Details

analyze452.0ms (7.5%)

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)

sample41.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	33×	body	2048	valid
9.0ms	172×	body	128	valid
5.0ms	24×	body	1024	valid
3.0ms	9×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	25×	body	128	nan
1.0ms	10×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify402.0ms (6.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (304.0ms)

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

Error

32.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (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))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.5b	(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_2828`
14×	`*-un-lft-identity_binary64_2806`
9×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
8×	`add-log-exp_binary64_2845` `add-cube-cbrt_binary64_2841`
6×	`times-frac_binary64_2812` `sqrt-prod_binary64_2822` `difference-of-squares_binary64_2775` `associate-/l*_binary64_2751`
5×	`pow1_binary64_2867`
4×	`cancel-sign-sub-inv_binary64_2772` `flip3--_binary64_2810` `flip--_binary64_2781`
3×	`distribute-lft-out--_binary64_2758`
2×	`sqrt-div_binary64_2823` `associate-/l/_binary64_2753` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `diff-log_binary64_2898` `sub-neg_binary64_2799`
1×	`pow1/2_binary64_2886` `div-inv_binary64_2803` `associate-/r*_binary64_2750` `sqrt-pow1_binary64_2824` `div-sub_binary64_2811` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `rem-sqrt-square_binary64_2819` `clear-num_binary64_2805` `frac-2neg_binary64_2817`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
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))

series261.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
62.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
37.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify89.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune123.0ms (2%)

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

Error

6.0b

Counts

87 → 9

Compiler

Compiled 2157 to 1290 computations (40.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
10.4b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite47.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
22×	`times-frac_binary64_2812`
21×	`*-un-lft-identity_binary64_2806`
17×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840`
13×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
12×	`add-sqr-sqrt_binary64_2828`
11×	`add-cube-cbrt_binary64_2841` `associate-/l*_binary64_2751`
6×	`add-log-exp_binary64_2845` `associate-/r/_binary64_2752`
5×	`distribute-lft-out_binary64_2757` `associate-/r*_binary64_2750` `pow1_binary64_2867`
4×	`div-inv_binary64_2803` `flip-+_binary64_2780` `flip3-+_binary64_2809`
3×	`sqrt-prod_binary64_2822`
2×	`sqrt-div_binary64_2823` `clear-num_binary64_2805` `frac-2neg_binary64_2817`
1×	`associate-/l/_binary64_2753` `pow1/2_binary64_2886` `flip3--_binary64_2810` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `sum-log_binary64_2897` `flip--_binary64_2781` `+-commutative_binary64_2736`

Counts

4 → 102

Calls

4 calls:

14.0ms	(/.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)))))
7.0ms	(+.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)))

series487.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

199.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
160.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
66.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

simplify95.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4956	3121
1	4956	3121

prune147.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	116	7	123

Error

5.9b

Counts

123 → 7

Compiler

Compiled 3241 to 1987 computations (38.7% saved)

localize11.0ms (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)))))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
21.5b	(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_2806`
15×	`add-sqr-sqrt_binary64_2828`
14×	`add-cube-cbrt_binary64_2841`
12×	`times-frac_binary64_2812`
8×	`add-log-exp_binary64_2845`
6×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
5×	`distribute-lft-out_binary64_2757` `pow1_binary64_2867`
4×	`associate-/r*_binary64_2750`
3×	`sqrt-prod_binary64_2822` `associate-/l*_binary64_2751`
2×	`sqrt-div_binary64_2823` `flip3--_binary64_2810` `flip-+_binary64_2780` `flip--_binary64_2781` `flip3-+_binary64_2809` `associate-/r/_binary64_2752`
1×	`pow1/2_binary64_2886` `cancel-sign-sub-inv_binary64_2772` `div-inv_binary64_2803` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `sqrt-pow1_binary64_2824` `diff-log_binary64_2898` `sub-neg_binary64_2799` `rem-sqrt-square_binary64_2819` `sum-log_binary64_2897` `clear-num_binary64_2805` `frac-2neg_binary64_2817` `+-commutative_binary64_2736`

