Details

analyze772.0ms (6.7%)

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)

sample40.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	197×	body	128	valid
8.0ms	29×	body	2048	valid
5.0ms	256×	pre	128	true
3.0ms	10×	body	4096	valid
3.0ms	14×	body	1024	valid
1.0ms	4×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 34 to 33 computations (2.9% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15

prune9.0ms (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

58.5b

Counts

2 → 1

Compiler

Compiled 20 to 22 computations (-10% saved)

localize7.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(hypot.f64 1 x)
0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
2.8b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_78`
24×	`add-sqr-sqrt_binary64_100`
15×	`add-cube-cbrt_binary64_113`
12×	`sqrt-prod_binary64_94`
9×	`times-frac_binary64_84`
8×	`add-log-exp_binary64_117`
7×	`cancel-sign-sub-inv_binary64_44`
6×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
5×	`pow1_binary64_139`
4×	`difference-of-squares_binary64_47` `distribute-lft-out_binary64_29`
3×	`distribute-lft-out--_binary64_30` `associate-/l_binary64_23` `associate-/r_binary64_22`
2×	`flip-+_binary64_52` `sqrt-div_binary64_95` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `diff-log_binary64_170` `frac-2neg_binary64_89` `div-inv_binary64_75` `flip--_binary64_53` `clear-num_binary64_77` `pow1/2_binary64_158` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 80

Calls

8 calls:

11.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
6.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
0.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series188.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
53.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
40.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
32.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 276 to 300 computations (-8.7% saved)

simplify99.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4823	1444
1	4823	1444

prune158.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	8	93

Error

58.5b

Counts

93 → 8

Compiler

Compiled 1563 to 1433 computations (8.3% saved)

localize10.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(hypot.f64 1 x)
0.0b	(exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
2.8b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
2.8b	(log.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64_78`
36×	`add-sqr-sqrt_binary64_100`
20×	`sqrt-prod_binary64_94`
19×	`add-cube-cbrt_binary64_113`
14×	`cancel-sign-sub-inv_binary64_44`
11×	`log-prod_binary64_164` `log-pow_binary64_167`
10×	`exp-prod_binary64_130`
9×	`times-frac_binary64_84`
8×	`exp-sum_binary64_124` `difference-of-squares_binary64_47`
6×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `distribute-lft-out--_binary64_30` `add-exp-log_binary64_116` `pow1_binary64_139`
5×	`distribute-lft-out_binary64_29`
3×	`associate-/l_binary64_23` `associate-/r_binary64_22`
2×	`sqrt-div_binary64_95` `sub-neg_binary64_71`
1×	`sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `diff-log_binary64_170` `frac-2neg_binary64_89` `div-inv_binary64_75` `flip--_binary64_53` `exp-diff_binary64_126` `rem-log-exp_binary64_119` `log-div_binary64_165` `clear-num_binary64_77` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 99

Calls

8 calls:

12.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
12.0ms	(log.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
7.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
0.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series322.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(log.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
61.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
58.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
28.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 324 to 348 computations (-7.4% saved)

simplify101.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4861	1818
1	4861	1818

prune153.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	112	7	119

Error

58.5b

Counts

119 → 7

Compiler

Compiled 2059 to 1902 computations (7.6% saved)

localize22.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(exp.f64 (.f64 (.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
2.8b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
2.8b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
2.8b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
2.8b	(log.f64 (exp.f64 (.f64 (.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64_78`
35×	`add-sqr-sqrt_binary64_100`
24×	`sqrt-prod_binary64_94`
21×	`cancel-sign-sub-inv_binary64_44`
12×	`difference-of-squares_binary64_47`
11×	`add-log-exp_binary64_117` `add-cube-cbrt_binary64_113`
9×	`distribute-lft-out--_binary64_30`
6×	`distribute-lft-out_binary64_29`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
3×	`flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `log-prod_binary64_164` `log-pow_binary64_167` `sub-neg_binary64_71`
1×	`exp-to-pow_binary64_140` `rem-log-exp_binary64_119` `exp-prod_binary64_130`

Counts

4 → 89

Calls

8 calls:

11.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
2.0ms	(log.f64 (exp.f64 (.f64 (.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))
0.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series407.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

