Details

analyze777.0ms (11.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample41.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	189×	body	128	valid
7.0ms	26×	body	2048	valid
5.0ms	256×	pre	128	true
5.0ms	14×	body	4096	valid
4.0ms	19×	body	1024	valid
1.0ms	7×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify173.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 13.4b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.5b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
15.8b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_2436`
20×	`add-sqr-sqrt_binary64_2457`
19×	`add-cube-cbrt_binary64_2468`
18×	`times-frac_binary64_2442`
15×	`sqrt-prod_binary64_2451`
6×	`associate-/r*_binary64_2382`
5×	`add-log-exp_binary64_2472` `add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
4×	`pow1_binary64_2494` `sqrt-div_binary64_2452`
3×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/l*_binary64_2383`
2×	`associate-/r/_binary64_2384`
1×	`distribute-lft-out_binary64_2389` `cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `pow1/2_binary64_2513` `div-exp_binary64_2484` `sum-log_binary64_2524` `clear-num_binary64_2435` `rem-sqrt-square_binary64_2449` `+-commutative_binary64_2368` `frac-2neg_binary64_2447` `sqrt-pow1_binary64_2453`

Counts

3 → 68

Calls

3 calls:

14.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
9.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series214.0ms (3.1%)

Counts

3 → 9

Calls

3 calls:

97.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
65.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
52.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify93.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4896	1838
1	4896	1838

prune127.0ms (1.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	66	11	77
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	12	78

Merged error: 13.1b

Counts

78 → 12

Compiler

Compiled 2210 to 1451 computations (34.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
9.0b	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
15.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
15.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-prod_binary64_2451`
30×	`add-sqr-sqrt_binary64_2457`
28×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
27×	`times-frac_binary64_2442`
9×	`associate-/r*_binary64_2382`
8×	`sqrt-div_binary64_2452`
6×	`add-log-exp_binary64_2472` `add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `pow1_binary64_2494`
4×	`flip3-+_binary64_2439` `flip-+_binary64_2410`
3×	`associate-/l*_binary64_2383`
2×	`associate-/r/_binary64_2384` `pow1/2_binary64_2513` `rem-sqrt-square_binary64_2449` `sqrt-pow1_binary64_2453`
1×	`cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `div-exp_binary64_2484` `sum-log_binary64_2524` `clear-num_binary64_2435` `+-commutative_binary64_2368` `frac-2neg_binary64_2447`

Counts

4 → 94

Calls

4 calls:

11.0ms	(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
4.0ms	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))

series364.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

165.0ms	(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
94.0ms	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
54.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
51.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4921	2724
1	4921	2724

prune235.0ms (3.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	4	6	10
Picked	0	1	1
Done	0	1	1
Total	105	13	118

Merged error: 13.1b

Counts

118 → 13

Compiler

Compiled 4557 to 3003 computations (34.1% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

9.0b	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))))
15.2b	(cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))
15.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
15.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite58.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`cbrt-prod_binary64_2464`
60×	`sqrt-prod_binary64_2451`
54×	`times-frac_binary64_2442`
47×	`add-sqr-sqrt_binary64_2457`
45×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
33×	`unpow-prod-down_binary64_2512` `cube-prod_binary64_2461`
12×	`sqrt-div_binary64_2452`
6×	`add-log-exp_binary64_2472` `pow1_binary64_2494`
5×	`flip3-+_binary64_2439` `flip-+_binary64_2410`
4×	`associate-/r/_binary64_2384` `add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
2×	`div-inv_binary64_2433` `pow1/2_binary64_2513` `rem-sqrt-square_binary64_2449` `sqrt-pow1_binary64_2453`
1×	`pow1/3_binary64_2515` `rem-cbrt-cube_binary64_2459` `sum-log_binary64_2524` `cube-mult_binary64_2463` `unpow3_binary64_2499` `sqr-pow_binary64_2408` `+-commutative_binary64_2368` `cube-div_binary64_2462` `cbrt-div_binary64_2465`

