Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 20 to 16 computations (20% saved)

sample51.0ms (0.6%)

Algorithm

1×

intervals

Results

14.0ms	256×	pre	128	true
11.0ms	189×	body	128	valid
9.0ms	38×	body	1024	valid
4.0ms	20×	body	512	valid
1.0ms	8×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify470.0ms (5.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (347.0ms)

Iter	Nodes	Cost
0	5018	19

prune5.0ms (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: 16.6b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
1.9b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite49.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_2124`
26×	`add-sqr-sqrt_binary64_2146`
25×	`times-frac_binary64_2130`
19×	`distribute-lft-out_binary64_2075`
14×	`add-cube-cbrt_binary64_2159`
6×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
5×	`associate-/l_binary64_2069` `associate-/r_binary64_2068`
4×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
2×	`associate-/r/_binary64_2070` `pow1_binary64_2185` `flip3-+_binary64_2127` `div-sub_binary64_2129` `flip-+_binary64_2098` `associate-/l/_binary64_2071`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `associate-+l-_binary64_2059` `sum-log_binary64_2215` `+-commutative_binary64_2054` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

2 → 65

Calls

2 calls:

33.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series85.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

45.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
40.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify99.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	6172	1488

prune119.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 15.9b

Counts

72 → 10

Compiler

Compiled 1705 to 960 computations (43.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
1.9b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite89.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`*-un-lft-identity_binary64_2124`
54×	`add-sqr-sqrt_binary64_2146`
37×	`times-frac_binary64_2130`
27×	`add-cube-cbrt_binary64_2159`
24×	`distribute-lft-out_binary64_2075`
16×	`cancel-sign-sub-inv_binary64_2090`
11×	`add-log-exp_binary64_2163`
10×	`difference-of-squares_binary64_2093` `associate-/r*_binary64_2068`
8×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
6×	`associate-/l*_binary64_2069`
5×	`distribute-lft-out--_binary64_2076`
4×	`associate-/r/_binary64_2070` `pow1_binary64_2185` `diff-log_binary64_2216` `associate--r+_binary64_2060` `difference-of-sqr-1_binary64_2094`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `sub-neg_binary64_2117`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `frac-sub_binary64_2133` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`
1×	`associate--r-_binary64_2063`

Counts

4 → 128

Calls

4 calls:

37.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
10.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

series168.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
44.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
29.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
27.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

simplify111.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4935	2917
1	4935	2917

prune205.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	135	5	140
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	145	5	150

Merged error: 2.5b

Counts

150 → 5

Compiler

Compiled 3864 to 2294 computations (40.6% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
0.1b	(/.f64 (-.f64 (+.f64 beta (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))) (.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))))
1.9b	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)
9.5b	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

rewrite182.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`*-un-lft-identity_binary64_2124`
54×	`add-sqr-sqrt_binary64_2146`
39×	`times-frac_binary64_2130`
27×	`unpow-prod-down_binary64_2203` `add-cube-cbrt_binary64_2159` `cube-prod_binary64_2152`
24×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
21×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
18×	`distribute-lft-out_binary64_2075` `associate-/l/_binary64_2071`
16×	`frac-sub_binary64_2133`
14×	`frac-times_binary64_2134`
13×	`associate-*r/_binary64_2066`
12×	`difference-of-squares_binary64_2093` `associate-/r/_binary64_2070`
10×	`pow1_binary64_2185`
8×	`flip--_binary64_2099` `flip3--_binary64_2128`
7×	`associate-*l/_binary64_2067`
6×	`add-log-exp_binary64_2163` `prod-exp_binary64_2173` `difference-of-sqr-1_binary64_2094` `cbrt-unprod_binary64_2157`
4×	`cbrt-undiv_binary64_2158` `sqr-pow_binary64_2096` `distribute-rgt-in_binary64_2074` `div-exp_binary64_2175` `distribute-lft-in_binary64_2073`
3×	`pow-prod-down_binary64_2195` `cancel-sign-sub-inv_binary64_2090` `pow-unpow_binary64_2201` `associate-/l_binary64_2069` `associate-l*_binary64_2065` `div-inv_binary64_2121`
2×	`pow-exp_binary64_2192` `rem-cube-cbrt_binary64_2147`
1×	`unpow3_binary64_2190` `clear-num_binary64_2123` `cube-mult_binary64_2154` `pow-pow_binary64_2196` `distribute-lft-out--_binary64_2076` `-commutative_binary64_2055` `associate-/r_binary64_2068` `diff-log_binary64_2216` `sub-neg_binary64_2117` `pow-to-exp_binary64_2193` `associate-r_binary64_2064` `cube-div_binary64_2153` `div-sub_binary64_2129` `frac-2neg_binary64_2135`