193.0ms	(log.f64 (exp.f64 (.f64 (.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))
74.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
70.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
69.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 786 to 774 computations (1.5% saved)

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5162	2017

prune279.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	100	8	108

Error

58.5b

Counts

108 → 8

Compiler

Compiled 4068 to 3759 computations (7.6% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0b	(hypot.f64 1 x)
0.0b	(hypot.f64 1 x)
0.5b	(sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.5b	(sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.5b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
2.8b	(-.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite61.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`sqrt-prod_binary64_94`
63×	`add-sqr-sqrt_binary64_100`
40×	`sqrt-pow1_binary64_96`
39×	`*-un-lft-identity_binary64_78`
32×	`sqrt-div_binary64_95`
31×	`pow1_binary64_139`
20×	`add-cube-cbrt_binary64_113` `pow1/2_binary64_158`
18×	`swap-sqr_binary64_45`
12×	`rem-sqrt-square_binary64_91`
10×	`associate-l_binary64_19` `associate-r_binary64_18`
9×	`pow-prod-up_binary64_148` `unswap-sqr_binary64_46`
8×	`flip-+_binary64_52` `distribute-lft-out_binary64_29` `flip3-+_binary64_81`
6×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116`
5×	`pow-sqr_binary64_51` `pow-prod-down_binary64_149`
4×	`sqr-abs_binary64_93` `frac-times_binary64_88`
2×	`associate-l/_binary64_21` `difference-of-squares_binary64_47` `associate-r/_binary64_20`
1×	`pow2_binary64_159` `*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip3--_binary64_82` `diff-log_binary64_170` `sqrt-unprod_binary64_98` `flip--_binary64_53` `rem-square-sqrt_binary64_90` `cancel-sign-sub-inv_binary64_44` `pow-plus_binary64_141` `sub-neg_binary64_71`

Counts

4 → 150

Calls

8 calls:

23.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
10.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
7.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
3.0ms	(-.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
0.0ms	(hypot.f64 1 x)

series474.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
150.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
67.0ms	(-.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
65.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

Compiler

Compiled 420 to 432 computations (-2.9% saved)

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4970	2840
1	4970	2840

prune271.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	162	8	170

Error

58.5b

Counts

170 → 8

Compiler

Compiled 3506 to 3185 computations (9.2% saved)

regimes1.3s (11.2%)

Accuracy

Total 11.6b remaining (99.5%)

Threshold costs 0b (0%)

Compiler

Compiled 12197 to 11375 computations (6.7% saved)

bsearch32.0ms (0.3%)

Steps

Iters	Range		Point
9	-3.9972777348462	-1.4791311676242958e-07	-3.9489225518133

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	50
1	29	50

end87.0ms (0.7%)

Compiler: Compiled 1416 to 1294 computations (8.6% saved)

sample6.5s (56.1%)

Algorithm

1×

intervals

Results

308.0ms	6023×	body	128	valid
215.0ms	806×	body	2048	valid
148.0ms	8000×	pre	128	true
108.0ms	496×	body	1024	valid
94.0ms	282×	body	4096	valid
39.0ms	259×	body	512	valid
16.0ms	134×	body	256	valid

Compiler

Compiled 4238 to 3881 computations (8.4% saved)

Pareto

-0.6005450648817112

Details

analyze772.0ms (6.7%)

sample40.0ms (0.3%)

simplify8.0ms (0.1%)

prune9.0ms (0.1%)

localize7.0ms (0.1%)

rewrite33.0ms (0.3%)

series188.0ms (1.6%)

simplify99.0ms (0.9%)

prune158.0ms (1.4%)

localize10.0ms (0.1%)

rewrite43.0ms (0.4%)

series322.0ms (2.8%)

simplify101.0ms (0.9%)

prune153.0ms (1.3%)

localize22.0ms (0.2%)

rewrite46.0ms (0.4%)

series407.0ms (3.5%)

simplify76.0ms (0.7%)

prune279.0ms (2.4%)

localize11.0ms (0.1%)

rewrite61.0ms (0.5%)

series474.0ms (4.1%)

simplify87.0ms (0.7%)

prune271.0ms (2.3%)

regimes1.3s (11.2%)

bsearch32.0ms (0.3%)

simplify3.0ms (0%)

end87.0ms (0.7%)

sample6.5s (56.1%)

Profiling