Details

analyze1.0s (11.9%)

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)

sample27.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	214×	body	128	valid
2.0ms	17×	body	512	valid
1.0ms	17×	body	256	valid
1.0ms	7×	body	1024	valid
1.0ms	25×	body	128	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify230.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	4872	19
1	4872	19

prune8.0ms (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: 15.3b

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)
3.0b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
10.5b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_17810`
21×	`add-sqr-sqrt_binary64_17832`
11×	`cancel-sign-sub-inv_binary64_17776`
10×	`add-exp-log_binary64_17848` `add-cbrt-cube_binary64_17846` `times-frac_binary64_17816`
9×	`add-cube-cbrt_binary64_17845`
8×	`add-log-exp_binary64_17849`
6×	`distribute-lft-out--_binary64_17762`
5×	`associate-/r_binary64_17754` `flip3--_binary64_17814` `flip--_binary64_17785` `difference-of-squares_binary64_17779` `associate-l*_binary64_17751` `pow1_binary64_17871`
4×	`associate-/r/_binary64_17756` `associate-*l/_binary64_17753`
3×	`associate-r_binary64_17750`
2×	`cbrt-unprod_binary64_17843` `prod-exp_binary64_17859` `div-inv_binary64_17807` `div-exp_binary64_17861` `cbrt-undiv_binary64_17844` `diff-log_binary64_17902` `frac-sub_binary64_17819` `associate-/l/_binary64_17757`
1×	`unswap-sqr_binary64_17778` `pow-prod-down_binary64_17881` `sum-log_binary64_17901` `clear-num_binary64_17809` `-commutative_binary64_17741` `associate-/l_binary64_17755` `flip-+_binary64_17784` `flip3-+_binary64_17813` `distribute-lft-out_binary64_17761` `associate--l+_binary64_17747` `frac-2neg_binary64_17821` `sub-neg_binary64_17803`

Counts

3 → 80

Calls

3 calls:

12.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
9.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
7.0ms	(*.f64 (-.f64 z t) y)

series1.0s (11.8%)

Counts

3 → 70

Calls

3 calls:

463.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
446.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
104.0ms	(*.f64 (-.f64 z t) y)

Compiler

Compiled 2116 to 1602 computations (24.3% saved)

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4994	2687
1	4994	2687

prune149.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	142	8	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	8	151

Merged error: 0.5b

Counts

151 → 8

Compiler

Compiled 2740 to 584 computations (78.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 y (/.f64 t (/.f64 (-.f64 a t) y))) (/.f64 z (/.f64 (-.f64 a t) y)))
6.3b	(+.f64 y (/.f64 t (/.f64 (-.f64 a t) y)))
7.2b	(/.f64 z (/.f64 (-.f64 a t) y))
11.4b	(/.f64 t (/.f64 (-.f64 a t) y))

rewrite142.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

339×	`times-frac_binary64_17816`
238×	`add-sqr-sqrt_binary64_17832`
237×	`*-un-lft-identity_binary64_17810`
163×	`add-cube-cbrt_binary64_17845`
62×	`cancel-sign-sub-inv_binary64_17776`
38×	`associate-/r*_binary64_17754`
36×	`difference-of-squares_binary64_17779`
35×	`distribute-lft-out--_binary64_17762`
14×	`div-inv_binary64_17807` `add-exp-log_binary64_17848` `add-cbrt-cube_binary64_17846`
11×	`add-log-exp_binary64_17849`
7×	`associate-/r/_binary64_17756`
6×	`associate-/l*_binary64_17755` `div-exp_binary64_17861` `cbrt-undiv_binary64_17844`
4×	`pow1_binary64_17871`
2×	`sum-log_binary64_17901` `clear-num_binary64_17809` `flip-+_binary64_17784` `flip3-+_binary64_17813` `distribute-lft-out_binary64_17761` `diff-log_binary64_17902` `frac-sub_binary64_17819` `frac-2neg_binary64_17821` `distribute-rgt1-in_binary64_17766`
1×	`flip3--_binary64_17814` `flip--_binary64_17785` `+-commutative_binary64_17740` `associate--l+_binary64_17747` `distribute-rgt-out_binary64_17763` `sub-neg_binary64_17803` `distribute-rgt-out--_binary64_17764`