Counts

4 → 172

Calls

4 calls:

55.0ms	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)
35.0ms	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
26.0ms	(/.f64 (-.f64 (+.f64 beta (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))) (.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))))
10.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)

series679.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

414.0ms	(/.f64 (-.f64 (+.f64 beta (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))) (.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))))
116.0ms	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
86.0ms	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)
63.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)

simplify125.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5032	8516

prune1.0s (12.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	180	4	184
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	182	7	189

Merged error: 2.5b

Counts

189 → 7

Compiler

Compiled 17006 to 9984 computations (41.3% saved)

localize31.0ms (0.4%)

Local error

Found 4 expressions with local error:

9.5b	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)))
14.0b	(cbrt.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))))
14.0b	(cbrt.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))))
14.0b	(cbrt.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))))

rewrite122.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`associate-*r/_binary64_2066`
15×	`cbrt-div_binary64_2156`
13×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`pow1_binary64_2185`
8×	`flip3-+_binary64_2127` `frac-times_binary64_2134` `flip-+_binary64_2098`
5×	`add-cube-cbrt_binary64_2159` `prod-exp_binary64_2173` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124` `cbrt-unprod_binary64_2157`
4×	`add-log-exp_binary64_2163` `associate-*l/_binary64_2067` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
3×	`pow-prod-down_binary64_2195` `associate-l_binary64_2065` `pow1/3_binary64_2206` `cbrt-prod_binary64_2155`
1×	`cbrt-undiv_binary64_2158` `-commutative_binary64_2055` `associate-r*_binary64_2064` `div-exp_binary64_2175`

Counts

4 → 71

Calls

4 calls:

27.0ms	(cbrt.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))))
25.0ms	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)))
24.0ms	(cbrt.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))))
23.0ms	(cbrt.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))))

series964.0ms (12%)

Counts

4 → 12

Calls

4 calls:

300.0ms	(cbrt.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))))
298.0ms	(cbrt.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))))
292.0ms	(cbrt.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))))
73.0ms	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)))

simplify51.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5175	2842

prune456.0ms (5.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	83	7	90

Merged error: 2.5b

Counts

90 → 7

Compiler

Compiled 9809 to 5765 computations (41.2% saved)

regimes679.0ms (8.5%)

Compiler: Compiled 11735 to 7742 computations (34% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	230	87
1	230	87

end0.0ms (0%)

sample2.2s (27.1%)

Algorithm

1×

intervals

Results

194.0ms	5989×	body	128	valid
139.0ms	8000×	pre	128	true
130.0ms	1018×	body	1024	valid
57.0ms	603×	body	512	valid
18.0ms	297×	body	256	valid
14.0ms	93×	body	2048	valid

Compiler

Compiled 2411 to 1594 computations (33.9% saved)

Details

analyze3.0ms (0%)

sample51.0ms (0.6%)

simplify470.0ms (5.9%)

prune5.0ms (0.1%)

localize16.0ms (0.2%)

rewrite49.0ms (0.6%)

series85.0ms (1.1%)

simplify99.0ms (1.2%)

prune119.0ms (1.5%)

localize19.0ms (0.2%)

rewrite89.0ms (1.1%)

series168.0ms (2.1%)

simplify111.0ms (1.4%)

prune205.0ms (2.6%)

localize19.0ms (0.2%)

rewrite182.0ms (2.3%)

series679.0ms (8.5%)

simplify125.0ms (1.6%)

prune1.0s (12.8%)

localize31.0ms (0.4%)

rewrite122.0ms (1.5%)

series964.0ms (12%)

simplify51.0ms (0.6%)

prune456.0ms (5.7%)

regimes679.0ms (8.5%)

bsearch4.0ms (0.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.2s (27.1%)

Profiling