Details

analyze1.2s (18.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

Compiler

Compiled 15 to 13 computations (13.3% saved)

sample34.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
4.0ms	88×	body	128	nan
1.0ms	24×	body	128	invalid

Compiler

Compiled 29 to 30 computations (-3.4% saved)

simplify16.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	175	21
1	175	21

prune3.0ms (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: 23.2b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 z z) (.f64 t a))
6.4b	(.f64 (.f64 x y) z)
8.5b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
26.0b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
9×	`sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
4×	`sqrt-div_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
2×	`associate-/r/_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 76

Calls

4 calls:

11.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
6.0ms	(.f64 (.f64 x y) z)
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series479.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

269.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
113.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
50.0ms	(-.f64 (.f64 z z) (.f64 t a))
47.0ms	(.f64 (.f64 x y) z)

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5243	1472

prune284.0ms (4.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	11	89

Merged error: 3.5b

Counts

89 → 11

Compiler

Compiled 5734 to 2800 computations (51.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
0.4b	(-.f64 (.f64 z z) (.f64 t a))
3.1b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
26.0b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64`
47×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
33×	`sqrt-prod_binary64`
25×	`associate-/r*_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64`
4×	`div-inv_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-/r/_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 132

Calls

4 calls:

12.0ms	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
8.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series519.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

246.0ms	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
116.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
102.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
54.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5034	3422

prune335.0ms (5.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	145	10	155

Merged error: 3.0b

Counts

155 → 10

Compiler

Compiled 7683 to 3366 computations (56.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.4b	(-.f64 (.f64 z z) (.f64 t a))
3.2b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
26.0b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
34×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
24×	`associate-r_binary64` `sqrt-prod_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
3×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
2×	`div-inv_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-r/_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 112

Calls

4 calls:

15.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
7.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series481.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

244.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
98.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
83.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
56.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5283	2521

prune109.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	124	10	134

Merged error: 3.0b

Counts

134 → 10

Compiler

Compiled 2901 to 597 computations (79.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
0.4b	(-.f64 (.f64 z z) (.f64 t a))
3.2b	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
26.0b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite82.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

258×	`times-frac_binary64`
143×	`add-sqr-sqrt_binary64`
142×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
71×	`associate-r_binary64`
66×	`sqrt-prod_binary64`
45×	`add-exp-log_binary64`
30×	`add-cbrt-cube_binary64`
22×	`associate-/r*_binary64`
15×	`prod-exp_binary64`
12×	`div-exp_binary64`
11×	`pow1_binary64`
9×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `div-inv_binary64`
6×	`add-log-exp_binary64` `rec-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/l*_binary64`
2×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-r/_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 237

Calls

4 calls:

26.0ms	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
11.0ms	(/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series488.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

252.0ms	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
98.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
89.0ms	(/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
49.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify111.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4966	6249
1	4966	6249

prune196.0ms (3.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	249	10	259

Merged error: 3.0b

Counts

259 → 10

Compiler

Compiled 6365 to 1229 computations (80.7% saved)

regimes283.0ms (4.5%)

Compiler: Compiled 927 to 906 computations (2.3% saved)

bsearch128.0ms (2.1%)

Steps

Iters	Range		Point
9	1.3965138984018186e+119	1.5547054322034453e+126	3.819796553361413e+121
10	1.2562995004500699e+42	1.3329189308007037e+57	1.2732782527458712e+42
8	-3.0194332596060814e-247	-8.891433069464272e-252	-8.759496516960208e-250
9	-1.3594911010482564e+85	-6.610135653059698e+79	-2.9064435797870745e+82

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	97
1	84	97

end0.0ms (0%)

sample1.2s (18.7%)

Algorithm

1×

intervals

Results

436.0ms	8000×	body	128	valid
108.0ms	2245×	body	128	nan
44.0ms	859×	body	128	invalid

Compiler

Compiled 230 to 177 computations (23% saved)

Details

analyze1.2s (18.6%)

sample34.0ms (0.5%)

simplify16.0ms (0.3%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

rewrite31.0ms (0.5%)

series479.0ms (7.7%)

simplify56.0ms (0.9%)

prune284.0ms (4.6%)

localize10.0ms (0.2%)

rewrite43.0ms (0.7%)

series519.0ms (8.3%)

simplify56.0ms (0.9%)

prune335.0ms (5.4%)

localize13.0ms (0.2%)

rewrite42.0ms (0.7%)

series481.0ms (7.7%)

simplify83.0ms (1.3%)

prune109.0ms (1.8%)

localize12.0ms (0.2%)

rewrite82.0ms (1.3%)

series488.0ms (7.8%)

simplify111.0ms (1.8%)

prune196.0ms (3.1%)

regimes283.0ms (4.5%)

bsearch128.0ms (2.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.2s (18.7%)

Profiling