Details

analyze422.0ms (6.6%)

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)

sample45.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	32×	body	2560	valid
8.0ms	158×	body	80	valid
7.0ms	33×	body	1280	valid
3.0ms	18×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	21×	body	80	nan
1.0ms	11×	body	80	invalid
0.0ms	3×	body	160	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify152.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	310	18
1	310	18

prune12.0ms (0.2%)

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: 36.3b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite231.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

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×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `insert-posit16` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 86

Calls

4 calls:

199.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series485.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
129.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
118.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
60.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify119.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4981	2218
1	4981	2218

prune120.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	86	12	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	12	99

Merged error: 5.7b

Counts

99 → 12

Compiler

Compiled 2161 to 478 computations (77.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
3.0b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
8.4b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite54.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
154×	`*-un-lft-identity_binary64`
93×	`add-sqr-sqrt_binary64`
92×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
31×	`distribute-lft-out_binary64`
21×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64` `insert-posit16`
3×	`div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `neg-sub0_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 220

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
14.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series809.0ms (12.6%)

Counts

4 → 12

Calls

4 calls:

366.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
272.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
114.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
56.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify160.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5486	8149

prune208.0ms (3.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	230	2	232
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	236	8	244

Merged error: 5.6b

Counts

244 → 8

Compiler

Compiled 6693 to 916 computations (86.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.6b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
15×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
12×	`distribute-lft-out_binary64`
10×	`associate-/l*_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `neg-mul-1_binary64`
4×	`associate-/r*_binary64` `insert-posit16`
3×	`sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `distribute-frac-neg_binary64` `sum-log_binary64`

Counts

4 → 112

Calls

4 calls:

12.0ms	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
7.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series597.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

319.0ms	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
109.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
57.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify128.0ms (2%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5179	3123

prune109.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	124	8	132

Merged error: 5.6b

Counts

132 → 8

Compiler

Compiled 2957 to 728 computations (75.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
3.0b	(.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (/.f64 1 a))
8.4b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`times-frac_binary64`
63×	`*-un-lft-identity_binary64`
53×	`add-sqr-sqrt_binary64`
35×	`add-cube-cbrt_binary64`
30×	`associate-l_binary64`
28×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
13×	`distribute-lft-out_binary64` `associate-r_binary64`
9×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64` `div-exp_binary64`
8×	`prod-exp_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
5×	`cbrt-undiv_binary64`
4×	`associate-/r*_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `insert-posit16`
3×	`div-inv_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `1-exp_binary64` `rec-exp_binary64` `distribute-frac-neg_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `neg-sub0_binary64` `associate-r/_binary64` `distribute-lft-neg-out_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 155

Calls

4 calls:

24.0ms	(.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (/.f64 1 a))
11.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series821.0ms (12.8%)

Counts

4 → 12

Calls

4 calls:

368.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
290.0ms	(.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (/.f64 1 a))
111.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
52.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify130.0ms (2%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4958	4324
1	4958	4324

prune135.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	167	8	175

Merged error: 5.6b

Counts

175 → 8

Compiler

Compiled 4317 to 838 computations (80.6% saved)

regimes139.0ms (2.2%)

Compiler: Compiled 381 to 270 computations (29.1% saved)

bsearch95.0ms (1.5%)

Steps

Iters	Range		Point
6	4.5692926712568396e+76	1.8617608274947834e+77	1.696534500200679e+77
9	-1.228114932890865e-75	-7.793351147685176e-83	-7.947315750646704e-83
10	-1.1811763235928494e+40	-2.1433411707996265e+30	-1.1639527502413392e+40

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	136	97
1	136	97

end0.0ms (0%)

sample1.3s (20.3%)

Algorithm

1×

intervals

Results

273.0ms	1051×	body	2560	valid
242.0ms	5082×	body	80	valid
192.0ms	936×	body	1280	valid
78.0ms	485×	body	640	valid
36.0ms	798×	body	80	nan
31.0ms	103×	body	5120	valid
25.0ms	205×	body	320	valid
14.0ms	138×	body	160	valid
13.0ms	268×	body	80	invalid

Compiler

Compiled 203 to 130 computations (36% saved)

Details

analyze422.0ms (6.6%)

sample45.0ms (0.7%)

simplify152.0ms (2.4%)

prune12.0ms (0.2%)

localize10.0ms (0.2%)

rewrite231.0ms (3.6%)

series485.0ms (7.6%)

simplify119.0ms (1.9%)

prune120.0ms (1.9%)

localize11.0ms (0.2%)

rewrite54.0ms (0.8%)

series809.0ms (12.6%)

simplify160.0ms (2.5%)

prune208.0ms (3.2%)

localize13.0ms (0.2%)

rewrite34.0ms (0.5%)

series597.0ms (9.3%)

simplify128.0ms (2%)

prune109.0ms (1.7%)

localize12.0ms (0.2%)

rewrite53.0ms (0.8%)

series821.0ms (12.8%)

simplify130.0ms (2%)

prune135.0ms (2.1%)

regimes139.0ms (2.2%)

bsearch95.0ms (1.5%)

simplify9.0ms (0.1%)

end0.0ms (0%)

sample1.3s (20.3%)

Profiling