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)

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms	189×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	24×	body	1280	valid
3.0ms	24×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	7×	body	160	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify316.0ms (8.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (306.0ms)

Iter	Nodes	Cost
0	5019	19

prune7.0ms (0.2%)

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: 15.8b

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))
2.1b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
19×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`associate-/r_binary64` `associate-/l_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1_binary64` `associate-/r/_binary64` `div-sub_binary64` `flip-+_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

2 → 65

Calls

2 calls:

18.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series21.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

13.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
8.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify88.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	6349	1488

prune79.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 15.1b

Counts

72 → 11

Compiler

Compiled 1759 to 990 computations (43.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
2.1b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite64.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
24×	`distribute-lft-out_binary64` `add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`
10×	`associate-/r*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64`
4×	`pow1_binary64` `diff-log_binary64` `associate-/r/_binary64` `distribute-lft-out--_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-sub_binary64`
1×	`associate--r+_binary64` `associate--r-_binary64`

Counts

4 → 112

Calls

4 calls:

30.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series41.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
12.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
7.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
7.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

simplify82.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4923	2582
1	4923	2582

prune137.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	116	8	124
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	126	9	135

Merged error: 3.5b

Counts

135 → 9

Compiler

Compiled 3529 to 2106 computations (40.3% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
0.0b	(/.f64 (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
0.1b	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
2.0b	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)

rewrite106.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

200×	`add-sqr-sqrt_binary64`
147×	`*-un-lft-identity_binary64`
142×	`times-frac_binary64`
60×	`add-cube-cbrt_binary64` `difference-of-squares_binary64`
51×	`unpow-prod-down_binary64` `cube-prod_binary64`
30×	`difference-of-sqr-1_binary64`
28×	`distribute-lft-out_binary64`
22×	`associate-/l*_binary64`
21×	`associate-l_binary64`
16×	`sqr-pow_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/r/_binary64`
7×	`pow1_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
5×	`distribute-lft-out--_binary64`
4×	`associate-r_binary64` `div-inv_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `flip--_binary64` `frac-times_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `cube-div_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `unpow3_binary64` `associate-l/_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 247

Calls

4 calls:

33.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
25.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
23.0ms	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)
10.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)

series92.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
22.0ms	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)
17.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
15.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))

simplify166.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5026	12184

prune697.0ms (18.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	257	2	259
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	259	9	268

Merged error: 3.5b

Counts

268 → 9

Compiler

Compiled 15061 to 9383 computations (37.7% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.8b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.8b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.8b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
2.1b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite34.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
15×	`cbrt-prod_binary64`
9×	`distribute-lft-out_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
3×	`flip3-+_binary64` `pow1/3_binary64` `times-frac_binary64` `flip-+_binary64`
2×	`difference-of-sqr-1_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 63

Calls

4 calls:

14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))

series66.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
17.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
17.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify100.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4938	1406
1	4938	1406

prune94.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	75	9	84

Merged error: 3.5b

Counts

84 → 9

Compiler

Compiled 3636 to 1984 computations (45.4% saved)

regimes96.0ms (2.5%)

Compiler: Compiled 850 to 584 computations (31.3% saved)

bsearch15.0ms (0.4%)

Steps

Iters	Range		Point
8	6.523692746418254e+25	1.0827483834328634e+30	6.629639534794314e+25

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	235	111
1	235	111

end0.0ms (0%)

sample1.4s (36.3%)

Algorithm

1×

intervals

Results

187.0ms	5879×	body	80	valid
132.0ms	822×	body	1280	valid
124.0ms	8000×	pre	80	true
90.0ms	738×	body	640	valid
32.0ms	350×	body	320	valid
13.0ms	211×	body	160	valid

Compiler

Compiled 515 to 354 computations (31.3% saved)

Details

analyze2.0ms (0.1%)

sample24.0ms (0.6%)

simplify316.0ms (8.3%)

prune7.0ms (0.2%)

localize8.0ms (0.2%)

rewrite32.0ms (0.8%)

series21.0ms (0.5%)

simplify88.0ms (2.3%)

prune79.0ms (2.1%)

localize13.0ms (0.3%)

rewrite64.0ms (1.7%)

series41.0ms (1.1%)

simplify82.0ms (2.1%)

prune137.0ms (3.6%)

localize17.0ms (0.5%)

rewrite106.0ms (2.8%)

series92.0ms (2.4%)

simplify166.0ms (4.4%)

prune697.0ms (18.3%)

localize20.0ms (0.5%)

rewrite34.0ms (0.9%)

series66.0ms (1.7%)

simplify100.0ms (2.6%)

prune94.0ms (2.5%)

regimes96.0ms (2.5%)

bsearch15.0ms (0.4%)

simplify7.0ms (0.2%)

end0.0ms (0%)

sample1.4s (36.3%)

Profiling