Details

analyze380.0ms (8.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56%	4%	10
47.3%	48.7%	4%	11
48.4%	45.8%	5.8%	12
58.6%	32.4%	9%	13
63.4%	27.5%	9%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample15.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	80	valid
1.0ms	25×	body	80	invalid

Compiler

Compiled 15 to 16 computations (-6.7% saved)

simplify200.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (191.0ms)

Iter	Nodes	Cost
0	5200	10

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 15.5b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 x (+.f64 y z))
14.9b	(/.f64 (*.f64 x (+.f64 y z)) z)

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
4×	`pow1_binary64` `associate-r_binary64` `associate-*r/_binary64`
3×	`associate-/r_binary64` `associate-l*_binary64` `times-frac_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

2 → 46

Calls

2 calls:

7.0ms	(/.f64 (*.f64 x (+.f64 y z)) z)
6.0ms	(*.f64 x (+.f64 y z))

series17.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

10.0ms	(/.f64 (*.f64 x (+.f64 y z)) z)
7.0ms	(*.f64 x (+.f64 y z))

simplify101.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4996	553
1	4996	553

prune43.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	45	7	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	7	53

Merged error: 0.0b

Counts

53 → 7

Compiler

Compiled 654 to 208 computations (68.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 z (+.f64 y z))
2.2b	(/.f64 x (/.f64 z (+.f64 y z)))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64`
94×	`*-un-lft-identity_binary64`
62×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
22×	`associate-/r*_binary64`
16×	`distribute-lft-out_binary64`
11×	`associate-/r/_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `div-inv_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
2×	`add-log-exp_binary64` `pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

2 → 123

Calls

2 calls:

8.0ms	(/.f64 x (/.f64 z (+.f64 y z)))
5.0ms	(/.f64 z (+.f64 y z))

series16.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

10.0ms	(/.f64 x (/.f64 z (+.f64 y z)))
6.0ms	(/.f64 z (+.f64 y z))

simplify116.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4957	2384
1	4957	2384

prune70.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	125	4	129
Fresh	5	1	6
Picked	0	1	1
Done	0	0	0
Total	130	6	136

Merged error: 0b

Counts

136 → 6

Compiler

Compiled 1993 to 403 computations (79.8% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 y (/.f64 x z)))
6.5b	(*.f64 y (/.f64 x z))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-l_binary64`
2×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

2 → 43

Calls

2 calls:

7.0ms	(*.f64 y (/.f64 x z))
3.0ms	(+.f64 x (*.f64 y (/.f64 x z)))

series13.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

7.0ms	(+.f64 x (*.f64 y (/.f64 x z)))
5.0ms	(*.f64 y (/.f64 x z))

simplify72.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5165	562

prune30.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	49	6	55

Merged error: 0b

Counts

55 → 6

Compiler

Compiled 635 to 191 computations (69.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 x (sqrt.f64 (/.f64 z (+.f64 z y)))) (sqrt.f64 (/.f64 z (+.f64 y z))))
0.1b	(/.f64 x (sqrt.f64 (/.f64 z (+.f64 z y))))
1.9b	(sqrt.f64 (/.f64 z (+.f64 y z)))
1.9b	(sqrt.f64 (/.f64 z (+.f64 z y)))

rewrite306.0ms (7%)

Algorithm

1×	rewrite-expression-head

Rules

4571×	`times-frac_binary64`
2623×	`*-un-lft-identity_binary64`
2538×	`sqrt-prod_binary64`
1783×	`add-sqr-sqrt_binary64`
1777×	`add-cube-cbrt_binary64`
423×	`distribute-lft-out_binary64`
306×	`associate-/r/_binary64`
165×	`div-inv_binary64`
141×	`flip3-+_binary64` `flip-+_binary64`
71×	`associate-/l*_binary64`
42×	`associate-/r*_binary64`
26×	`sqrt-div_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `rem-sqrt-square_binary64` `div-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64`

Counts

4 → 1693

Calls

4 calls:

52.0ms	(/.f64 (/.f64 x (sqrt.f64 (/.f64 z (+.f64 z y)))) (sqrt.f64 (/.f64 z (+.f64 y z))))
9.0ms	(/.f64 x (sqrt.f64 (/.f64 z (+.f64 z y))))
6.0ms	(sqrt.f64 (/.f64 z (+.f64 y z)))
6.0ms	(sqrt.f64 (/.f64 z (+.f64 z y)))

series80.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt.f64 (/.f64 z (+.f64 z y)))
21.0ms	(/.f64 x (sqrt.f64 (/.f64 z (+.f64 z y))))
19.0ms	(/.f64 (/.f64 x (sqrt.f64 (/.f64 z (+.f64 z y)))) (sqrt.f64 (/.f64 z (+.f64 y z))))
17.0ms	(sqrt.f64 (/.f64 z (+.f64 y z)))

simplify790.0ms (18.1%)

Algorithm

1×	egg-herbie

Counts

1705 → 1705

Iterations

Useful iterations: 0 (148.0ms)

Iter	Nodes	Cost
0	4976	79994
1	4976	79994

prune998.0ms (22.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1705	0	1705
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	1705	6	1711

Merged error: 0b

Counts

1711 → 6

Compiler

Compiled 54260 to 7032 computations (87% saved)

regimes131.0ms (3%)

Compiler: Compiled 186 to 156 computations (16.1% saved)

bsearch30.0ms (0.7%)

Steps

Iters	Range		Point
9	1.952793258948592e+243	8.550068181727294e+248	7.478347114349664e+247
9	6.84022783259995e-173	2.5867909489518894e-167	2.556206366461948e-167

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	45
1	27	45

end0.0ms (0%)

sample873.0ms (20%)

Algorithm

1×

intervals

Results

197.0ms	8000×	body	80	valid
20.0ms	740×	body	80	invalid

Compiler

Compiled 106 to 81 computations (23.6% saved)

Details

analyze380.0ms (8.7%)

sample15.0ms (0.4%)

simplify200.0ms (4.6%)

prune5.0ms (0.1%)

localize5.0ms (0.1%)

rewrite15.0ms (0.3%)

series17.0ms (0.4%)

simplify101.0ms (2.3%)

prune43.0ms (1%)

localize7.0ms (0.2%)

rewrite20.0ms (0.5%)

series16.0ms (0.4%)

simplify116.0ms (2.7%)

prune70.0ms (1.6%)

localize5.0ms (0.1%)

rewrite12.0ms (0.3%)

series13.0ms (0.3%)

simplify72.0ms (1.6%)

prune30.0ms (0.7%)

localize10.0ms (0.2%)

rewrite306.0ms (7%)

series80.0ms (1.8%)

simplify790.0ms (18.1%)

prune998.0ms (22.9%)

regimes131.0ms (3%)

bsearch30.0ms (0.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample873.0ms (20%)

Profiling