Details

analyze511.0ms (8.6%)

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)

sample43.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	175×	body	128	valid
8.0ms	29×	body	2048	valid
6.0ms	25×	body	1024	valid
5.0ms	14×	body	4096	valid
2.0ms	9×	body	512	valid
1.0ms	23×	body	128	nan
1.0ms	13×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify404.0ms (6.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (310.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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

Merged error: 33.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize12.0ms (0.2%)

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))
0.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite34.0ms (0.6%)

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:

11.0ms	(/.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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series256.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
60.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
31.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify103.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4895	1979
1	4895	1979

prune117.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	78	8	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	8	87

Merged error: 5.6b

Counts

87 → 8

Compiler

Compiled 2145 to 1171 computations (45.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
0.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_782`
18×	`*-un-lft-identity_binary64_760`
14×	`add-cube-cbrt_binary64_795`
13×	`associate-r_binary64_700`
10×	`times-frac_binary64_766`
9×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799`
7×	`pow1_binary64_821`
6×	`associate-l_binary64_701`
5×	`sqrt-prod_binary64_776` `flip--_binary64_735` `flip3--_binary64_764`
4×	`cancel-sign-sub-inv_binary64_726` `difference-of-squares_binary64_729`
2×	`diff-log_binary64_852` `unswap-sqr_binary64_728` `associate-*l/_binary64_703` `prod-exp_binary64_809` `sqrt-div_binary64_777` `distribute-lft-out--_binary64_712` `frac-times_binary64_770` `cbrt-unprod_binary64_793` `sub-neg_binary64_753`
1×	`rem-sqrt-square_binary64_773` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `associate-r/_binary64_702` `pow1/2_binary64_840` `div-exp_binary64_811` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

4 → 83

Calls

4 calls:

17.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series267.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
66.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
34.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5317	2202

prune105.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	96	7	103

Merged error: 5.6b

Counts

103 → 7

Compiler

Compiled 2294 to 1258 computations (45.2% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.6b	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
15.4b	(.f64 (.f64 a (*.f64 c -4)) (/.f64 1/2 a))
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
14×	`*-un-lft-identity_binary64_760` `pow1_binary64_821`
13×	`associate-r_binary64_700` `add-sqr-sqrt_binary64_782`
12×	`prod-exp_binary64_809` `add-cube-cbrt_binary64_795` `cbrt-unprod_binary64_793`
9×	`times-frac_binary64_766`
8×	`add-log-exp_binary64_799`
6×	`pow-prod-down_binary64_831`
3×	`cbrt-undiv_binary64_794` `sqrt-prod_binary64_776` `div-exp_binary64_811`
2×	`sqrt-div_binary64_777` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `rem-sqrt-square_binary64_773` `distribute-lft-out_binary64_711` `flip3-+_binary64_763` `cancel-sign-sub-inv_binary64_726` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `flip-+_binary64_734` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-l_binary64_701` `associate-r/_binary64_702` `pow1/2_binary64_840` `sub-neg_binary64_753` `-commutative_binary64_691`

Counts

4 → 77

Calls

4 calls:

10.0ms	(.f64 (.f64 a (*.f64 c -4)) (/.f64 1/2 a))
7.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series164.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
31.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
10.0ms	(.f64 (.f64 a (*.f64 c -4)) (/.f64 1/2 a))

simplify59.0ms (1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5158	1466

prune103.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	88	8	96

Merged error: 5.5b

Counts

96 → 8

Compiler

Compiled 2446 to 1376 computations (43.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 c -2) (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.6b	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_760`
9×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799` `add-sqr-sqrt_binary64_782`
7×	`add-cube-cbrt_binary64_795`
5×	`pow1_binary64_821`
4×	`associate-/r*_binary64_704` `times-frac_binary64_766`
3×	`distribute-lft-out_binary64_711` `sqrt-prod_binary64_776`
2×	`cbrt-undiv_binary64_794` `associate-/r/_binary64_706` `flip3-+_binary64_763` `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` `cancel-sign-sub-inv_binary64_726` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `associate-/l*_binary64_705` `+-commutative_binary64_690` `sum-log_binary64_851` `cbrt-unprod_binary64_793` `pow1/2_binary64_840` `clear-num_binary64_759` `sub-neg_binary64_753`

Counts

4 → 64

Calls

4 calls:

10.0ms	(/.f64 (.f64 c -2) (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b))
7.0ms	(+.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))))

series342.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

187.0ms	(/.f64 (.f64 c -2) (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b))
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
61.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
32.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4933	1690
1	4933	1690

prune75.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	76	8	84

Merged error: 5.5b

Counts

84 → 8

Compiler

Compiled 1710 to 912 computations (46.7% saved)

regimes672.0ms (11.3%)

Compiler: Compiled 4224 to 3136 computations (25.8% saved)

bsearch110.0ms (1.9%)

Steps

Iters	Range	Point
7	7.482650775739311e+127	6.940404749714049e+129	1.928533493233392e+129
9	4.1267928365631376e-194	6.602297926380012e-187	4.190818973144896e-194
7	-3.1670677211042097e+132	-3.885194447819339e+130	-3.475153330017618e+131

Iters

Range

Point

7.482650775739311e+127

6.940404749714049e+129

1.928533493233392e+129

4.1267928365631376e-194

6.602297926380012e-187

4.190818973144896e-194

-3.1670677211042097e+132

-3.885194447819339e+130

-3.475153330017618e+131

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	82
1	102	82

end0.0ms (0%)

sample2.2s (37.9%)

Algorithm

1×

intervals

Results

340.0ms	1171×	body	2048	valid
322.0ms	5164×	body	128	valid
162.0ms	702×	body	1024	valid
147.0ms	394×	body	4096	valid
67.0ms	385×	body	512	valid
40.0ms	703×	body	128	nan
25.0ms	380×	body	128	invalid
23.0ms	184×	body	256	valid

Compiler

Compiled 1148 to 840 computations (26.8% saved)

Details

analyze511.0ms (8.6%)

sample43.0ms (0.7%)

simplify404.0ms (6.8%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite34.0ms (0.6%)

series256.0ms (4.3%)

simplify103.0ms (1.7%)

prune117.0ms (2%)

localize13.0ms (0.2%)

rewrite41.0ms (0.7%)

series267.0ms (4.5%)

simplify79.0ms (1.3%)

prune105.0ms (1.8%)

localize19.0ms (0.3%)

rewrite32.0ms (0.5%)

series164.0ms (2.8%)

simplify59.0ms (1%)

prune103.0ms (1.7%)

localize12.0ms (0.2%)

rewrite31.0ms (0.5%)

series342.0ms (5.8%)

simplify72.0ms (1.2%)

prune75.0ms (1.3%)

regimes672.0ms (11.3%)

bsearch110.0ms (1.9%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (37.9%)

Profiling