Details

analyze2.0ms (0.1%)

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)

sample23.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms	194×	body	128	valid
4.0ms	256×	pre	128	true
3.0ms	25×	body	1024	valid
2.0ms	24×	body	512	valid
1.0ms	12×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify295.0ms (7.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	4878	19
1	4878	19

prune2.0ms (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: 16.8b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
3.0b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_2099`
26×	`add-sqr-sqrt_binary64_2120`
25×	`times-frac_binary64_2105`
19×	`distribute-lft-out_binary64_2052`
14×	`add-cube-cbrt_binary64_2131`
6×	`difference-of-squares_binary64_2068` `distribute-lft-out--_binary64_2053`
5×	`associate-/r_binary64_2045` `associate-/l_binary64_2046`
4×	`add-cbrt-cube_binary64_2132` `add-log-exp_binary64_2135` `add-exp-log_binary64_2134`
2×	`flip3-+_binary64_2102` `pow1_binary64_2157` `associate-/l/_binary64_2048` `associate-/r/_binary64_2047` `div-sub_binary64_2104` `flip-+_binary64_2073`
1×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `sum-log_binary64_2187` `frac-2neg_binary64_2110` `+-commutative_binary64_2031` `flip3--_binary64_2103` `flip--_binary64_2074` `clear-num_binary64_2098` `div-inv_binary64_2096` `associate-+l-_binary64_2036`

Counts

2 → 65

Calls

2 calls:

21.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
12.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series160.0ms (4%)

Counts

2 → 6

Calls

2 calls:

97.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
63.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify63.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5354	1488

prune92.0ms (2.3%)

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: 15.8b

Counts

72 → 10

Compiler

Compiled 1722 to 963 computations (44.1% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
3.0b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite44.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_2099`
34×	`add-sqr-sqrt_binary64_2120`
33×	`times-frac_binary64_2105`
24×	`distribute-lft-out_binary64_2052`
23×	`add-cube-cbrt_binary64_2131`
10×	`associate-/r*_binary64_2045`
7×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
6×	`associate-/l*_binary64_2046`
5×	`add-log-exp_binary64_2135`
4×	`difference-of-squares_binary64_2068` `associate-/r/_binary64_2047`
3×	`pow1_binary64_2157`
2×	`cbrt-undiv_binary64_2130` `flip3-+_binary64_2102` `div-exp_binary64_2147` `frac-2neg_binary64_2110` `clear-num_binary64_2098` `div-inv_binary64_2096` `difference-of-sqr-1_binary64_2069` `flip-+_binary64_2073`
1×	`sub-neg_binary64_2092` `flip3--_binary64_2103` `flip--_binary64_2074` `distribute-lft-out--_binary64_2053` `diff-log_binary64_2188`

Counts

3 → 92

Calls

3 calls:

16.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
11.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

series225.0ms (5.7%)

Counts

3 → 9

Calls

3 calls:

94.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
67.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
64.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

simplify63.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4923	1705
1	4923	1705

prune139.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	96	5	101
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	105	6	111

Merged error: 4.1b

Counts

111 → 6

Compiler

Compiled 2738 to 1621 computations (40.8% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
3.0b	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
3.0b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite65.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`*-un-lft-identity_binary64_2099`
48×	`add-sqr-sqrt_binary64_2120`
36×	`times-frac_binary64_2105`
26×	`add-cube-cbrt_binary64_2131`
24×	`distribute-lft-out_binary64_2052`
11×	`log-pow_binary64_2185`
10×	`associate-/r*_binary64_2045` `exp-prod_binary64_2148`
8×	`difference-of-squares_binary64_2068` `add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
6×	`add-log-exp_binary64_2135` `associate-/l*_binary64_2046`
5×	`pow1_binary64_2157`
4×	`log-prod_binary64_2182` `associate-/r/_binary64_2047` `difference-of-sqr-1_binary64_2069`
2×	`sub-neg_binary64_2092` `cbrt-undiv_binary64_2130` `flip3-+_binary64_2102` `div-exp_binary64_2147` `frac-2neg_binary64_2110` `clear-num_binary64_2098` `div-inv_binary64_2096` `distribute-lft-out--_binary64_2053` `flip-+_binary64_2073`
1×	`log-div_binary64_2183` `flip3--_binary64_2103` `flip--_binary64_2074` `rem-log-exp_binary64_2137` `exp-sum_binary64_2142` `exp-diff_binary64_2144` `diff-log_binary64_2188`

