Details

analyze453.0ms (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
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 (0.5%)

Algorithm

1×

intervals

Results

10.0ms	39×	body	2048	valid
9.0ms	168×	body	128	valid
5.0ms	17×	body	4096	valid
3.0ms	18×	body	1024	valid
1.0ms	10×	body	512	valid
1.0ms	21×	body	128	nan
1.0ms	17×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify404.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (308.0ms)

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: 37.4b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
28.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_782`
14×	`*-un-lft-identity_binary64_760`
9×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
8×	`add-cube-cbrt_binary64_795` `add-log-exp_binary64_799`
6×	`sqrt-prod_binary64_776` `difference-of-squares_binary64_729` `associate-/l*_binary64_705` `times-frac_binary64_766`
5×	`pow1_binary64_821`
4×	`cancel-sign-sub-inv_binary64_726` `flip--_binary64_735` `flip3--_binary64_764`
3×	`distribute-lft-out--_binary64_712`
2×	`diff-log_binary64_852` `cbrt-undiv_binary64_794` `associate-/l/_binary64_707` `sqrt-div_binary64_777` `div-exp_binary64_811` `sub-neg_binary64_753`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `prod-exp_binary64_809` `sqrt-pow1_binary64_778` `associate-/r*_binary64_704` `div-inv_binary64_757` `div-sub_binary64_765` `cbrt-unprod_binary64_793` `pow1/2_binary64_840` `clear-num_binary64_759`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series261.0ms (3.5%)

Counts

4 → 36

Calls

4 calls:

112.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
69.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
53.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
27.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5277	2693

prune161.0ms (2.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	97	13	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	13	111

Merged error: 11.4b

Counts

111 → 13

Compiler

Compiled 2833 to 1494 computations (47.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
0.8b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
1.3b	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
28.0b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_782`
14×	`*-un-lft-identity_binary64_760`
9×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
8×	`add-cube-cbrt_binary64_795` `add-log-exp_binary64_799`
6×	`sqrt-prod_binary64_776` `difference-of-squares_binary64_729` `associate-/l*_binary64_705` `times-frac_binary64_766`
5×	`pow1_binary64_821`
3×	`cancel-sign-sub-inv_binary64_726` `distribute-lft-out--_binary64_712`
2×	`cbrt-undiv_binary64_794` `flip3-+_binary64_763` `associate-/l/_binary64_707` `sqrt-div_binary64_777` `flip-+_binary64_734` `div-exp_binary64_811` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `prod-exp_binary64_809` `sqrt-pow1_binary64_778` `associate-/r*_binary64_704` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `div-sub_binary64_765` `cbrt-unprod_binary64_793` `pow1/2_binary64_840` `clear-num_binary64_759` `sub-neg_binary64_753`

Counts

4 → 73

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
4.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
4.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series254.0ms (3.4%)

Counts

4 → 36

Calls

4 calls:

108.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
68.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
50.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))
27.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5171	2670

prune118.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	112	10	122

Merged error: 11.1b

Counts

122 → 10

Compiler

Compiled 2744 to 1554 computations (43.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
4.5b	(/.f64 (/.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))) (.f64 a 2))
12.3b	(/.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
28.0b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite54.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_766`
52×	`*-un-lft-identity_binary64_760`
31×	`add-sqr-sqrt_binary64_782`
30×	`add-cube-cbrt_binary64_795`
21×	`associate-/l*_binary64_705`
18×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
11×	`distribute-lft-out_binary64_711`
7×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
6×	`associate-/r/_binary64_706` `flip3-+_binary64_763` `add-log-exp_binary64_799` `flip-+_binary64_734`
5×	`associate-/r*_binary64_704` `pow1_binary64_821`
4×	`div-inv_binary64_757`
3×	`sqrt-prod_binary64_776` `associate-/l/_binary64_707`
2×	`frac-2neg_binary64_771` `prod-exp_binary64_809` `sqrt-div_binary64_777` `cbrt-unprod_binary64_793` `clear-num_binary64_759`
1×	`rem-sqrt-square_binary64_773` `sqrt-pow1_binary64_778` `+-commutative_binary64_690` `sum-log_binary64_851` `pow1/2_binary64_840`