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 (.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)))

series326.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4891	1972
1	4891	1972

prune99.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	84	7	91

Error

5.9b

Counts

91 → 7

Compiler

Compiled 2239 to 1384 computations (38.2% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

10.1b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
12×	`add-sqr-sqrt_binary64_2828`
9×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841` `sqrt-prod_binary64_2822`
7×	`pow1_binary64_2867`
6×	`sqrt-div_binary64_2823`
4×	`add-log-exp_binary64_2845`
3×	`pow1/2_binary64_2886` `times-frac_binary64_2812` `div-exp_binary64_2857` `flip3--_binary64_2810` `cbrt-undiv_binary64_2840` `associate-/r*_binary64_2750` `sqrt-pow1_binary64_2824` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `rem-sqrt-square_binary64_2819` `flip--_binary64_2781`
2×	`associate-/r/_binary64_2752`
1×	`div-inv_binary64_2803` `flip-+_binary64_2780` `flip3-+_binary64_2809` `clear-num_binary64_2805` `associate-/l*_binary64_2751` `frac-2neg_binary64_2817`

Counts

4 → 70

Calls

4 calls:

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

series384.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
55.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4973	1823
1	4973	1823

prune156.0ms (2.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	82	7	89

Error

5.9b

Counts

89 → 7

Compiler

Compiled 3894 to 2357 computations (39.5% saved)

regimes564.0ms (9.4%)

Accuracy

Total 1.0b remaining (14.9%)

Threshold costs 1.0b (14.9%)

Compiler

Compiled 3744 to 2880 computations (23.1% saved)

bsearch109.0ms (1.8%)

Steps

Iters	Range	Point
7	6.1964526172169535e+134	1.9152122692699513e+136	8.912861377839782e+134
10	-1.1228739214406659e-236	-7.143985414855799e-248	-3.3856076934378627e-242
9	-1.4477785457512157e+153	-5.651711623551278e+145	-6.97667166683124e+151

Iters

Range

Point

6.1964526172169535e+134

1.9152122692699513e+136

8.912861377839782e+134

-1.1228739214406659e-236

-7.143985414855799e-248

-3.3856076934378627e-242

-1.4477785457512157e+153

-5.651711623551278e+145

-6.97667166683124e+151

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	105	82
1	105	82

end0.0ms (0%)

sample1.9s (32.2%)

Algorithm

1×

intervals

Results

277.0ms	5208×	body	128	valid
267.0ms	1099×	body	2048	valid
142.0ms	733×	body	1024	valid
131.0ms	430×	body	4096	valid
51.0ms	362×	body	512	valid
33.0ms	674×	body	128	nan
18.0ms	364×	body	128	invalid
16.0ms	168×	body	256	valid

Compiler

Compiled 986 to 750 computations (23.9% saved)

Details

analyze452.0ms (7.5%)

sample41.0ms (0.7%)

simplify402.0ms (6.7%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite39.0ms (0.6%)

series261.0ms (4.3%)

simplify89.0ms (1.5%)

prune123.0ms (2%)

localize13.0ms (0.2%)

rewrite47.0ms (0.8%)

series487.0ms (8.1%)

simplify95.0ms (1.6%)

prune147.0ms (2.4%)

localize11.0ms (0.2%)

rewrite31.0ms (0.5%)

series326.0ms (5.4%)

simplify76.0ms (1.3%)

prune99.0ms (1.6%)

localize20.0ms (0.3%)

rewrite32.0ms (0.5%)

series384.0ms (6.4%)

simplify67.0ms (1.1%)

prune156.0ms (2.6%)

regimes564.0ms (9.4%)

bsearch109.0ms (1.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.9s (32.2%)

Profiling