Details

analyze999.0ms (13.5%)

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
3.5%	96.2%	0.2%	10
9.8%	89.9%	0.2%	11
14.1%	85.7%	0.2%	12
22.6%	77.1%	0.2%	13
23.7%	76%	0.2%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample28.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	229×	body	128	valid
1.0ms	9×	body	1024	valid
1.0ms	10×	body	512	valid
1.0ms	33×	body	128	invalid
0.0ms	6×	body	256	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify345.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (174.0ms)

Iter	Nodes	Cost
0	4749	19
1	4749	19

prune2.0ms (0%)

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: 15.2b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 z t) y)
1.8b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
11.7b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_16591`
21×	`add-sqr-sqrt_binary64_16613`
11×	`cancel-sign-sub-inv_binary64_16557`
10×	`times-frac_binary64_16597` `add-cbrt-cube_binary64_16627` `add-exp-log_binary64_16629`
9×	`add-cube-cbrt_binary64_16626`
8×	`add-log-exp_binary64_16630`
6×	`distribute-lft-out--_binary64_16543`
5×	`flip--_binary64_16566` `associate-/r_binary64_16535` `associate-l*_binary64_16532` `pow1_binary64_16652` `flip3--_binary64_16595` `difference-of-squares_binary64_16560`
4×	`associate-/r/_binary64_16537` `associate-*l/_binary64_16534`
3×	`associate-r_binary64_16531`
2×	`diff-log_binary64_16683` `prod-exp_binary64_16640` `associate-/l/_binary64_16538` `div-inv_binary64_16588` `cbrt-unprod_binary64_16624` `frac-sub_binary64_16600` `cbrt-undiv_binary64_16625` `div-exp_binary64_16642`
1×	`frac-2neg_binary64_16602` `sub-neg_binary64_16584` `associate-/l_binary64_16536` `associate--l+_binary64_16528` `sum-log_binary64_16682` `-commutative_binary64_16522` `flip3-+_binary64_16594` `distribute-lft-out_binary64_16542` `pow-prod-down_binary64_16662` `clear-num_binary64_16590` `unswap-sqr_binary64_16559` `flip-+_binary64_16565`

Counts

3 → 80

Calls

3 calls:

13.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
10.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
7.0ms	(*.f64 (-.f64 z t) y)

series553.0ms (7.5%)

Counts

3 → 9

Calls

3 calls:

346.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
153.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
53.0ms	(*.f64 (-.f64 z t) y)

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5392	1513

prune485.0ms (6.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	76	13	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	13	90

Merged error: 2.9b

Counts

90 → 13

Compiler

Compiled 10433 to 5775 computations (44.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 a t))
0.5b	(cbrt.f64 (-.f64 a t))
4.8b	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
6.9b	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))

rewrite71.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_16613`
36×	`times-frac_binary64_16597`
35×	`*-un-lft-identity_binary64_16591`
30×	`associate-r_binary64_16531`
27×	`cbrt-prod_binary64_16622`
25×	`add-exp-log_binary64_16629`
23×	`add-cube-cbrt_binary64_16626`
18×	`cbrt-div_binary64_16623` `add-cbrt-cube_binary64_16627`
17×	`associate-l_binary64_16532`
10×	`associate-/r/_binary64_16537` `flip--_binary64_16566` `flip3--_binary64_16595`
9×	`add-log-exp_binary64_16630`
8×	`prod-exp_binary64_16640` `cbrt-unprod_binary64_16624`
7×	`frac-times_binary64_16601` `cbrt-undiv_binary64_16625` `div-exp_binary64_16642`
6×	`distribute-lft-out--_binary64_16543` `unswap-sqr_binary64_16559` `pow1_binary64_16652` `frac-sub_binary64_16600` `difference-of-squares_binary64_16560`
5×	`associate-l/_binary64_16534` `associate-r/_binary64_16533`
3×	`flip3-+_binary64_16594` `flip-+_binary64_16565`
2×	`diff-log_binary64_16683` `div-inv_binary64_16588` `pow1/3_binary64_16673`
1×	`sub-neg_binary64_16584` `associate--l+_binary64_16528` `sum-log_binary64_16682` `*-commutative_binary64_16522` `cancel-sign-sub-inv_binary64_16557` `pow-prod-down_binary64_16662`

Counts

4 → 127

Calls

4 calls:

39.0ms	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
8.0ms	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))
4.0ms	(cbrt.f64 (-.f64 a t))
3.0ms	(cbrt.f64 (-.f64 a t))

series1.1s (14.2%)

Counts

4 → 12

Calls

4 calls:

376.0ms	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))
251.0ms	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
218.0ms	(cbrt.f64 (-.f64 a t))
206.0ms	(cbrt.f64 (-.f64 a t))

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5299	3521

prune231.0ms (3.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	138	14	152

Merged error: 2.9b

Counts

152 → 14

Compiler

Compiled 6032 to 2015 computations (66.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 a t) y)
2.8b	(-.f64 (+.f64 x y) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
11.8b	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))

rewrite116.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

373×	`times-frac_binary64_16597`
313×	`add-sqr-sqrt_binary64_16613`
309×	`*-un-lft-identity_binary64_16591`
152×	`add-cube-cbrt_binary64_16626`
100×	`cancel-sign-sub-inv_binary64_16557`
79×	`difference-of-squares_binary64_16560`
78×	`distribute-lft-out--_binary64_16543`
22×	`associate-/r*_binary64_16535`
14×	`div-inv_binary64_16588`
10×	`associate-/l*_binary64_16536` `add-cbrt-cube_binary64_16627` `add-exp-log_binary64_16629`
8×	`add-log-exp_binary64_16630`
4×	`associate-/l/_binary64_16538` `cbrt-undiv_binary64_16625` `div-exp_binary64_16642`
3×	`flip--_binary64_16566` `pow1_binary64_16652` `flip3--_binary64_16595` `div-sub_binary64_16596`
2×	`associate-/r/_binary64_16537` `diff-log_binary64_16683` `frac-2neg_binary64_16602` `clear-num_binary64_16590` `frac-sub_binary64_16600`
1×	`sub-neg_binary64_16584` `associate--l+_binary64_16528` `sum-log_binary64_16682` `flip3-+_binary64_16594` `distribute-lft-out_binary64_16542` `associate--r-_binary64_16530` `flip-+_binary64_16565`

