Details

analyze693.0ms (10.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5132	96
0	3	3
1	3	3

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)

sample42.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	40×	body	2048	valid
9.0ms	159×	body	128	valid
6.0ms	28×	body	1024	valid
3.0ms	10×	body	4096	valid
2.0ms	10×	body	512	valid
1.0ms	19×	body	128	nan
1.0ms	9×	body	256	valid
1.0ms	14×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify319.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (314.0ms)

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: 33.5b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize14.0ms (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))
1.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
20.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite35.0ms (0.5%)

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

series259.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
60.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
37.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify92.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune125.0ms (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

Merged error: 4.9b

Counts

87 → 9

Compiler

Compiled 2174 to 1301 computations (40.2% saved)

localize15.0ms (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))))
4.5b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
9.0b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
20.3b	(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_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:

15.0ms	(/.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))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series483.0ms (7.6%)

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)))))
162.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify94.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4956	3121
1	4956	3121

prune153.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	114	9	123

Merged error: 4.8b

Counts

123 → 9

Compiler

Compiled 3320 to 2042 computations (38.5% 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)))))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
20.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite30.0ms (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 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)))

series323.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
64.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4891	1972
1	4891	1972

prune104.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	84	9	93

Merged error: 4.8b

Counts

93 → 9

Compiler

Compiled 2293 to 1426 computations (37.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
8.9b	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
20.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_2828` `add-log-exp_binary64_2845`
6×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841` `sqrt-prod_binary64_2822` `pow1_binary64_2867`
4×	`sqrt-div_binary64_2823` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
3×	`flip3--_binary64_2810` `flip--_binary64_2781`
2×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819`
1×	`cancel-sign-sub-inv_binary64_2772` `diff-log_binary64_2898` `sub-neg_binary64_2799` `flip-+_binary64_2780` `sum-log_binary64_2897` `flip3-+_binary64_2809` `+-commutative_binary64_2736`

Counts

4 → 53

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))

series218.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
31.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify90.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4910	1280
1	4910	1280

prune94.0ms (1.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	65	9	74

Merged error: 4.8b

Counts

74 → 9

Compiler

Compiled 2275 to 1411 computations (38% saved)

regimes751.0ms (11.7%)

Compiler: Compiled 4632 to 3576 computations (22.8% saved)

bsearch87.0ms (1.4%)

Steps

Iters	Range	Point
9	3.240667004624162e+54	6.900588731769942e+61	1.3389678122082543e+61
9	-2.8570170725650746e-224	-3.553196571313925e-229	-3.089056825403424e-228
0	-1.0331933023904229e+81	-1.0032634201183365e+81	-1.0182283612543797e+81

Iters

Range

Point

3.240667004624162e+54

6.900588731769942e+61

1.3389678122082543e+61

-2.8570170725650746e-224

-3.553196571313925e-229

-3.089056825403424e-228

-1.0331933023904229e+81

-1.0032634201183365e+81

-1.0182283612543797e+81

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	105	82
1	105	82

end0.0ms (0%)

sample2.2s (34.2%)

Algorithm

1×

intervals

Results

293.0ms	5209×	body	128	valid
284.0ms	1129×	body	2048	valid
155.0ms	747×	body	1024	valid
119.0ms	382×	body	4096	valid
56.0ms	360×	body	512	valid
35.0ms	676×	body	128	nan
20.0ms	367×	body	128	invalid
18.0ms	173×	body	256	valid

Compiler

Compiled 1208 to 924 computations (23.5% saved)

Details

analyze693.0ms (10.8%)

sample42.0ms (0.7%)

simplify319.0ms (5%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite35.0ms (0.5%)

series259.0ms (4.1%)

simplify92.0ms (1.4%)

prune125.0ms (2%)

localize15.0ms (0.2%)

rewrite52.0ms (0.8%)

series483.0ms (7.6%)

simplify94.0ms (1.5%)

prune153.0ms (2.4%)

localize14.0ms (0.2%)

rewrite30.0ms (0.5%)

series323.0ms (5.1%)

simplify76.0ms (1.2%)

prune104.0ms (1.6%)

localize15.0ms (0.2%)

rewrite22.0ms (0.3%)

series218.0ms (3.4%)

simplify90.0ms (1.4%)

prune94.0ms (1.5%)

regimes751.0ms (11.7%)

bsearch87.0ms (1.4%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (34.2%)

Profiling