Details

analyze455.0ms (6.9%)

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)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	172×	body	128	valid
6.0ms	26×	body	2048	valid
5.0ms	27×	body	1024	valid
4.0ms	11×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	24×	body	128	nan
1.0ms	18×	body	128	invalid
1.0ms	6×	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 (67.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune5.0ms (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: 35.0b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize11.0ms (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)
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite41.0ms (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:

15.0ms	(/.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))

series529.0ms (8%)

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))
125.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
73.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5031	1979

prune455.0ms (6.9%)

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: 7.0b

Counts

87 → 9

Compiler

Compiled 9255 to 6459 computations (30.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.5b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
9.7b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite52.0ms (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)))

series941.0ms (14.2%)

Counts

4 → 12

Calls

4 calls:

370.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
310.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
138.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
123.0ms	(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 (42.0ms)

Iter	Nodes	Cost
0	5005	3121

prune262.0ms (4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	115	8	123

Merged error: 6.9b

Counts

123 → 8

Compiler

Compiled 5639 to 3725 computations (33.9% 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))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite31.0ms (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:

8.0ms	(/.f64 c (+.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)))

series682.0ms (10.3%)

Counts

4 → 12

Calls

4 calls:

346.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
135.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
116.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
85.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5099	1969

prune110.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	85	7	92

Merged error: 6.9b

Counts

92 → 7

Compiler

Compiled 2405 to 1517 computations (36.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) c))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64_429`
80×	`*-un-lft-identity_binary64_423`
55×	`add-sqr-sqrt_binary64_445`
54×	`add-cube-cbrt_binary64_458`
16×	`associate-/r*_binary64_367`
15×	`add-exp-log_binary64_461`
13×	`distribute-lft-out_binary64_374`
9×	`add-cbrt-cube_binary64_459`
8×	`add-log-exp_binary64_462`
7×	`div-exp_binary64_474`
6×	`pow1_binary64_484`
5×	`div-inv_binary64_420`
3×	`sqrt-prod_binary64_439` `associate-/l*_binary64_368` `cbrt-undiv_binary64_457`
2×	`rec-exp_binary64_473` `1-exp_binary64_467` `sqrt-div_binary64_440` `flip3--_binary64_427` `flip--_binary64_398`
1×	`sub-neg_binary64_416` `flip-+_binary64_397` `diff-log_binary64_515` `cancel-sign-sub-inv_binary64_389` `+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `associate-/r/_binary64_369` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434` `pow-flip_binary64_497` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `inv-pow_binary64_508` `sum-log_binary64_514`

Counts

4 → 127

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) c))
7.0ms	(+.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)))

series578.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

277.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) c))
121.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
67.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5286	4178

prune185.0ms (2.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	139	7	146

Merged error: 6.9b

Counts

146 → 7

Compiler

Compiled 4092 to 2569 computations (37.2% saved)

regimes139.0ms (2.1%)

Compiler: Compiled 372 to 312 computations (16.1% saved)

bsearch112.0ms (1.7%)

Steps

Iters	Range	Point
8	5.047843856159705e+79	3.275486995190224e+82	1.7935647805371114e+82
11	-3.290852731649204e-307	2.1876641165742222e-285	-1.4618690896455906e-308
8	-1.6249009059312762e+154	-3.534796202621665e+151	-2.598568989113781e+152

Iters

Range

Point

5.047843856159705e+79

3.275486995190224e+82

1.7935647805371114e+82

-3.290852731649204e-307

2.1876641165742222e-285

-1.4618690896455906e-308

-1.6249009059312762e+154

-3.534796202621665e+151

-2.598568989113781e+152

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	105	82
1	105	82

end0.0ms (0%)

sample1.4s (20.7%)

Algorithm

1×

intervals

Results

293.0ms	1134×	body	2048	valid
263.0ms	5060×	body	128	valid
160.0ms	792×	body	1024	valid
132.0ms	417×	body	4096	valid
58.0ms	403×	body	512	valid
33.0ms	666×	body	128	nan
22.0ms	194×	body	256	valid
20.0ms	380×	body	128	invalid

Compiler

Compiled 195 to 151 computations (22.6% saved)

Details

analyze455.0ms (6.9%)

sample38.0ms (0.6%)

simplify232.0ms (3.5%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

rewrite41.0ms (0.6%)

series529.0ms (8%)

simplify71.0ms (1.1%)

prune455.0ms (6.9%)

localize14.0ms (0.2%)

rewrite52.0ms (0.8%)

series941.0ms (14.2%)

simplify75.0ms (1.1%)

prune262.0ms (4%)

localize12.0ms (0.2%)

rewrite31.0ms (0.5%)

series682.0ms (10.3%)

simplify71.0ms (1.1%)

prune110.0ms (1.7%)

localize13.0ms (0.2%)

rewrite45.0ms (0.7%)

series578.0ms (8.8%)

simplify73.0ms (1.1%)

prune185.0ms (2.8%)

regimes139.0ms (2.1%)

bsearch112.0ms (1.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (20.7%)

Profiling