Counts

4 → 285

Calls

4 calls:

52.0ms	(-.f64 (+.f64 y (/.f64 t (/.f64 (-.f64 a t) y))) (/.f64 z (/.f64 (-.f64 a t) y)))
26.0ms	(+.f64 y (/.f64 t (/.f64 (-.f64 a t) y)))
9.0ms	(/.f64 t (/.f64 (-.f64 a t) y))
9.0ms	(/.f64 z (/.f64 (-.f64 a t) y))

series725.0ms (8.4%)

Counts

4 → 68

Calls

4 calls:

322.0ms	(-.f64 (+.f64 y (/.f64 t (/.f64 (-.f64 a t) y))) (/.f64 z (/.f64 (-.f64 a t) y)))
180.0ms	(/.f64 z (/.f64 (-.f64 a t) y))
117.0ms	(+.f64 y (/.f64 t (/.f64 (-.f64 a t) y)))
106.0ms	(/.f64 t (/.f64 (-.f64 a t) y))

Compiler

Compiled 2545 to 1861 computations (26.9% saved)

simplify128.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

353 → 353

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4984	8185
1	4984	8185

prune302.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	351	2	353
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	355	6	361

Merged error: 0.3b

Counts

361 → 6

Compiler

Compiled 9741 to 1512 computations (84.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t)))
0.0b	(/.f64 t (-.f64 a t))
3.4b	(*.f64 y (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))))
3.7b	(+.f64 1 (/.f64 t (-.f64 a t)))

rewrite89.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary64_17832` `*-un-lft-identity_binary64_17810`
63×	`cancel-sign-sub-inv_binary64_17776`
62×	`times-frac_binary64_17816`
43×	`add-cube-cbrt_binary64_17845`
23×	`distribute-rgt-in_binary64_17760` `distribute-lft-in_binary64_17759`
17×	`difference-of-squares_binary64_17779` `distribute-lft-out--_binary64_17762`
11×	`add-log-exp_binary64_17849`
8×	`associate-/r/_binary64_17756` `add-exp-log_binary64_17848` `add-cbrt-cube_binary64_17846`
7×	`associate-r_binary64_17750`
6×	`flip3--_binary64_17814` `flip--_binary64_17785` `pow1_binary64_17871`
5×	`associate-/r*_binary64_17754`
4×	`div-inv_binary64_17807` `associate-*r/_binary64_17752` `frac-sub_binary64_17819`
3×	`associate-/l_binary64_17755` `flip-+_binary64_17784` `flip3-+_binary64_17813` `distribute-lft-out_binary64_17761` `associate--l+_binary64_17747` `associate-l*_binary64_17751` `sub-neg_binary64_17803`
2×	`sum-log_binary64_17901` `diff-log_binary64_17902`
1×	`cbrt-unprod_binary64_17843` `unswap-sqr_binary64_17778` `pow-prod-down_binary64_17881` `prod-exp_binary64_17859` `clear-num_binary64_17809` `*-commutative_binary64_17741` `+-commutative_binary64_17740` `div-exp_binary64_17861` `cbrt-undiv_binary64_17844` `frac-2neg_binary64_17821`

Counts

4 → 161

Calls

4 calls:

31.0ms	(*.f64 y (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))))
23.0ms	(-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t)))
10.0ms	(+.f64 1 (/.f64 t (-.f64 a t)))
6.0ms	(/.f64 t (-.f64 a t))

series613.0ms (7.1%)

Counts

4 → 64

Calls

4 calls:

341.0ms	(*.f64 y (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))))
167.0ms	(-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t)))
57.0ms	(+.f64 1 (/.f64 t (-.f64 a t)))
48.0ms	(/.f64 t (-.f64 a t))

Compiler

Compiled 2057 to 1649 computations (19.8% saved)

simplify94.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5009	4660

prune192.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	224	1	225
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	226	5	231