Counts

4 → 116

Calls

4 calls:

18.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
9.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
9.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))

series404.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
108.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
63.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
55.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))

simplify67.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4995	2160
1	4995	2160

prune175.0ms (4.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	128	6	134

Merged error: 4.1b

Counts

134 → 6

Compiler

Compiled 3682 to 2280 computations (38.1% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 beta)
0.6b	(cbrt.f64 beta)
3.0b	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
3.0b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite46.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_2120`
16×	`*-un-lft-identity_binary64_2099`
11×	`log-pow_binary64_2185`
10×	`exp-prod_binary64_2148`
8×	`difference-of-squares_binary64_2068` `add-cube-cbrt_binary64_2131`
6×	`times-frac_binary64_2105` `add-log-exp_binary64_2135` `cbrt-prod_binary64_2127`
5×	`pow1_binary64_2157`
4×	`log-prod_binary64_2182` `add-cbrt-cube_binary64_2132` `difference-of-sqr-1_binary64_2069` `add-exp-log_binary64_2134`
2×	`sub-neg_binary64_2092` `pow1/3_binary64_2178` `distribute-lft-out--_binary64_2053`
1×	`log-div_binary64_2183` `flip3--_binary64_2103` `flip--_binary64_2074` `rem-log-exp_binary64_2137` `exp-sum_binary64_2142` `exp-diff_binary64_2144` `diff-log_binary64_2188`

Counts

4 → 64

Calls

4 calls:

20.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
1.0ms	(cbrt.f64 beta)
1.0ms	(cbrt.f64 beta)

series624.0ms (15.6%)

Counts

4 → 12

Calls

4 calls:

191.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
174.0ms	(cbrt.f64 beta)
153.0ms	(cbrt.f64 beta)
105.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)

simplify88.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4860	1102
1	4860	1102

prune240.0ms (6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	74	8	82

Merged error: 4.1b

Counts

82 → 8

Compiler

Compiled 2560 to 1361 computations (46.8% saved)

regimes85.0ms (2.1%)

Compiler: Compiled 468 to 338 computations (27.8% saved)

bsearch23.0ms (0.6%)

Steps

Iters	Range		Point
8	1358.4816071781802	4310309.915128441	199951.55748759874

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	197	99
1	197	99

end0.0ms (0%)

sample964.0ms (24.2%)

Algorithm

1×

intervals

Results

196.0ms	5947×	body	128	valid
142.0ms	8000×	pre	128	true
132.0ms	1030×	body	1024	valid
55.0ms	609×	body	512	valid
21.0ms	334×	body	256	valid
13.0ms	80×	body	2048	valid

Compiler

Compiled 316 to 223 computations (29.4% saved)

Details

analyze2.0ms (0.1%)

sample23.0ms (0.6%)

simplify295.0ms (7.4%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

rewrite39.0ms (1%)

series160.0ms (4%)

simplify63.0ms (1.6%)

prune92.0ms (2.3%)

localize11.0ms (0.3%)

rewrite44.0ms (1.1%)

series225.0ms (5.7%)

simplify63.0ms (1.6%)

prune139.0ms (3.5%)

localize16.0ms (0.4%)

rewrite65.0ms (1.6%)

series404.0ms (10.1%)

simplify67.0ms (1.7%)

prune175.0ms (4.4%)

localize17.0ms (0.4%)

rewrite46.0ms (1.1%)

series624.0ms (15.6%)

simplify88.0ms (2.2%)

prune240.0ms (6%)

regimes85.0ms (2.1%)

bsearch23.0ms (0.6%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample964.0ms (24.2%)

Profiling