Details

analyze462.0ms (7.3%)

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)

sample37.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	173×	body	128	valid
6.0ms	27×	body	2048	valid
4.0ms	24×	body	1024	valid
4.0ms	12×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	24×	body	128	nan
1.0ms	6×	body	256	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify237.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

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: 31.7b

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))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
18.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite39.0ms (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))

series517.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

208.0ms	(/.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)))
119.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
67.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify72.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5031	1979

prune368.0ms (5.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	8	87

Merged error: 5.6b

Counts

87 → 8

Compiler

Compiled 7331 to 5152 computations (29.7% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.4b	(+.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))
10.1b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
18.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite54.0ms (0.9%)

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:

17.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.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)))

series925.0ms (14.6%)

Counts

4 → 12

Calls

4 calls:

366.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
303.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
134.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5005	3121

prune295.0ms (4.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	114	8	122

Merged error: 5.5b

Counts

122 → 8

Compiler

Compiled 6141 to 4149 computations (32.4% 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)))))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
18.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite34.0ms (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)))

series639.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

320.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
131.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
123.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5099	1969

prune133.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	84	8	92

Merged error: 5.5b

Counts

92 → 8

Compiler

Compiled 2781 to 1810 computations (34.9% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
18.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
18.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
18.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_445`
9×	`*-un-lft-identity_binary64_423` `sqrt-prod_binary64_439`
7×	`add-cube-cbrt_binary64_458` `pow1_binary64_484`
6×	`sqrt-div_binary64_440` `add-log-exp_binary64_462`
4×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
3×	`rem-sqrt-square_binary64_436` `flip3--_binary64_427` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `flip--_binary64_398`
1×	`flip-+_binary64_397` `+-commutative_binary64_353` `distribute-lft-out_binary64_374` `flip3-+_binary64_426` `sum-log_binary64_514`

Counts

4 → 57

Calls

4 calls:

7.0ms	(+.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)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series486.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify41.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4934	1379
1	4934	1379

prune158.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	69	8	77

Merged error: 5.5b

Counts

77 → 8

Compiler

Compiled 3907 to 2387 computations (38.9% saved)

regimes121.0ms (1.9%)

Compiler: Compiled 549 to 426 computations (22.4% saved)

bsearch90.0ms (1.4%)

Steps

Iters	Range	Point
7	5.299135082393502e+130	9.634242899973525e+131	3.1009093014776278e+131
6	-8.912885875042921e-268	-9.446306041754426e-269	-1.5159330162823798e-268
8	-8.039036545206531e+90	-9.901707510965063e+86	-7.1093208455340995e+90

Iters

Range

Point

5.299135082393502e+130

9.634242899973525e+131

3.1009093014776278e+131

-8.912885875042921e-268

-9.446306041754426e-269

-1.5159330162823798e-268

-8.039036545206531e+90

-9.901707510965063e+86

-7.1093208455340995e+90

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 (21.7%)

Algorithm

1×

intervals

Results

280.0ms	5240×	body	128	valid
276.0ms	1101×	body	2048	valid
133.0ms	701×	body	1024	valid
127.0ms	415×	body	4096	valid
52.0ms	363×	body	512	valid
38.0ms	675×	body	128	nan
21.0ms	404×	body	128	invalid
18.0ms	180×	body	256	valid

Compiler

Compiled 254 to 189 computations (25.6% saved)

Details

analyze462.0ms (7.3%)

sample37.0ms (0.6%)

simplify237.0ms (3.7%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite39.0ms (0.6%)

series517.0ms (8.2%)

simplify72.0ms (1.1%)

prune368.0ms (5.8%)

localize17.0ms (0.3%)

rewrite54.0ms (0.9%)

series925.0ms (14.6%)

simplify74.0ms (1.2%)

prune295.0ms (4.7%)

localize12.0ms (0.2%)

rewrite34.0ms (0.5%)

series639.0ms (10.1%)

simplify71.0ms (1.1%)

prune133.0ms (2.1%)

localize20.0ms (0.3%)

rewrite30.0ms (0.5%)

series486.0ms (7.7%)

simplify41.0ms (0.7%)

prune158.0ms (2.5%)

regimes121.0ms (1.9%)

bsearch90.0ms (1.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (21.7%)

Profiling