Details

analyze446.0ms (6.8%)

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)

sample36.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	176×	body	128	valid
7.0ms	30×	body	2048	valid
6.0ms	28×	body	1024	valid
2.0ms	6×	body	4096	valid
2.0ms	11×	body	512	valid
1.0ms	17×	body	128	nan
1.0ms	14×	body	128	invalid
0.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify232.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune6.0ms (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: 32.0b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_445`
14×	`*-un-lft-identity_binary64_423`
9×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
8×	`add-cube-cbrt_binary64_458` `add-log-exp_binary64_462`
6×	`times-frac_binary64_429` `sqrt-prod_binary64_439` `difference-of-squares_binary64_392` `associate-/l*_binary64_368`
5×	`pow1_binary64_484`
4×	`cancel-sign-sub-inv_binary64_389` `flip3--_binary64_427` `flip--_binary64_398`
3×	`distribute-lft-out--_binary64_375`
2×	`sqrt-div_binary64_440` `sub-neg_binary64_416` `diff-log_binary64_515` `associate-/l/_binary64_370` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
1×	`prod-exp_binary64_472` `rem-sqrt-square_binary64_436` `div-sub_binary64_428` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `associate-/r*_binary64_367` `cbrt-unprod_binary64_456`

Counts

4 → 74

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series523.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5031	1979

prune420.0ms (6.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	78	8	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	9	87

Merged error: 6.3b

Counts

87 → 9

Compiler

Compiled 8164 to 5769 computations (29.3% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
2.7b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
10.6b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
22×	`times-frac_binary64_429`
21×	`*-un-lft-identity_binary64_423`
17×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
13×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
12×	`add-sqr-sqrt_binary64_445`
11×	`add-cube-cbrt_binary64_458` `associate-/l*_binary64_368`
6×	`associate-/r/_binary64_369` `add-log-exp_binary64_462`
5×	`distribute-lft-out_binary64_374` `pow1_binary64_484` `associate-/r*_binary64_367`
4×	`flip-+_binary64_397` `flip3-+_binary64_426` `div-inv_binary64_420`
3×	`sqrt-prod_binary64_439`
2×	`sqrt-div_binary64_440` `clear-num_binary64_422` `frac-2neg_binary64_434`
1×	`+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `flip3--_binary64_427` `associate-/l/_binary64_370` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `flip--_binary64_398` `sum-log_binary64_514`

Counts

4 → 102

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series908.0ms (13.8%)

Counts

4 → 12

Calls

4 calls:

360.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
302.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
120.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5005	3121

prune332.0ms (5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	2	5	7
Picked	1	0	1
Done	1	0	1
Total	114	9	123

Merged error: 6.2b

Counts

123 → 9

Compiler

Compiled 6924 to 4743 computations (31.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_423`
15×	`add-sqr-sqrt_binary64_445`
14×	`add-cube-cbrt_binary64_458`
12×	`times-frac_binary64_429`
8×	`add-log-exp_binary64_462`
6×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
5×	`distribute-lft-out_binary64_374` `pow1_binary64_484`
4×	`associate-/r*_binary64_367`
3×	`sqrt-prod_binary64_439` `associate-/l*_binary64_368`
2×	`sqrt-div_binary64_440` `flip-+_binary64_397` `flip3--_binary64_427` `associate-/r/_binary64_369` `flip3-+_binary64_426` `flip--_binary64_398`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `cancel-sign-sub-inv_binary64_389` `+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `sum-log_binary64_514`

Counts

4 → 72

Calls

4 calls:

9.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series625.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

331.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
127.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
105.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5099	1969

prune111.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 6.2b

Counts

93 → 9

Compiler

Compiled 2460 to 1566 computations (36.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_423`
18×	`associate-r_binary64_363`
16×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
14×	`add-sqr-sqrt_binary64_445`
13×	`add-cube-cbrt_binary64_458`
12×	`times-frac_binary64_429`
10×	`pow1_binary64_484`
8×	`add-log-exp_binary64_462`
6×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
4×	`distribute-lft-out_binary64_374`
3×	`pow-prod-down_binary64_494` `sqrt-prod_binary64_439`
2×	`sqrt-div_binary64_440` `flip-+_binary64_397` `flip3--_binary64_427` `associate-/r/_binary64_369` `flip3-+_binary64_426` `flip--_binary64_398` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
1×	`sub-neg_binary64_416` `associate-l_binary64_364` `diff-log_binary64_515` `cancel-sign-sub-inv_binary64_389` `+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `associate-r/_binary64_365` `-commutative_binary64_354` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `sum-log_binary64_514`

Counts

4 → 77

Calls

4 calls:

14.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series648.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

346.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
121.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify89.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4891	1915
1	4891	1915

prune144.0ms (2.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	7	7
Picked	0	1	1
Done	1	0	1
Total	88	10	98

Merged error: 6.2b

Counts

98 → 10

Compiler

Compiled 2916 to 1939 computations (33.5% saved)

regimes137.0ms (2.1%)

Compiler: Compiled 537 to 441 computations (17.9% saved)

bsearch110.0ms (1.7%)

Steps

Iters	Range	Point
11	1.533617338164353e+90	3.5739920072306705e+109	6.972667102848289e+99
8	-7.009141771871467e-292	-2.349509325897326e-294	-1.8145284637786566e-293
8	-1.0322269454701605e+98	-2.7621719849249905e+94	-1.3014879836557515e+97

Iters

Range

Point

1.533617338164353e+90

3.5739920072306705e+109

6.972667102848289e+99

-7.009141771871467e-292

-2.349509325897326e-294

-1.8145284637786566e-293

-1.0322269454701605e+98

-2.7621719849249905e+94

-1.3014879836557515e+97

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	103	85
1	103	85

end0.0ms (0%)

sample1.4s (21.1%)

Algorithm

1×

intervals

Results

299.0ms	1206×	body	2048	valid
274.0ms	5148×	body	128	valid
136.0ms	708×	body	1024	valid
128.0ms	412×	body	4096	valid
52.0ms	358×	body	512	valid
34.0ms	679×	body	128	nan
23.0ms	399×	body	128	invalid
21.0ms	168×	body	256	valid

Compiler

Compiled 252 to 196 computations (22.2% saved)

Details

analyze446.0ms (6.8%)

sample36.0ms (0.5%)

simplify232.0ms (3.5%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite37.0ms (0.6%)

series523.0ms (7.9%)

simplify70.0ms (1.1%)

prune420.0ms (6.4%)

localize17.0ms (0.3%)

rewrite51.0ms (0.8%)

series908.0ms (13.8%)

simplify75.0ms (1.1%)

prune332.0ms (5%)

localize12.0ms (0.2%)

rewrite33.0ms (0.5%)

series625.0ms (9.5%)

simplify68.0ms (1%)

prune111.0ms (1.7%)

localize12.0ms (0.2%)

rewrite38.0ms (0.6%)

series648.0ms (9.8%)

simplify89.0ms (1.4%)

prune144.0ms (2.2%)

regimes137.0ms (2.1%)

bsearch110.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (21.1%)

Profiling