Details

analyze639.0ms (10.4%)

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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	168×	body	128	valid
8.0ms	34×	body	2048	valid
5.0ms	27×	body	1024	valid
4.0ms	12×	body	4096	valid
1.0ms	8×	body	512	valid
1.0ms	19×	body	128	nan
1.0ms	7×	body	256	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify423.0ms (6.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (326.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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: 32.5b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
19.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_760`
15×	`add-sqr-sqrt_binary64_782`
14×	`add-cube-cbrt_binary64_795`
12×	`times-frac_binary64_766`
8×	`add-log-exp_binary64_799`
6×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
5×	`distribute-lft-out_binary64_711` `pow1_binary64_821`
4×	`associate-/l*_binary64_705`
3×	`sqrt-prod_binary64_776` `associate-/r*_binary64_704`
2×	`flip3-+_binary64_763` `associate-/l/_binary64_707` `sqrt-div_binary64_777` `flip-+_binary64_734` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `cancel-sign-sub-inv_binary64_726` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `pow1/2_binary64_840` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series231.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
65.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
31.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify87.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4970	2025
1	4970	2025

prune119.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	9	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	9	85

Merged error: 4.2b

Counts

85 → 9

Compiler

Compiled 2206 to 1201 computations (45.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.5b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
7.2b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
19.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite56.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_766`
59×	`add-sqr-sqrt_binary64_782`
44×	`*-un-lft-identity_binary64_760`
30×	`add-cube-cbrt_binary64_795`
27×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
14×	`difference-of-squares_binary64_729`
13×	`sqrt-prod_binary64_776` `associate-/l*_binary64_705`
10×	`cbrt-undiv_binary64_794` `associate-/r/_binary64_706` `div-exp_binary64_811`
9×	`associate-/r*_binary64_704`
7×	`distribute-lft-out--_binary64_712` `flip--_binary64_735` `flip3--_binary64_764`
6×	`prod-exp_binary64_809` `cancel-sign-sub-inv_binary64_726` `add-log-exp_binary64_799` `div-inv_binary64_757` `cbrt-unprod_binary64_793`
5×	`pow1_binary64_821`
2×	`frac-2neg_binary64_771` `sqrt-div_binary64_777` `clear-num_binary64_759`
1×	`diff-log_binary64_852` `rem-sqrt-square_binary64_773` `associate-/l/_binary64_707` `sqrt-pow1_binary64_778` `pow1/2_binary64_840` `sub-neg_binary64_753`

Counts

4 → 136

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
12.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series498.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

214.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
160.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
63.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify106.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5011	5032

prune208.0ms (3.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	150	7	157

Merged error: 4.2b

Counts

157 → 7

Compiler

Compiled 4789 to 2548 computations (46.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
19.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_782`
28×	`*-un-lft-identity_binary64_760`
18×	`add-cube-cbrt_binary64_795` `times-frac_binary64_766`
11×	`sqrt-prod_binary64_776`
10×	`difference-of-squares_binary64_729`
8×	`add-log-exp_binary64_799`
7×	`cancel-sign-sub-inv_binary64_726`
6×	`add-exp-log_binary64_798` `associate-/r*_binary64_704` `add-cbrt-cube_binary64_796`
5×	`distribute-lft-out--_binary64_712` `pow1_binary64_821`
4×	`flip--_binary64_735` `flip3--_binary64_764`
3×	`associate-/l*_binary64_705`
2×	`diff-log_binary64_852` `associate-/r/_binary64_706` `sqrt-div_binary64_777` `sub-neg_binary64_753`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `pow1/2_binary64_840` `div-exp_binary64_811` `clear-num_binary64_759`

Counts

4 → 88

Calls

4 calls:

10.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series331.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

180.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
60.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
55.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
35.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4882	2580
1	4882	2580

prune124.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	100	7	107

Merged error: 4.2b

Counts

107 → 7

Compiler

Compiled 2930 to 1738 computations (40.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
19.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_782`
18×	`*-un-lft-identity_binary64_760`
13×	`add-exp-log_binary64_798` `add-cube-cbrt_binary64_795` `associate-r_binary64_700`
11×	`times-frac_binary64_766`
9×	`add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799`
7×	`pow1_binary64_821`
4×	`prod-exp_binary64_809` `associate-l_binary64_701`
3×	`unswap-sqr_binary64_728` `flip3-+_binary64_763` `sqrt-prod_binary64_776` `flip-+_binary64_734`
2×	`associate-*l/_binary64_703` `distribute-lft-out_binary64_711` `sqrt-div_binary64_777` `frac-times_binary64_770` `cbrt-unprod_binary64_793` `div-exp_binary64_811` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `rem-sqrt-square_binary64_773` `cbrt-undiv_binary64_794` `cancel-sign-sub-inv_binary64_726` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-r/_binary64_702` `rec-exp_binary64_810` `pow1/2_binary64_840` `sub-neg_binary64_753` `pow-prod-down_binary64_831` `un-div-inv_binary64_758` `1-exp_binary64_804` `-commutative_binary64_691`

Counts

4 → 80

Calls

4 calls:

16.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series224.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
60.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
32.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify87.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4913	2065
1	4913	2065

prune95.0ms (1.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	92	7	99

Merged error: 4.2b

Counts

99 → 7

Compiler

Compiled 2221 to 1246 computations (43.9% saved)

regimes591.0ms (9.6%)

Compiler: Compiled 3422 to 2654 computations (22.4% saved)

bsearch112.0ms (1.8%)

Steps

Iters	Range	Point
9	5.828750640646838e+81	5.297160775919267e+86	2.9789013216469393e+85
8	3.88928738868131e-218	3.4015789084544133e-215	4.018752297937222e-218
10	-1.956459480299143e+157	-3.2998053309226353e+143	-2.6627498847930204e+144

Iters

Range

Point

5.828750640646838e+81

5.297160775919267e+86

2.9789013216469393e+85

3.88928738868131e-218

3.4015789084544133e-215

4.018752297937222e-218

-1.956459480299143e+157

-3.2998053309226353e+143

-2.6627498847930204e+144

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	98	89
1	98	89

end0.0ms (0%)

sample1.9s (31.3%)

Algorithm

1×

intervals

Results

285.0ms	1115×	body	2048	valid
268.0ms	5203×	body	128	valid
143.0ms	742×	body	1024	valid
126.0ms	421×	body	4096	valid
47.0ms	332×	body	512	valid
35.0ms	691×	body	128	nan
20.0ms	407×	body	128	invalid
18.0ms	187×	body	256	valid

Compiler

Compiled 952 to 727 computations (23.6% saved)

Details

analyze639.0ms (10.4%)

sample39.0ms (0.6%)

simplify423.0ms (6.9%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite29.0ms (0.5%)

series231.0ms (3.8%)

simplify87.0ms (1.4%)

prune119.0ms (1.9%)

localize12.0ms (0.2%)

rewrite56.0ms (0.9%)

series498.0ms (8.1%)

simplify106.0ms (1.7%)

prune208.0ms (3.4%)

localize13.0ms (0.2%)

rewrite37.0ms (0.6%)

series331.0ms (5.4%)

simplify79.0ms (1.3%)

prune124.0ms (2%)

localize12.0ms (0.2%)

rewrite38.0ms (0.6%)

series224.0ms (3.7%)

simplify87.0ms (1.4%)

prune95.0ms (1.6%)

regimes591.0ms (9.6%)

bsearch112.0ms (1.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.9s (31.3%)

Profiling