Details

analyze446.0ms (4.5%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample40.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	166×	body	128	valid
7.0ms	30×	body	2048	valid
6.0ms	20×	body	4096	valid
5.0ms	23×	body	1024	valid
2.0ms	12×	body	512	valid
1.0ms	16×	body	128	invalid
1.0ms	16×	body	128	nan
0.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify428.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (328.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 35.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_2465`
15×	`add-sqr-sqrt_binary64_2487`
14×	`add-cube-cbrt_binary64_2500`
12×	`times-frac_binary64_2471`
8×	`add-log-exp_binary64_2504`
6×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
5×	`pow1_binary64_2526` `distribute-lft-out_binary64_2416`
4×	`associate-/l*_binary64_2410`
3×	`sqrt-prod_binary64_2481` `associate-/r*_binary64_2409`
2×	`flip3-+_binary64_2468` `flip--_binary64_2440` `associate-/l/_binary64_2412` `flip-+_binary64_2439` `sqrt-div_binary64_2482` `flip3--_binary64_2469`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556` `pow1/2_binary64_2545` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `frac-2neg_binary64_2476` `sqrt-pow1_binary64_2483`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series646.0ms (6.5%)

Counts

4 → 72

Calls

4 calls:

198.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
171.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
159.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2108 to 1794 computations (14.9% saved)

simplify88.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4959	2989
1	4959	2989

prune180.0ms (1.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	129	15	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	130	15	145

Merged error: 16.1b

Counts

145 → 15

Compiler

Compiled 3180 to 1765 computations (44.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.7b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
11.2b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite59.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_2471`
59×	`add-sqr-sqrt_binary64_2487`
44×	`*-un-lft-identity_binary64_2465`
30×	`add-cube-cbrt_binary64_2500`
27×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
14×	`difference-of-squares_binary64_2434`
13×	`sqrt-prod_binary64_2481` `associate-/l*_binary64_2410`
10×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `associate-/r/_binary64_2411`
9×	`associate-/r*_binary64_2409`
7×	`flip--_binary64_2440` `distribute-lft-out--_binary64_2417` `flip3--_binary64_2469`
6×	`add-log-exp_binary64_2504` `cancel-sign-sub-inv_binary64_2431` `div-inv_binary64_2462` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
5×	`pow1_binary64_2526`
2×	`clear-num_binary64_2464` `frac-2neg_binary64_2476` `sqrt-div_binary64_2482`
1×	`pow1/2_binary64_2545` `associate-/l/_binary64_2412` `sub-neg_binary64_2458` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `sqrt-pow1_binary64_2483`

Counts

4 → 136

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
12.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series1.0s (10.1%)

Counts

4 → 75

Calls

4 calls:

356.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
339.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
177.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
140.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3105 to 2453 computations (21% saved)

simplify90.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4976	6471
1	4976	6471

prune307.0ms (3.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	204	7	211
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	211	15	226

Merged error: 13.1b

Counts

226 → 15

Compiler

Compiled 6364 to 3377 computations (46.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_2487`
28×	`*-un-lft-identity_binary64_2465`
18×	`times-frac_binary64_2471` `add-cube-cbrt_binary64_2500`
11×	`sqrt-prod_binary64_2481`
10×	`difference-of-squares_binary64_2434`
8×	`add-log-exp_binary64_2504`
7×	`cancel-sign-sub-inv_binary64_2431`
6×	`associate-/r*_binary64_2409` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
5×	`distribute-lft-out--_binary64_2417` `pow1_binary64_2526`
4×	`flip--_binary64_2440` `flip3--_binary64_2469`
3×	`associate-/l*_binary64_2410`
2×	`sub-neg_binary64_2458` `diff-log_binary64_2557` `associate-/r/_binary64_2411` `sqrt-div_binary64_2482`
1×	`pow1/2_binary64_2545` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `frac-2neg_binary64_2476` `sqrt-pow1_binary64_2483`

Counts

4 → 88

Calls

4 calls:

8.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series736.0ms (7.3%)

