Details

analyze764.0ms (7.6%)

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample50.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	40×	body	2048	valid
9.0ms	167×	body	128	valid
8.0ms	17×	body	4096	valid
3.0ms	17×	body	1024	valid
1.0ms	8×	body	512	valid
1.0ms	22×	body	128	nan
1.0ms	13×	body	128	invalid
1.0ms	7×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify188.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune11.0ms (0.1%)

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

Error

32.7b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite175.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

32.5b

Rules

37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`sqrt-prod_binary64`
6×	`associate-/l*_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
4×	`pow1_binary64`
3×	`flip3--_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64` `associate-/r*_binary64`
2×	`sqrt-div_binary64` `associate-/l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `diff-log_binary64` `sub-neg_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

3 → 74

Calls

3 calls:

25.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1767 to 270 computations (84.7% saved)

series500.0ms (5%)

Error

4.3b

Counts

3 → 45

Calls

3 calls:

181.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
147.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
134.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1855 to 1292 computations (30.4% saved)

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5039	2480

prune128.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	109	10	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	109	11	120

Error

4.2b

Counts

120 → 11

Compiler

Compiled 2261 to 491 computations (78.3% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite110.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

Rules

29×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64` `associate-r_binary64`
12×	`add-exp-log_binary64`
11×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`
6×	`pow1_binary64` `associate-l_binary64`
5×	`add-log-exp_binary64` `sqrt-prod_binary64`
4×	`flip3--_binary64` `flip--_binary64` `difference-of-squares_binary64` `prod-exp_binary64`
3×	`cancel-sign-sub-inv_binary64` `unswap-sqr_binary64`
2×	`sqrt-div_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `diff-log_binary64` `sub-neg_binary64` `pow-prod-down_binary64` `1-exp_binary64` `rec-exp_binary64` `cbrt-undiv_binary64` `un-div-inv_binary64` `associate-r/_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

3 → 75

Calls

3 calls:

15.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
8.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1885 to 511 computations (72.9% saved)

series517.0ms (5.2%)

Error

4.2b

Counts

3 → 45

Calls

3 calls:

196.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
139.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
129.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2011 to 1460 computations (27.4% saved)

simplify119.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4957	2232
1	4957	2232

prune120.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	122	9	131

Error

4.2b

Counts

131 → 9

Compiler

Compiled 2267 to 674 computations (70.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2) a)
5.4b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
21.7b	(-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2)
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite121.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

Rules

52×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64` `times-frac_binary64`
16×	`log-prod_binary64` `exp-sum_binary64`
15×	`difference-of-squares_binary64`
11×	`sqrt-prod_binary64`
7×	`pow1_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-prod_binary64`
5×	`distribute-lft-out--_binary64`
4×	`flip3--_binary64` `sqrt-div_binary64` `flip--_binary64`
3×	`cancel-sign-sub-inv_binary64` `log-pow_binary64` `associate-/r*_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `log-div_binary64` `exp-diff_binary64` `associate-/l/_binary64`
1×	`rem-sqrt-square_binary64` `diff-log_binary64` `sub-neg_binary64` `rem-exp-log_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 101

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2) a)
11.0ms	(-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2)
6.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2719 to 428 computations (84.3% saved)

series864.0ms (8.7%)

Error

4.2b

Counts

4 → 59

Calls

4 calls:

272.0ms	(/.f64 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2) a)
249.0ms	(-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2)
171.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
128.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2849 to 1856 computations (34.9% saved)

simplify100.0ms (1%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4935	2935
1	4935	2935

prune147.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	160	9	169

Error

4.2b

Counts

169 → 9

Compiler

Compiled 2872 to 591 computations (79.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (pow.f64 E.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2) a)
5.5b	(pow.f64 E.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
21.5b	(-.f64 (pow.f64 E.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2)
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite194.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

Rules

70×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
27×	`times-frac_binary64`
25×	`difference-of-squares_binary64`
24×	`add-cube-cbrt_binary64`
16×	`log-prod_binary64` `unpow-prod-up_binary64`
11×	`sqrt-prod_binary64`
9×	`associate-/l*_binary64`
8×	`pow1_binary64` `unpow-prod-down_binary64`
7×	`add-exp-log_binary64`
6×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `sqr-pow_binary64` `pow-unpow_binary64`
5×	`distribute-lft-out--_binary64`
4×	`flip3--_binary64` `sqrt-div_binary64` `flip--_binary64`
3×	`cancel-sign-sub-inv_binary64` `log-pow_binary64` `associate-/r*_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `log-div_binary64` `pow-sub_binary64` `pow-exp_binary64` `associate-/l/_binary64`
1×	`rem-sqrt-square_binary64` `diff-log_binary64` `sub-neg_binary64` `pow-pow_binary64` `pow-to-exp_binary64` `e-exp-1_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 118

Calls

4 calls:

26.0ms	(/.f64 (-.f64 (pow.f64 E.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2) a)
14.0ms	(-.f64 (pow.f64 E.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2)
13.0ms	(pow.f64 E.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 3421 to 543 computations (84.1% saved)

series945.0ms (9.5%)

Error

4.2b

Counts

4 → 61

Calls

4 calls:

290.0ms	(/.f64 (-.f64 (pow.f64 E.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2) a)
271.0ms	(pow.f64 E.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
193.0ms	(-.f64 (pow.f64 E.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2)
153.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2699 to 1727 computations (36% saved)

simplify116.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4984	4397
1	4984	4397

prune157.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	176	3	179
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	179	9	188

Error

4.2b

Counts

188 → 9

Compiler

Compiled 3713 to 650 computations (82.5% saved)

regimes1.4s (14.5%)

Accuracy

Total 4.2b remaining (41.6%)

Threshold costs 0b (0%)

Compiler

Compiled 6548 to 3880 computations (40.7% saved)

bsearch125.0ms (1.3%)

Steps

Iters	Range		Point
11	1.1174011683600933e-45	3.628657409365908e-18	1.5799928252193864e-43
7	-1.5891801823886744e+154	-1.1494260700583236e+152	-1.398584845046497e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	65	53
1	65	53

end0.0ms (0%)

sample3.0s (29.5%)

Algorithm

1×

intervals

Results

331.0ms	1118×	body	2048	valid
300.0ms	5200×	body	128	valid
160.0ms	699×	body	1024	valid
154.0ms	413×	body	4096	valid
63.0ms	357×	body	512	valid
47.0ms	817×	body	128	nan
30.0ms	213×	body	256	valid
13.0ms	246×	body	128	invalid

Compiler

Compiled 1669 to 990 computations (40.7% saved)

Details

analyze764.0ms (7.6%)

sample50.0ms (0.5%)

simplify188.0ms (1.9%)

prune11.0ms (0.1%)

localize12.0ms (0.1%)

rewrite175.0ms (1.7%)

series500.0ms (5%)

simplify81.0ms (0.8%)

prune128.0ms (1.3%)

localize17.0ms (0.2%)

rewrite110.0ms (1.1%)

series517.0ms (5.2%)

simplify119.0ms (1.2%)

prune120.0ms (1.2%)

localize12.0ms (0.1%)

rewrite121.0ms (1.2%)

series864.0ms (8.7%)

simplify100.0ms (1%)

prune147.0ms (1.5%)

localize13.0ms (0.1%)

rewrite194.0ms (1.9%)

series945.0ms (9.5%)

simplify116.0ms (1.2%)

prune157.0ms (1.6%)

regimes1.4s (14.5%)

bsearch125.0ms (1.3%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample3.0s (29.5%)

Profiling