×	body	256	valid

Compiler

Compiled 1492 to 1159 computations (22.3% saved)

Details

analyze783.0ms (10.7%)

sample42.0ms (0.6%)

simplify99.0ms (1.4%)

prune3.0ms (0%)

localize12.0ms (0.2%)

rewrite55.0ms (0.7%)

series508.0ms (6.9%)

simplify71.0ms (1%)

prune406.0ms (5.5%)

localize13.0ms (0.2%)

rewrite49.0ms (0.7%)

series429.0ms (5.9%)

simplify100.0ms (1.4%)

prune259.0ms (3.5%)

localize14.0ms (0.2%)

rewrite32.0ms (0.4%)

series471.0ms (6.4%)

simplify63.0ms (0.9%)

prune144.0ms (2%)

localize16.0ms (0.2%)

rewrite33.0ms (0.4%)

series451.0ms (6.2%)

simplify63.0ms (0.9%)

prune163.0ms (2.2%)

regimes741.0ms (10.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (31.4%)

Profiling