Counts

4 → 123

Calls

4 calls:

20.0ms	(cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
4.0ms	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))))

series386.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))
107.0ms	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))))
55.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
51.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5222	4083

prune322.0ms (4.7%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	9	10
Picked	0	1	1
Done	0	2	2
Total	135	13	148

Merged error: 13.1b

Counts

148 → 13

Compiler

Compiled 5982 to 3939 computations (34.2% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (.f64 x (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))))
9.9b	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (.f64 x (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))))))
15.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
15.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

rewrite74.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-exp-log_binary64_2471`
36×	`prod-exp_binary64_2482`
33×	`sqrt-prod_binary64_2451` `associate-l_binary64_2379`
27×	`add-sqr-sqrt_binary64_2457` `times-frac_binary64_2442`
25×	`add-cube-cbrt_binary64_2468` `add-cbrt-cube_binary64_2469` `*-un-lft-identity_binary64_2436`
18×	`div-exp_binary64_2484`
11×	`pow1_binary64_2494`
10×	`cbrt-unprod_binary64_2466`
9×	`rec-exp_binary64_2483` `1-exp_binary64_2477`
8×	`sqrt-div_binary64_2452`
6×	`add-log-exp_binary64_2472`
5×	`cbrt-undiv_binary64_2467`
4×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-*r/_binary64_2380`
3×	`pow-prod-down_binary64_2504`
2×	`un-div-inv_binary64_2434` `associate-/r/_binary64_2384` `pow1/2_binary64_2513` `rem-sqrt-square_binary64_2449` `frac-times_binary64_2446` `sqrt-pow1_binary64_2453`
1×	`-commutative_binary64_2369` `div-inv_binary64_2433` `sum-log_binary64_2524` `associate-r_binary64_2378` `+-commutative_binary64_2368` `associate-l/_binary64_2381`

Counts

4 → 116

Calls

4 calls:

33.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (.f64 x (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))))
7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
5.0ms	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (.f64 x (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))))))

series279.0ms (4%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (.f64 x (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))))))
89.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (.f64 x (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))))
46.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
46.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify99.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4975	2952
1	4975	2952

prune431.0ms (6.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	1	8	9
Picked	0	1	1
Done	2	1	3
Total	129	12	141

Merged error: 13.1b

Counts

141 → 12

Compiler

Compiled 4191 to 2845 computations (32.1% saved)

regimes661.0ms (9.6%)

Compiler: Compiled 10653 to 7826 computations (26.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	26
1	21	26

end0.0ms (0%)

sample2.3s (33.1%)

Algorithm

1×

intervals

Results

330.0ms	6106×	body	128	valid
202.0ms	757×	body	2048	valid
157.0ms	8000×	pre	128	true
109.0ms	533×	body	1024	valid
84.0ms	256×	body	4096	valid
37.0ms	240×	body	512	valid
11.0ms	108×	body	256	valid

Compiler

Compiled 1556 to 1149 computations (26.2% saved)

Details

analyze777.0ms (11.3%)

sample41.0ms (0.6%)

simplify173.0ms (2.5%)

prune3.0ms (0%)

localize11.0ms (0.2%)

rewrite36.0ms (0.5%)

series214.0ms (3.1%)

simplify93.0ms (1.4%)

prune127.0ms (1.8%)

localize15.0ms (0.2%)

rewrite41.0ms (0.6%)

series364.0ms (5.3%)

simplify61.0ms (0.9%)

prune235.0ms (3.4%)

localize24.0ms (0.3%)

rewrite58.0ms (0.8%)

series386.0ms (5.6%)

simplify67.0ms (1%)

prune322.0ms (4.7%)

localize22.0ms (0.3%)

rewrite74.0ms (1.1%)

series279.0ms (4%)

simplify99.0ms (1.4%)

prune431.0ms (6.3%)

regimes661.0ms (9.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (33.1%)

Profiling