Counts

4 → 118

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))) (.f64 a 2))
13.0ms	(/.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
6.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series414.0ms (5.5%)

Counts

4 → 36

Calls

4 calls:

160.0ms	(/.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
140.0ms	(/.f64 (/.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))) (.f64 a 2))
64.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
51.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

simplify93.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4902	5459
1	4902	5459

prune257.0ms (3.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	148	6	154
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	154	10	164

Merged error: 8.7b

Counts

164 → 10

Compiler

Compiled 5415 to 3315 computations (38.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 (.f64 c -4) 1) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4))))))
0.8b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
1.1b	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
28.0b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`times-frac_binary64_766`
41×	`*-un-lft-identity_binary64_760`
24×	`add-sqr-sqrt_binary64_782`
23×	`add-cube-cbrt_binary64_795`
18×	`add-exp-log_binary64_798`
13×	`add-cbrt-cube_binary64_796`
9×	`distribute-lft-out_binary64_711` `div-exp_binary64_811`
8×	`add-log-exp_binary64_799`
7×	`associate-/l*_binary64_705`
6×	`div-inv_binary64_757`
5×	`cbrt-undiv_binary64_794` `pow1_binary64_821`
4×	`flip3-+_binary64_763` `associate-/r*_binary64_704` `flip-+_binary64_734`
3×	`sqrt-prod_binary64_776`
2×	`prod-exp_binary64_809` `associate-/r/_binary64_706` `sqrt-div_binary64_777` `+-commutative_binary64_690` `sum-log_binary64_851` `1-exp_binary64_804`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `associate-/l/_binary64_707` `sqrt-pow1_binary64_778` `cbrt-unprod_binary64_793` `pow1/2_binary64_840` `clear-num_binary64_759`

Counts

4 → 98

Calls

4 calls:

12.0ms	(/.f64 (/.f64 (.f64 c -4) 1) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4))))))
6.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
4.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
4.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series260.0ms (3.5%)

Counts

4 → 36

Calls

4 calls:

126.0ms	(/.f64 (/.f64 (.f64 c -4) 1) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4))))))
61.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
47.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))
26.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))

simplify94.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4933	3824
1	4933	3824

prune167.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	136	8	144

Merged error: 8.3b

Counts

144 → 8

Compiler

Compiled 3666 to 2290 computations (37.5% saved)

regimes1.4s (19.3%)

Compiler: Compiled 7340 to 5566 computations (24.2% saved)

bsearch88.0ms (1.2%)

Steps

Iters	Range		Point
6	110632895444587.38	585185954016272.5	574334605182495.0
7	-3.533817548895532e-307	8.926476802587335e-309	-3.835865055607966e-308
8	-2.487386300594002e+108	-3.374205273953666e+104	-4.751555112720535e+107

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	95	101
1	95	101

end0.0ms (0%)

sample2.6s (35.3%)

Algorithm

1×

intervals

Results

286.0ms	1137×	body	2048	valid
279.0ms	5239×	body	128	valid
137.0ms	660×	body	1024	valid
131.0ms	421×	body	4096	valid
53.0ms	349×	body	512	valid
36.0ms	670×	body	128	nan
20.0ms	381×	body	128	invalid
19.0ms	194×	body	256	valid

Compiler

Compiled 1953 to 1471 computations (24.7% saved)

Details

analyze453.0ms (6%)

sample40.0ms (0.5%)

simplify404.0ms (5.4%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite36.0ms (0.5%)

series261.0ms (3.5%)

simplify67.0ms (0.9%)

prune161.0ms (2.1%)

localize11.0ms (0.1%)

rewrite37.0ms (0.5%)

series254.0ms (3.4%)

simplify68.0ms (0.9%)

prune118.0ms (1.6%)

localize13.0ms (0.2%)

rewrite54.0ms (0.7%)

series414.0ms (5.5%)

simplify93.0ms (1.2%)

prune257.0ms (3.4%)

localize12.0ms (0.2%)

rewrite37.0ms (0.5%)

series260.0ms (3.5%)

simplify94.0ms (1.3%)

prune167.0ms (2.2%)

regimes1.4s (19.3%)

bsearch88.0ms (1.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.6s (35.3%)

Profiling