Details

analyze913.0ms (9.1%)

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
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample70.0ms (0.7%)

Algorithm

1×

intervals

Results

44.0ms	256×	body	128	valid
4.0ms	25×	body	128	nan
2.0ms	11×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify834.0ms (8.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (669.0ms)

Iter	Nodes	Cost
0	4219	54
1	4219	54

prune16.0ms (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: 20.0b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize40.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100`
9×	`*-un-lft-identity_binary64_78`
8×	`add-log-exp_binary64_117`
7×	`sqrt-prod_binary64_94` `add-cube-cbrt_binary64_113`
6×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `flip3--_binary64_82` `flip--_binary64_53` `add-exp-log_binary64_116` `sqrt-div_binary64_95` `cancel-sign-sub-inv_binary64_44`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `difference-of-squares_binary64_47` `pow1/2_binary64_158` `sub-neg_binary64_71`
1×	`distribute-lft-out--_binary64_30`

Counts

4 → 59

Calls

4 calls:

14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series381.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
106.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
104.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
61.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify124.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4911	1395
1	4911	1395

prune263.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	66	5	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	5	72

Merged error: 6.5b

Counts

72 → 5

Compiler

Compiled 3207 to 1922 computations (40.1% saved)

localize59.0ms (0.6%)

Local error

Found 4 expressions with local error:

9.5b	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`add-log-exp_binary64_117` `cbrt-prod_binary64_109`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `cbrt-div_binary64_110` `add-exp-log_binary64_116`
3×	`sqrt-prod_binary64_94` `flip3--_binary64_82` `flip--_binary64_53`
2×	`pow1/3_binary64_160` `sqrt-div_binary64_95`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 52

Calls

4 calls:

9.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
6.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))

series679.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

224.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
177.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
162.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify131.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4964	1672
1	4964	1672

prune285.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	63	6	69

Merged error: 6.5b

Counts

69 → 6

Compiler

Compiled 3834 to 2341 computations (38.9% saved)

localize50.0ms (0.5%)

Local error

Found 4 expressions with local error:

6.9b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) b)
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite47.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_100`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`add-log-exp_binary64_117` `cbrt-prod_binary64_109`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `cbrt-div_binary64_110` `flip3--_binary64_82` `flip--_binary64_53` `add-exp-log_binary64_116`
3×	`sqrt-prod_binary64_94` `cancel-sign-sub-inv_binary64_44`
2×	`pow1/3_binary64_160` `sqrt-div_binary64_95`
1×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `pow1/2_binary64_158` `sub-neg_binary64_71`

Counts

4 → 55

Calls

4 calls:

19.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) b)
8.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
8.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series652.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) b)
178.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
163.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify93.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5072	1687

prune272.0ms (2.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	67	6	73

Merged error: 6.5b

Counts

73 → 6

Compiler

Compiled 3938 to 2397 computations (39.1% saved)

localize50.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
3.5b	(/.f64 (*.f64 a c) b)
4.2b	(/.f64 (.f64 c 2) (-.f64 (-.f64 (.f64 2 (/.f64 (*.f64 a c) b)) b) b))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite56.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64_114` `add-sqr-sqrt_binary64_100` `add-exp-log_binary64_116`
13×	`*-un-lft-identity_binary64_78`
9×	`add-cube-cbrt_binary64_113`
8×	`times-frac_binary64_84` `associate-/r*_binary64_22`
6×	`add-log-exp_binary64_117`
5×	`pow1_binary64_139`
4×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
3×	`sqrt-prod_binary64_94` `flip3--_binary64_82` `flip--_binary64_53`
2×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `distribute-lft-out--_binary64_30` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `sqrt-div_binary64_95` `difference-of-squares_binary64_47` `associate-/r/_binary64_24` `clear-num_binary64_77`
1×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158` `sub-neg_binary64_71`

Counts

4 → 75

Calls

4 calls:

23.0ms	(/.f64 (.f64 c 2) (-.f64 (-.f64 (.f64 2 (/.f64 (*.f64 a c) b)) b) b))
11.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(/.f64 (*.f64 a c) b)
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series325.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(/.f64 (.f64 c 2) (-.f64 (-.f64 (.f64 2 (/.f64 (*.f64 a c) b)) b) b))
105.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
61.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
33.0ms	(/.f64 (*.f64 a c) b)

simplify104.0ms (1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4941	1485
1	4941	1485

prune241.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	86	7	93

Merged error: 6.2b

Counts

93 → 7

Compiler

Compiled 3473 to 1899 computations (45.3% saved)

regimes722.0ms (7.2%)

Compiler: Compiled 4246 to 2922 computations (31.2% saved)

bsearch140.0ms (1.4%)

Steps

Iters	Range		Point
8	6.862653024323205e+99	2.7699007506807312e+103	1.5473348289606372e+103
9	-9.84058304742685e+132	-5.286056562420579e+127	-8.444790154581287e+129

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	159	167
1	159	167

end0.0ms (0%)

sample3.4s (33.9%)

Algorithm

1×

intervals

Results

1.3s	8000×	body	128	valid
111.0ms	698×	body	128	nan
58.0ms	370×	body	128	invalid

Compiler

Compiled 1192 to 815 computations (31.6% saved)

Details

analyze913.0ms (9.1%)

sample70.0ms (0.7%)

simplify834.0ms (8.3%)

prune16.0ms (0.2%)

localize40.0ms (0.4%)

rewrite41.0ms (0.4%)

series381.0ms (3.8%)

simplify124.0ms (1.2%)

prune263.0ms (2.6%)

localize59.0ms (0.6%)

rewrite34.0ms (0.3%)

series679.0ms (6.8%)

simplify131.0ms (1.3%)

prune285.0ms (2.8%)

localize50.0ms (0.5%)

rewrite47.0ms (0.5%)

series652.0ms (6.5%)

simplify93.0ms (0.9%)

prune272.0ms (2.7%)

localize50.0ms (0.5%)

rewrite56.0ms (0.6%)

series325.0ms (3.2%)

simplify104.0ms (1%)

prune241.0ms (2.4%)

regimes722.0ms (7.2%)

bsearch140.0ms (1.4%)

simplify9.0ms (0.1%)

end0.0ms (0%)

sample3.4s (33.9%)

Profiling