Details

analyze804.0ms (15%)

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)

sample43.0ms (0.8%)

Algorithm

1×

intervals

Results

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

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify173.0ms (3.2%)

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)

localize15.0ms (0.3%)

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 (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_2099`
20×	`add-sqr-sqrt_binary64_2120`
19×	`add-cube-cbrt_binary64_2131`
18×	`times-frac_binary64_2105`
15×	`sqrt-prod_binary64_2114`
6×	`associate-/r*_binary64_2045`
5×	`add-cbrt-cube_binary64_2132` `add-log-exp_binary64_2135` `add-exp-log_binary64_2134`
4×	`pow1_binary64_2157` `sqrt-div_binary64_2115`
3×	`flip3-+_binary64_2102` `associate-/l*_binary64_2046` `flip-+_binary64_2073`
2×	`associate-/r/_binary64_2047`
1×	`distribute-lft-out_binary64_2052` `cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `sum-log_binary64_2187` `frac-2neg_binary64_2110` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `+-commutative_binary64_2031` `clear-num_binary64_2098` `div-inv_binary64_2096` `sqrt-pow1_binary64_2116`

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)))

series197.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

76.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
69.0ms	(/.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)))

simplify91.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4896	1838
1	4896	1838

prune123.0ms (2.3%)

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)

localize18.0ms (0.3%)

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)))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-prod_binary64_2114`
30×	`add-sqr-sqrt_binary64_2120`
28×	`add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099`
27×	`times-frac_binary64_2105`
9×	`associate-/r*_binary64_2045`
8×	`sqrt-div_binary64_2115`
6×	`add-cbrt-cube_binary64_2132` `pow1_binary64_2157` `add-log-exp_binary64_2135` `add-exp-log_binary64_2134`
4×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
3×	`associate-/l*_binary64_2046`
2×	`associate-/r/_binary64_2047` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `sqrt-pow1_binary64_2116`
1×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `sum-log_binary64_2187` `frac-2neg_binary64_2110` `+-commutative_binary64_2031` `clear-num_binary64_2098` `div-inv_binary64_2096`

Counts

4 → 94

Calls

4 calls:

10.0ms	(/.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)))))))

series354.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
99.0ms	(+.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)))))))
47.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
46.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4921	2724
1	4921	2724

prune227.0ms (4.2%)

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)

localize23.0ms (0.4%)

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 (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`cbrt-prod_binary64_2127`
60×	`sqrt-prod_binary64_2114`
54×	`times-frac_binary64_2105`
47×	`add-sqr-sqrt_binary64_2120`
45×	`add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099`
33×	`unpow-prod-down_binary64_2175` `cube-prod_binary64_2124`
12×	`sqrt-div_binary64_2115`
6×	`pow1_binary64_2157` `add-log-exp_binary64_2135`
5×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
4×	`add-cbrt-cube_binary64_2132` `associate-/r/_binary64_2047` `add-exp-log_binary64_2134`
2×	`rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `div-inv_binary64_2096` `sqrt-pow1_binary64_2116`
1×	`sqr-pow_binary64_2071` `cbrt-div_binary64_2128` `pow1/3_binary64_2178` `cube-div_binary64_2125` `sum-log_binary64_2187` `unpow3_binary64_2162` `+-commutative_binary64_2031` `rem-cbrt-cube_binary64_2122` `cube-mult_binary64_2126`

Counts

4 → 123

Calls

4 calls:

18.0ms	(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 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
3.0ms	(+.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))))

series380.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))
95.0ms	(+.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))))
54.0ms	(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 (1.3%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5222	4083

prune299.0ms (5.6%)

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)

localize24.0ms (0.4%)

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)))

rewrite66.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-exp-log_binary64_2134`
36×	`prod-exp_binary64_2145`
33×	`associate-l_binary64_2042` `sqrt-prod_binary64_2114`
27×	`add-sqr-sqrt_binary64_2120` `times-frac_binary64_2105`
25×	`add-cube-cbrt_binary64_2131` `add-cbrt-cube_binary64_2132` `*-un-lft-identity_binary64_2099`
18×	`div-exp_binary64_2147`
11×	`pow1_binary64_2157`
10×	`cbrt-unprod_binary64_2129`
9×	`1-exp_binary64_2140` `rec-exp_binary64_2146`
8×	`sqrt-div_binary64_2115`
6×	`add-log-exp_binary64_2135`
5×	`cbrt-undiv_binary64_2130`
4×	`associate-*r/_binary64_2043` `flip3-+_binary64_2102` `flip-+_binary64_2073`
3×	`pow-prod-down_binary64_2167`
2×	`un-div-inv_binary64_2097` `associate-/r/_binary64_2047` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `frac-times_binary64_2109` `sqrt-pow1_binary64_2116`
1×	`-commutative_binary64_2032` `associate-l/_binary64_2044` `sum-log_binary64_2187` `+-commutative_binary64_2031` `associate-r_binary64_2041` `div-inv_binary64_2096`

Counts

4 → 116

Calls

4 calls:

31.0ms	(.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)))))))
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)))
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))))))))

series288.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(+.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))))))))
91.0ms	(.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)))))))
57.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
45.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify100.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4975	2952
1	4975	2952

prune213.0ms (4%)

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)

regimes83.0ms (1.6%)

Compiler: Compiled 1068 to 762 computations (28.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	50
1	25	50

end0.0ms (0%)

sample1.6s (29.2%)

Algorithm

1×

intervals

Results

331.0ms	6106×	body	128	valid
208.0ms	757×	body	2048	valid
150.0ms	8000×	pre	128	true
112.0ms	533×	body	1024	valid
87.0ms	256×	body	4096	valid
37.0ms	240×	body	512	valid
11.0ms	108×	body	256	valid

Compiler

Compiled 600 to 434 computations (27.7% saved)

Details

analyze804.0ms (15%)

sample43.0ms (0.8%)

simplify173.0ms (3.2%)

prune3.0ms (0%)

localize15.0ms (0.3%)

rewrite36.0ms (0.7%)

series197.0ms (3.7%)

simplify91.0ms (1.7%)

prune123.0ms (2.3%)

localize18.0ms (0.3%)

rewrite39.0ms (0.7%)

series354.0ms (6.6%)

simplify62.0ms (1.2%)

prune227.0ms (4.2%)

localize23.0ms (0.4%)

rewrite58.0ms (1.1%)

series380.0ms (7.1%)

simplify67.0ms (1.3%)

prune299.0ms (5.6%)

localize24.0ms (0.4%)

rewrite66.0ms (1.2%)

series288.0ms (5.4%)

simplify100.0ms (1.9%)

prune213.0ms (4%)

regimes83.0ms (1.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.6s (29.2%)

Profiling