Details

analyze1.1s (15.6%)

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

11.0ms	201×	body	128	valid
8.0ms	30×	body	2048	valid
5.0ms	256×	pre	128	true
3.0ms	9×	body	4096	valid
2.0ms	8×	body	1024	valid
1.0ms	5×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify159.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune5.0ms (0.1%)

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

Error

11.7b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.8b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
12.6b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite78.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_760`
21×	`add-sqr-sqrt_binary64_782`
20×	`add-cube-cbrt_binary64_795`
18×	`times-frac_binary64_766`
16×	`sqrt-prod_binary64_776`
8×	`pow1_binary64_821`
6×	`add-exp-log_binary64_798` `associate-/r*_binary64_704` `add-log-exp_binary64_799` `sqrt-div_binary64_777` `add-cbrt-cube_binary64_796`
4×	`flip3-+_binary64_763` `flip-+_binary64_734`
3×	`sqrt-pow1_binary64_778` `associate-/l*_binary64_705`
2×	`associate-/r/_binary64_706` `associate-*r/_binary64_702` `pow1/2_binary64_840`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `distribute-lft-out_binary64_711` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `div-exp_binary64_811` `clear-num_binary64_759` `pow-prod-down_binary64_831`

Counts

4 → 81

Calls

4 calls:

28.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
14.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
13.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
7.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series282.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
62.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
45.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
41.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))

simplify161.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	5604	2228

prune187.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	85	8	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Error

11.6b

Counts

94 → 8

Compiler

Compiled 2492 to 1633 computations (34.5% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
0.2b	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
3.3b	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
12.6b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite64.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64_782`
40×	`times-frac_binary64_766`
36×	`*-un-lft-identity_binary64_760`
34×	`add-cube-cbrt_binary64_795`
26×	`sqrt-prod_binary64_776`
24×	`associate-r_binary64_700`
17×	`add-exp-log_binary64_798`
11×	`add-cbrt-cube_binary64_796`
9×	`pow1_binary64_821`
6×	`associate-/r*_binary64_704` `add-log-exp_binary64_799` `sqrt-div_binary64_777`
5×	`unswap-sqr_binary64_728`
4×	`prod-exp_binary64_809` `associate-/r/_binary64_706` `flip3-+_binary64_763` `flip-+_binary64_734` `div-exp_binary64_811`
3×	`associate-/l_binary64_705` `associate-l*_binary64_701` `pow-flip_binary64_834`
2×	`cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `rec-exp_binary64_810` `cbrt-unprod_binary64_793` `pow1/2_binary64_840` `1-exp_binary64_804`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `inv-pow_binary64_845` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-r/_binary64_702` `clear-num_binary64_759` `pow-prod-down_binary64_831` `un-div-inv_binary64_758` `-commutative_binary64_691`

Counts

4 → 122

Calls

4 calls:

16.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
11.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
10.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
4.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))

series200.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
56.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
55.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
30.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify175.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4820	2897
1	4820	2897

prune244.0ms (3.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	134	8	142

Error

11.6b

Counts

142 → 8

Compiler

Compiled 3765 to 2573 computations (31.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
0.6b	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))
0.8b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
12.6b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite53.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_760`
23×	`add-sqr-sqrt_binary64_782`
22×	`add-cube-cbrt_binary64_795`
18×	`times-frac_binary64_766`
16×	`sqrt-prod_binary64_776`
6×	`add-exp-log_binary64_798` `associate-/r*_binary64_704` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
5×	`log-pow_binary64_849`
4×	`exp-prod_binary64_812` `sqrt-div_binary64_777`
3×	`flip3-+_binary64_763` `flip-+_binary64_734` `associate-/l*_binary64_705` `log-prod_binary64_846`
2×	`associate-/r/_binary64_706`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `distribute-lft-out_binary64_711` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `rem-log-exp_binary64_801` `pow1/2_binary64_840` `div-exp_binary64_811` `clear-num_binary64_759`

Counts

4 → 84

Calls

4 calls:

17.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
9.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
9.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
2.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))

series288.0ms (4%)

Counts

4 → 12

Calls

4 calls:

163.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))
64.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
34.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
27.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify136.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4887	2359
1	4887	2359

prune186.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Error

11.6b

Counts

104 → 8

Compiler

Compiled 2791 to 1902 computations (31.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))
3.0b	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))))))))
3.3b	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))))
12.6b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_782`
24×	`associate-r_binary64_700`
23×	`*-un-lft-identity_binary64_760`
22×	`times-frac_binary64_766`
21×	`add-cube-cbrt_binary64_795`
15×	`sqrt-prod_binary64_776`
13×	`add-exp-log_binary64_798`
9×	`add-cbrt-cube_binary64_796`
8×	`pow1_binary64_821`
6×	`add-log-exp_binary64_799`
5×	`unswap-sqr_binary64_728` `log-pow_binary64_849`
4×	`prod-exp_binary64_809` `exp-prod_binary64_812` `sqrt-div_binary64_777`
3×	`flip3-+_binary64_763` `flip-+_binary64_734` `associate-l_binary64_701` `log-prod_binary64_846`
2×	`associate-/r/_binary64_706` `cbrt-unprod_binary64_793` `div-exp_binary64_811`
1×	`rem-sqrt-square_binary64_773` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-r/_binary64_702` `rem-log-exp_binary64_801` `rec-exp_binary64_810` `pow1/2_binary64_840` `pow-prod-down_binary64_831` `un-div-inv_binary64_758` `1-exp_binary64_804` `-commutative_binary64_691`

Counts

4 → 91

Calls

4 calls:

16.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))
8.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
4.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))))
2.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))))))))

series289.0ms (4%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))))))))
45.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))))
37.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
37.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))

simplify107.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4970	2217
1	4970	2217

prune166.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	102	9	111

Error

11.6b

Counts

111 → 9

Compiler

Compiled 2807 to 1960 computations (30.2% saved)

regimes738.0ms (10.2%)

Accuracy

Total 0.4b remaining (3.3%)

Threshold costs 0.4b (3.3%)

Compiler

Compiled 9073 to 7076 computations (22% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	29
1	23	29

end0.0ms (0%)

sample2.4s (33.6%)

Algorithm

1×

intervals

Results

382.0ms	6057×	body	128	valid
275.0ms	849×	body	2048	valid
191.0ms	8000×	pre	128	true
118.0ms	474×	body	1024	valid
111.0ms	282×	body	4096	valid
41.0ms	223×	body	512	valid
14.0ms	115×	body	256	valid

Compiler

Compiled 1290 to 1000 computations (22.5% saved)

Details

analyze1.1s (15.6%)

sample41.0ms (0.6%)

simplify159.0ms (2.2%)

prune5.0ms (0.1%)

localize17.0ms (0.2%)

rewrite78.0ms (1.1%)

series282.0ms (3.9%)

simplify161.0ms (2.2%)

prune187.0ms (2.6%)

localize28.0ms (0.4%)

rewrite64.0ms (0.9%)

series200.0ms (2.8%)

simplify175.0ms (2.4%)

prune244.0ms (3.4%)

localize18.0ms (0.2%)

rewrite53.0ms (0.7%)

series288.0ms (4%)

simplify136.0ms (1.9%)

prune186.0ms (2.6%)

localize16.0ms (0.2%)

rewrite39.0ms (0.5%)

series289.0ms (4%)

simplify107.0ms (1.5%)

prune166.0ms (2.3%)

regimes738.0ms (10.2%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.4s (33.6%)

Profiling