Counts

3 → 296

Calls

3 calls:

54.0ms	(-.f64 (+.f64 x y) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
14.0ms	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))
7.0ms	(/.f64 (-.f64 a t) y)

series658.0ms (8.9%)

Counts

3 → 9

Calls

3 calls:

361.0ms	(-.f64 (+.f64 x y) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
249.0ms	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))
48.0ms	(/.f64 (-.f64 a t) y)

simplify117.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4991	8689
1	4991	8689

prune379.0ms (5.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	299	6	305
Fresh	8	4	12
Picked	0	1	1
Done	1	0	1
Total	308	11	319

Merged error: 2.4b

Counts

319 → 11

Compiler

Compiled 10341 to 2804 computations (72.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
1.5b	(*.f64 (/.f64 (-.f64 z t) (-.f64 a t)) y)
1.8b	(-.f64 (+.f64 x y) (*.f64 (/.f64 (-.f64 z t) (-.f64 a t)) y))

rewrite46.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64_16613`
71×	`*-un-lft-identity_binary64_16591`
51×	`times-frac_binary64_16597`
31×	`associate-l_binary64_16532`
27×	`add-cube-cbrt_binary64_16626`
22×	`distribute-lft-out--_binary64_16543` `difference-of-squares_binary64_16560`
10×	`add-cbrt-cube_binary64_16627` `add-exp-log_binary64_16629`
8×	`add-log-exp_binary64_16630`
5×	`associate-/r_binary64_16535` `associate-/l_binary64_16536` `pow1_binary64_16652`
4×	`associate-/r/_binary64_16537` `flip--_binary64_16566` `flip3--_binary64_16595`
3×	`associate-l/_binary64_16534` `associate-r*_binary64_16531`
2×	`diff-log_binary64_16683` `prod-exp_binary64_16640` `associate-/l/_binary64_16538` `div-inv_binary64_16588` `unswap-sqr_binary64_16559` `cbrt-unprod_binary64_16624` `frac-sub_binary64_16600` `cbrt-undiv_binary64_16625` `div-exp_binary64_16642`
1×	`frac-2neg_binary64_16602` `sub-neg_binary64_16584` `associate--l+_binary64_16528` `sum-log_binary64_16682` `*-commutative_binary64_16522` `flip3-+_binary64_16594` `cancel-sign-sub-inv_binary64_16557` `pow-prod-down_binary64_16662` `clear-num_binary64_16590` `flip-+_binary64_16565` `div-sub_binary64_16596`

Counts

3 → 118

Calls

3 calls:

15.0ms	(*.f64 (/.f64 (-.f64 z t) (-.f64 a t)) y)
12.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
7.0ms	(-.f64 (+.f64 x y) (*.f64 (/.f64 (-.f64 z t) (-.f64 a t)) y))

series719.0ms (9.7%)

Counts

3 → 9

Calls

3 calls:

367.0ms	(-.f64 (+.f64 x y) (*.f64 (/.f64 (-.f64 z t) (-.f64 a t)) y))
256.0ms	(*.f64 (/.f64 (-.f64 z t) (-.f64 a t)) y)
97.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5359	2303

prune105.0ms (1.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	127	11	138

Merged error: 2.4b

Counts

138 → 11

Compiler

Compiled 2862 to 675 computations (76.4% saved)

regimes147.0ms (2%)

Compiler: Compiled 1105 to 780 computations (29.4% saved)

bsearch46.0ms (0.6%)

Steps

Iters	Range		Point
10	5.534906324290591e+180	8.481134167345447e+191	6.965175920449405e+180
6	-1.4992631748636414e+229	-1.4620585128398298e+228	-8.703056610822989e+228

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	149	51
1	149	51

end0.0ms (0%)

sample1.0s (13.6%)

Algorithm

1×

intervals

Results

296.0ms	6812×	body	128	valid
51.0ms	348×	body	1024	valid
50.0ms	454×	body	512	valid
32.0ms	717×	body	128	invalid
29.0ms	325×	body	256	valid
11.0ms	61×	body	2048	valid

Compiler

Compiled 343 to 219 computations (36.2% saved)

Details

analyze999.0ms (13.5%)

sample28.0ms (0.4%)

simplify345.0ms (4.7%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite37.0ms (0.5%)

series553.0ms (7.5%)

simplify48.0ms (0.6%)

prune485.0ms (6.6%)

localize13.0ms (0.2%)

rewrite71.0ms (1%)

series1.1s (14.2%)

simplify84.0ms (1.1%)

prune231.0ms (3.1%)

localize9.0ms (0.1%)

rewrite116.0ms (1.6%)

series658.0ms (8.9%)

simplify117.0ms (1.6%)

prune379.0ms (5.1%)

localize9.0ms (0.1%)

rewrite46.0ms (0.6%)

series719.0ms (9.7%)

simplify67.0ms (0.9%)

prune105.0ms (1.4%)

regimes147.0ms (2%)

bsearch46.0ms (0.6%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.0s (13.6%)

Profiling