Details

analyze450.0ms (6.5%)

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 (0.5%)

Algorithm

1×

intervals

Results

9.0ms	172×	body	128	valid
7.0ms	32×	body	2048	valid
4.0ms	20×	body	1024	valid
3.0ms	11×	body	4096	valid
2.0ms	16×	body	512	valid
1.0ms	27×	body	128	nan
1.0ms	16×	body	128	invalid
0.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify394.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (302.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune3.0ms (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)

localize10.0ms (0.1%)

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))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_441`
14×	`*-un-lft-identity_binary64_419`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454`
6×	`times-frac_binary64_425` `difference-of-squares_binary64_388` `sqrt-prod_binary64_435` `associate-/l*_binary64_364`
5×	`pow1_binary64_480`
4×	`flip3--_binary64_423` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`
3×	`distribute-lft-out--_binary64_371`
2×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `diff-log_binary64_511` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `pow1/2_binary64_499` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `associate-/r*_binary64_363` `rem-sqrt-square_binary64_432` `div-sub_binary64_424`

Counts

4 → 74

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series256.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

100.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
63.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify87.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune116.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	7	87

Merged error: 6.2b

Counts

87 → 7

Compiler

Compiled 2070 to 1232 computations (40.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite106.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_425`
439×	`add-sqr-sqrt_binary64_441`
364×	`*-un-lft-identity_binary64_419`
290×	`add-cube-cbrt_binary64_454`
74×	`difference-of-squares_binary64_388`
71×	`associate-/r*_binary64_363`
40×	`sqrt-prod_binary64_435`
37×	`distribute-lft-out--_binary64_371`
25×	`add-exp-log_binary64_457`
17×	`div-inv_binary64_416`
15×	`div-exp_binary64_470`
13×	`add-cbrt-cube_binary64_455`
8×	`add-log-exp_binary64_458`
6×	`pow1_binary64_480` `cbrt-undiv_binary64_453`
5×	`associate-/r/_binary64_365`
4×	`cancel-sign-sub-inv_binary64_385`
3×	`1-exp_binary64_463` `flip3--_binary64_423` `rec-exp_binary64_469` `flip--_binary64_394` `associate-/l*_binary64_364`
2×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `diff-log_binary64_511`
1×	`clear-num_binary64_418` `inv-pow_binary64_504` `pow1/2_binary64_499` `frac-2neg_binary64_430` `pow-flip_binary64_493` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`

Counts

4 → 356

Calls

4 calls:

26.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series278.0ms (4%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
59.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
31.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify185.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4968	16295
1	4968	16295

prune716.0ms (10.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	366	2	368
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	366	9	375

Merged error: 6.2b

Counts

375 → 9

Compiler

Compiled 12728 to 7686 computations (39.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.2b	(/.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)))))
21.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite50.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
22×	`times-frac_binary64_425`
21×	`*-un-lft-identity_binary64_419`
17×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
12×	`add-sqr-sqrt_binary64_441`
11×	`add-cube-cbrt_binary64_454` `associate-/l*_binary64_364`
6×	`add-log-exp_binary64_458` `associate-/r/_binary64_365`
5×	`distribute-lft-out_binary64_370` `associate-/r*_binary64_363` `pow1_binary64_480`
4×	`flip3-+_binary64_422` `div-inv_binary64_416` `flip-+_binary64_393`
3×	`sqrt-prod_binary64_435`
2×	`sqrt-div_binary64_436` `clear-num_binary64_418` `frac-2neg_binary64_430`
1×	`pow1/2_binary64_499` `sum-log_binary64_510` `flip3--_binary64_423` `sqrt-pow1_binary64_437` `flip--_binary64_394` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349` `associate-/l/_binary64_366`

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

series478.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
153.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
74.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify94.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4956	3121
1	4956	3121

prune142.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	115	8	123

Merged error: 6.2b

Counts

123 → 8

Compiler

Compiled 3216 to 1976 computations (38.6% saved)

localize14.0ms (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)))))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
21.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_419`
15×	`add-sqr-sqrt_binary64_441`
14×	`add-cube-cbrt_binary64_454`
12×	`times-frac_binary64_425`
8×	`add-log-exp_binary64_458`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
5×	`distribute-lft-out_binary64_370` `pow1_binary64_480`
4×	`associate-/r*_binary64_363`
3×	`sqrt-prod_binary64_435` `associate-/l*_binary64_364`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip3--_binary64_423` `associate-/r/_binary64_365` `flip-+_binary64_393` `flip--_binary64_394`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `pow1/2_binary64_499` `div-inv_binary64_416` `sum-log_binary64_510` `frac-2neg_binary64_430` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

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

series325.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

167.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
66.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4891	1972
1	4891	1972

prune91.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	84	8	92

Merged error: 6.2b

Counts

92 → 8

Compiler

Compiled 2137 to 1308 computations (38.8% saved)

regimes836.0ms (12%)

Compiler: Compiled 4080 to 3148 computations (22.8% saved)

bsearch113.0ms (1.6%)

Steps

Iters	Range	Point
9	7.219295201900938e+58	2.43651205626012e+64	2.4128408816895354e+64
9	-1.2620066309661761e-304	7.831385335596643e-308	-2.460485954681045e-307
10	-2.6930881658428087e+160	-4.4990338465426374e+148	-5.9369607730911e+148

Iters

Range

Point

7.219295201900938e+58

2.43651205626012e+64

2.4128408816895354e+64

-1.2620066309661761e-304

7.831385335596643e-308

-2.460485954681045e-307

-2.6930881658428087e+160

-4.4990338465426374e+148

-5.9369607730911e+148

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	105	82
1	105	82

end0.0ms (0%)

sample2.0s (28.8%)

Algorithm

1×

intervals

Results

278.0ms	1151×	body	2048	valid
268.0ms	5236×	body	128	valid
131.0ms	693×	body	1024	valid
114.0ms	395×	body	4096	valid
48.0ms	341×	body	512	valid
35.0ms	684×	body	128	nan
20.0ms	184×	body	256	valid
20.0ms	347×	body	128	invalid

Compiler

Compiled 1070 to 817 computations (23.6% saved)

Details

analyze450.0ms (6.5%)

sample37.0ms (0.5%)

simplify394.0ms (5.7%)

prune3.0ms (0.1%)

localize10.0ms (0.1%)

rewrite33.0ms (0.5%)

series256.0ms (3.7%)

simplify87.0ms (1.2%)

prune116.0ms (1.7%)

localize11.0ms (0.2%)

rewrite106.0ms (1.5%)

series278.0ms (4%)

simplify185.0ms (2.7%)

prune716.0ms (10.3%)

localize13.0ms (0.2%)

rewrite50.0ms (0.7%)

series478.0ms (6.9%)

simplify94.0ms (1.4%)

prune142.0ms (2%)

localize14.0ms (0.2%)

rewrite28.0ms (0.4%)

series325.0ms (4.7%)

simplify72.0ms (1%)

prune91.0ms (1.3%)

regimes836.0ms (12%)

bsearch113.0ms (1.6%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.0s (28.8%)

Profiling