Details

analyze1.2s (13.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	52
1	67	52
0	2	2
1	2	2

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 (0.4%)

Algorithm

1×

intervals

Results

11.0ms	202×	body	128	valid
5.0ms	18×	body	2048	valid
4.0ms	256×	pre	128	true
4.0ms	20×	body	1024	valid
2.0ms	5×	body	4096	valid
1.0ms	5×	body	512	valid
1.0ms	6×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify13.0ms (0.1%)

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

12.5b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
1.1b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
15.3b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite155.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

12.2b

Rules

8×	`pow1_binary64_2526` `add-log-exp_binary64_2504`
7×	`*-un-lft-identity_binary64_2465`
6×	`add-sqr-sqrt_binary64_2487`
5×	`add-cube-cbrt_binary64_2500`
4×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `flip3-+_binary64_2468` `sqrt-div_binary64_2482` `flip-+_binary64_2439` `sqrt-prod_binary64_2481`
3×	`sqrt-pow1_binary64_2483`
2×	`pow1/2_binary64_2545` `sum-log_binary64_2556` `+-commutative_binary64_2395` `associate-*r/_binary64_2407`
1×	`rem-sqrt-square_binary64_2478` `distribute-lft-out_binary64_2416` `pow-prod-down_binary64_2536`

Counts

4 → 51

Calls

4 calls:

21.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
18.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
6.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 1524 to 983 computations (35.5% saved)

series814.0ms (8.9%)

Error

3.8b

Counts

4 → 58

Calls

4 calls:

280.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
193.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
139.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
123.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

Compiler

Compiled 2545 to 2273 computations (10.7% saved)

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5198	2115

prune155.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	5	110

Error

3.0b

Counts

110 → 5

Compiler

Compiled 2218 to 1430 computations (35.5% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (pow.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4))))) 3))
0.0b	(pow.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4))))) 3)
1.1b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))))
15.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))

rewrite202.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

3.0b

Rules

21×	`*-un-lft-identity_binary64_2465`
14×	`cbrt-prod_binary64_2496`
12×	`add-sqr-sqrt_binary64_2487`
11×	`add-cube-cbrt_binary64_2500`
8×	`unpow-prod-down_binary64_2544` `cube-prod_binary64_2493`
6×	`pow1_binary64_2526` `add-log-exp_binary64_2504`
5×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `distribute-lft-out_binary64_2416`
4×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `cube-div_binary64_2494`
3×	`sqrt-prod_binary64_2481` `pow-unpow_binary64_2542`
2×	`sqrt-div_binary64_2482` `unpow3_binary64_2531` `cube-mult_binary64_2495` `sqr-pow_binary64_2437` `cbrt-div_binary64_2497`
1×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `sum-log_binary64_2556` `+-commutative_binary64_2395` `pow-pow_binary64_2537` `pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `rem-cube-cbrt_binary64_2488` `pow1/3_binary64_2547` `rem-cbrt-cube_binary64_2489`

Counts

4 → 79

Calls

4 calls:

23.0ms	(cbrt.f64 (pow.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4))))) 3))
14.0ms	(pow.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4))))) 3)
12.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))

Compiler

Compiled 2813 to 1786 computations (36.5% saved)

series728.0ms (7.9%)

Error

3.0b

Counts

4 → 61

Calls

4 calls:

206.0ms	(pow.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4))))) 3)
184.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))))
165.0ms	(cbrt.f64 (pow.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4))))) 3))
110.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))

Compiler

Compiled 2541 to 2278 computations (10.4% saved)

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4994	3055
1	4994	3055

prune199.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	139	6	145

Error

3.0b

Counts

145 → 6

Compiler

Compiled 3237 to 2125 computations (34.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 p p) 4)
0.3b	(.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p p) 4)))))))
1.1b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))))
15.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))

rewrite178.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

3.0b

Rules

20×	`add-sqr-sqrt_binary64_2487`
14×	`pow1_binary64_2526` `sqrt-prod_binary64_2481` `*-un-lft-identity_binary64_2465`
11×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
10×	`add-cube-cbrt_binary64_2500` `associate-r_binary64_2405`
7×	`associate-l_binary64_2406`
6×	`add-log-exp_binary64_2504` `pow-prod-down_binary64_2536`
5×	`unswap-sqr_binary64_2433`
4×	`sqrt-div_binary64_2482` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
3×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `flip3-+_binary64_2468` `flip-+_binary64_2439`
2×	`distribute-lft-out_binary64_2416` `associate-r/_binary64_2407` `-commutative_binary64_2396`
1×	`rem-sqrt-square_binary64_2478` `sum-log_binary64_2556` `+-commutative_binary64_2395` `sqrt-unprod_binary64_2485`