Merged error: 0b

Counts

231 → 5

Compiler

Compiled 5133 to 1631 computations (68.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 y (-.f64 a t))
4.3b	(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))
12.7b	(*.f64 (-.f64 z t) (/.f64 y (-.f64 a t)))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64_17832`
39×	`*-un-lft-identity_binary64_17810`
31×	`times-frac_binary64_17816`
23×	`add-cube-cbrt_binary64_17845`
21×	`associate-r_binary64_17750`
10×	`add-exp-log_binary64_17848` `frac-sub_binary64_17819` `add-cbrt-cube_binary64_17846`
9×	`flip3--_binary64_17814` `flip--_binary64_17785`
8×	`difference-of-squares_binary64_17779` `distribute-lft-out--_binary64_17762` `add-log-exp_binary64_17849`
6×	`associate-*l/_binary64_17753` `frac-times_binary64_17820`
5×	`associate-/r_binary64_17754` `flip-+_binary64_17784` `flip3-+_binary64_17813` `associate-l*_binary64_17751` `pow1_binary64_17871`
4×	`associate-/r/_binary64_17756`
3×	`associate-/l_binary64_17755` `associate-r/_binary64_17752`
2×	`cbrt-unprod_binary64_17843` `unswap-sqr_binary64_17778` `prod-exp_binary64_17859` `div-inv_binary64_17807` `div-exp_binary64_17861` `cbrt-undiv_binary64_17844` `diff-log_binary64_17902`
1×	`cancel-sign-sub-inv_binary64_17776` `pow-prod-down_binary64_17881` `sum-log_binary64_17901` `clear-num_binary64_17809` `*-commutative_binary64_17741` `associate--l+_binary64_17747` `frac-2neg_binary64_17821` `sub-neg_binary64_17803`

Counts

3 → 107

Calls

3 calls:

14.0ms	(*.f64 (-.f64 z t) (/.f64 y (-.f64 a t)))
8.0ms	(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))
6.0ms	(/.f64 y (-.f64 a t))

series786.0ms (9.2%)

Counts

3 → 68

Calls

3 calls:

449.0ms	(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))
248.0ms	(*.f64 (-.f64 z t) (/.f64 y (-.f64 a t)))
89.0ms	(/.f64 y (-.f64 a t))

Compiler

Compiled 2171 to 1641 computations (24.4% saved)

simplify86.0ms (1%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5310	3593

prune124.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	175	5	180

Merged error: 0b

Counts

180 → 5

Compiler

Compiled 3487 to 655 computations (81.2% saved)

regimes842.0ms (9.8%)

Compiler: Compiled 7206 to 5106 computations (29.1% saved)

bsearch101.0ms (1.2%)

Steps

Iters	Range		Point
8	3.053430754471119e+163	1.2719053720058362e+166	6.614496158483137e+165
7	3.8428516327348116e+104	1.9647878397655096e+106	1.5506905253087662e+106
10	1.0670546973717408e-221	1.2145418834758068e-208	4.093149350033633e-213
9	-3.275449314736404e-65	-1.364264997492352e-73	-3.0630271737675854e-72

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	119	111
1	119	111

end0.0ms (0%)

sample1.7s (20.1%)

Algorithm

1×

intervals

Results

298.0ms	6778×	body	128	valid
55.0ms	484×	body	512	valid
51.0ms	313×	body	1024	valid
34.0ms	744×	body	128	invalid
32.0ms	362×	body	256	valid
12.0ms	63×	body	2048	valid

Compiler

Compiled 1359 to 928 computations (31.7% saved)

Details

analyze1.0s (11.9%)

sample27.0ms (0.3%)

simplify230.0ms (2.7%)

prune8.0ms (0.1%)

localize9.0ms (0.1%)

rewrite35.0ms (0.4%)

series1.0s (11.8%)

simplify75.0ms (0.9%)

prune149.0ms (1.7%)

localize11.0ms (0.1%)

rewrite142.0ms (1.6%)

series725.0ms (8.4%)

simplify128.0ms (1.5%)

prune302.0ms (3.5%)

localize10.0ms (0.1%)

rewrite89.0ms (1%)

series613.0ms (7.1%)

simplify94.0ms (1.1%)

prune192.0ms (2.2%)

localize9.0ms (0.1%)

rewrite39.0ms (0.5%)

series786.0ms (9.2%)

simplify86.0ms (1%)

prune124.0ms (1.4%)

regimes842.0ms (9.8%)

bsearch101.0ms (1.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.7s (20.1%)

Profiling