Counts

4 → 72

Calls

4 calls:

272.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
166.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
161.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
137.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2640 to 2273 computations (13.9% saved)

simplify96.0ms (1%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4940	3616
1	4940	3616

prune212.0ms (2.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	152	8	160
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	157	18	175

Merged error: 12.7b

Counts

175 → 18

Compiler

Compiled 4360 to 2704 computations (38% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 4 (.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) c)))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_2503`
14×	`add-sqr-sqrt_binary64_2487`
13×	`add-cbrt-cube_binary64_2501`
11×	`*-un-lft-identity_binary64_2465`
9×	`add-cube-cbrt_binary64_2500`
8×	`add-log-exp_binary64_2504`
7×	`sqrt-prod_binary64_2481` `cancel-sign-sub-inv_binary64_2431` `div-exp_binary64_2516`
5×	`pow1_binary64_2526`
4×	`cbrt-undiv_binary64_2499` `prod-exp_binary64_2514`
3×	`times-frac_binary64_2471` `flip--_binary64_2440` `flip3--_binary64_2469` `associate-/l*_binary64_2410`
2×	`difference-of-squares_binary64_2434` `sub-neg_binary64_2458` `diff-log_binary64_2557` `sqrt-div_binary64_2482` `1-exp_binary64_2509` `cbrt-unprod_binary64_2498`
1×	`associate-/r_binary64_2409` `pow1/2_binary64_2545` `associate-r/_binary64_2407` `clear-num_binary64_2464` `distribute-lft-out--_binary64_2417` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `associate-/r/_binary64_2411` `frac-2neg_binary64_2476` `sqrt-pow1_binary64_2483`

Counts

4 → 73

Calls

4 calls:

12.0ms	(/.f64 4 (.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) c)))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series811.0ms (8.1%)

Counts

4 → 72

Calls

4 calls:

336.0ms	(/.f64 4 (.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) c)))
172.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
170.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
133.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2790 to 2423 computations (13.2% saved)

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4939	2926
1	4939	2926

prune170.0ms (1.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	145	18	163

Merged error: 12.7b

Counts

163 → 18

Compiler

Compiled 3527 to 2274 computations (35.5% saved)

regimes1.5s (15.5%)

Compiler: Compiled 8592 to 6426 computations (25.2% saved)

bsearch66.0ms (0.7%)

Steps

Iters	Range		Point
7	5.352215957988127e+93	1.003314743233553e+96	5.072204432072848e+95
9	3.3680153201665277e-277	9.233270115749582e-270	1.5253865352374434e-276

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	88	73
1	88	73

end0.0ms (0%)

sample2.8s (28.4%)

Algorithm

1×

intervals

Results

276.0ms	1120×	body	2048	valid
266.0ms	5260×	body	128	valid
131.0ms	698×	body	1024	valid
123.0ms	396×	body	4096	valid
48.0ms	344×	body	512	valid
33.0ms	702×	body	128	nan
21.0ms	389×	body	128	invalid
17.0ms	182×	body	256	valid

Compiler

Compiled 2247 to 1673 computations (25.5% saved)

Details

analyze446.0ms (4.5%)

sample40.0ms (0.4%)

simplify428.0ms (4.3%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite30.0ms (0.3%)

series646.0ms (6.5%)

simplify88.0ms (0.9%)

prune180.0ms (1.8%)

localize13.0ms (0.1%)

rewrite59.0ms (0.6%)

series1.0s (10.1%)

simplify90.0ms (0.9%)

prune307.0ms (3.1%)

localize14.0ms (0.1%)

rewrite34.0ms (0.3%)

series736.0ms (7.3%)

simplify96.0ms (1%)

prune212.0ms (2.1%)

localize14.0ms (0.1%)

rewrite35.0ms (0.4%)

series811.0ms (8.1%)

simplify70.0ms (0.7%)

prune170.0ms (1.7%)

regimes1.5s (15.5%)

bsearch66.0ms (0.7%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.8s (28.4%)

Profiling