Counts

4 → 79

Calls

4 calls:

22.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))))
20.0ms	(.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p p) 4)))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
6.0ms	(.f64 (.f64 p p) 4)

Compiler

Compiled 2335 to 1458 computations (37.6% saved)

series677.0ms (7.4%)

Error

2.6b

Counts

4 → 49

Calls

4 calls:

281.0ms	(.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p p) 4)))))))
183.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))))
138.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
28.0ms	(.f64 (.f64 p p) 4)

Compiler

Compiled 2329 to 2073 computations (11% saved)

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4960	2634
1	4960	2634

prune178.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	126	8	134

Error

2.6b

Counts

134 → 8

Compiler

Compiled 2885 to 1896 computations (34.3% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 p (/.f64 (*.f64 x x) p))
0.2b	(/.f64 (*.f64 x x) p)
22.0b	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))

rewrite111.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

36×	`times-frac_binary64_2471`
21×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487` `*-un-lft-identity_binary64_2465`
17×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
10×	`associate-/r*_binary64_2409`
9×	`pow1_binary64_2526`
7×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499`
6×	`div-inv_binary64_2462`
4×	`associate-/l*_binary64_2410`
3×	`add-log-exp_binary64_2504` `pow-prod-down_binary64_2536` `sqrt-pow1_binary64_2483`
2×	`associate-*r/_binary64_2407` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `frac-2neg_binary64_2476` `clear-num_binary64_2464`
1×	`pow1/2_binary64_2545` `sqrt-div_binary64_2482` `sqrt-prod_binary64_2481` `associate-/r/_binary64_2411`

Counts

3 → 82

Calls

3 calls:

8.0ms	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))
6.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
5.0ms	(/.f64 (*.f64 x x) p)

Compiler

Compiled 1571 to 697 computations (55.6% saved)

series266.0ms (2.9%)

Error

Counts

3 → 18

Calls

3 calls:

99.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
96.0ms	(/.f64 (*.f64 x x) p)
54.0ms	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))

Compiler

Compiled 498 to 441 computations (11.4% saved)

simplify97.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5049	1152

prune88.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	4	1	5
Picked	1	0	1
Done	0	2	2
Total	103	5	108

Error

Counts

108 → 5

Compiler

Compiled 1465 to 647 computations (55.8% saved)

regimes1.3s (14.2%)

Accuracy

Total 5.8b remaining (99.4%)

Threshold costs 0b (0%)

Compiler

Compiled 9586 to 7572 computations (21% saved)

bsearch3.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	72
1	44	72

end0.0ms (0%)

sample2.5s (27%)

Algorithm

1×

intervals

Results

347.0ms	6046×	body	128	valid
222.0ms	783×	body	2048	valid
158.0ms	8000×	pre	128	true
114.0ms	505×	body	1024	valid
108.0ms	301×	body	4096	valid
40.0ms	228×	body	512	valid
15.0ms	137×	body	256	valid

Compiler

Compiled 1265 to 999 computations (21% saved)

Details

analyze1.2s (13.2%)

sample41.0ms (0.4%)

simplify13.0ms (0.1%)

prune5.0ms (0.1%)

localize22.0ms (0.2%)

rewrite155.0ms (1.7%)

series814.0ms (8.9%)

simplify49.0ms (0.5%)

prune155.0ms (1.7%)

localize28.0ms (0.3%)

rewrite202.0ms (2.2%)

series728.0ms (7.9%)

simplify85.0ms (0.9%)

prune199.0ms (2.2%)

localize14.0ms (0.2%)

rewrite178.0ms (1.9%)

series677.0ms (7.4%)

simplify68.0ms (0.7%)

prune178.0ms (1.9%)

localize11.0ms (0.1%)

rewrite111.0ms (1.2%)

series266.0ms (2.9%)

simplify97.0ms (1.1%)

prune88.0ms (1%)

regimes1.3s (14.2%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.5s (27%)

Profiling