Details

analyze49.0ms (1.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	74.9%	25.1%	4
18.7%	56.2%	25.1%	5
28.1%	34.3%	37.6%	6
34.3%	28.1%	37.6%	7
39%	17.2%	43.8%	8
41%	13.7%	45.4%	9
43.1%	8.4%	48.5%	10
44%	6.7%	49.3%	11
45%	4.1%	50.8%	12
45.4%	3.3%	51.2%	13
45.9%	2.1%	52%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample15.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	4×	body	128	nan
0.0ms	3×	body	128	invalid

Compiler

Compiled 17 to 17 computations (0% saved)

simplify168.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	188	12
1	188	12

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
0.2b	(*.f64 y (sqrt.f64 x))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_2457`
7×	`add-log-exp_binary64_2472`
6×	`associate-r_binary64_2378`
5×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
4×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `pow1_binary64_2494` `sqrt-prod_binary64_2451`
3×	`associate-l_binary64_2379`
2×	`sum-log_binary64_2524` `unswap-sqr_binary64_2404`
1×	`flip3-+_binary64_2439` `prod-exp_binary64_2482` `flip-+_binary64_2410` `*-commutative_binary64_2369` `diff-log_binary64_2525` `associate-+l-_binary64_2373` `pow-prod-down_binary64_2504` `cbrt-unprod_binary64_2466` `associate-+l+_binary64_2371` `+-commutative_binary64_2368` `sub-neg_binary64_2429`

Counts

2 → 36

Calls

2 calls:

7.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
5.0ms	(*.f64 y (sqrt.f64 x))

series100.0ms (3.1%)

Counts

2 → 6

Calls

2 calls:

56.0ms	(*.f64 y (sqrt.f64 x))
44.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

simplify54.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5298	567

prune40.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	5	43

Merged error: 0.0b

Counts

43 → 5

Compiler

Compiled 624 to 313 computations (49.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 x))
0.1b	(sqrt.f64 (sqrt.f64 x))
0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

rewrite31.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod_binary64_2451`
25×	`add-sqr-sqrt_binary64_2457`
18×	`associate-r_binary64_2378`
15×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436` `pow1_binary64_2494`
11×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
8×	`sqrt-pow1_binary64_2453`
4×	`prod-exp_binary64_2482` `pow-prod-down_binary64_2504` `add-log-exp_binary64_2472` `pow1/2_binary64_2513` `cbrt-unprod_binary64_2466` `rem-sqrt-square_binary64_2449` `associate-l_binary64_2379`
3×	`unswap-sqr_binary64_2404`
2×	`*-commutative_binary64_2369`

Counts

4 → 88

Calls

4 calls:

11.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
9.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
2.0ms	(sqrt.f64 (sqrt.f64 x))
2.0ms	(sqrt.f64 (sqrt.f64 x))

series324.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(sqrt.f64 (sqrt.f64 x))
88.0ms	(sqrt.f64 (sqrt.f64 x))
79.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
59.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

simplify66.0ms (2%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5279	1029

prune87.0ms (2.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	99	6	105

Merged error: 0b

Counts

105 → 6

Compiler

Compiled 1734 to 665 computations (61.6% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (*.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 x)))
0.3b	(.f64 (.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x))))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite36.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-prod_binary64_2451`
21×	`associate-r_binary64_2378`
18×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `pow1_binary64_2494`
13×	`add-sqr-sqrt_binary64_2457` `add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
9×	`prod-exp_binary64_2482` `pow-prod-down_binary64_2504` `cbrt-unprod_binary64_2466` `cbrt-prod_binary64_2464`
4×	`add-log-exp_binary64_2472`
2×	`pow1/3_binary64_2515` `-commutative_binary64_2369` `associate-l*_binary64_2379`

Counts

4 → 76

Calls

4 calls:

15.0ms	(.f64 (.f64 (*.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 x)))
11.0ms	(.f64 (.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x))))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series737.0ms (22.6%)

Counts

4 → 12

Calls

4 calls:

233.0ms	(.f64 (.f64 (*.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 x)))
196.0ms	(.f64 (.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x))))
154.0ms	(cbrt.f64 x)
153.0ms	(cbrt.f64 x)

simplify68.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5097	1631

prune87.0ms (2.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	88	6	94

Merged error: 0b

Counts

94 → 6

Compiler

Compiled 2121 to 681 computations (67.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 y (fabs.f64 (cbrt.f64 x)))
0.3b	(.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_2457`
12×	`associate-r_binary64_2378`
11×	`add-exp-log_binary64_2471` `add-cube-cbrt_binary64_2468` `add-cbrt-cube_binary64_2469` `*-un-lft-identity_binary64_2436` `pow1_binary64_2494`
9×	`cbrt-prod_binary64_2464`
6×	`sqrt-prod_binary64_2451`
4×	`prod-exp_binary64_2482` `pow-prod-down_binary64_2504` `add-log-exp_binary64_2472` `cbrt-unprod_binary64_2466` `associate-l_binary64_2379`
2×	`pow1/3_binary64_2515` `*-commutative_binary64_2369`
1×	`unswap-sqr_binary64_2404`

Counts

4 → 64

Calls

4 calls:

8.0ms	(.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
4.0ms	(*.f64 y (fabs.f64 (cbrt.f64 x)))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series464.0ms (14.2%)

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt.f64 x)
145.0ms	(cbrt.f64 x)
143.0ms	(.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
28.0ms	(*.f64 y (fabs.f64 (cbrt.f64 x)))

simplify77.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5070	847

prune63.0ms (1.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	76	6	82

Merged error: 0b

Counts

82 → 6

Compiler

Compiled 1276 to 482 computations (62.2% saved)

regimes76.0ms (2.3%)

Compiler: Compiled 650 to 439 computations (32.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms (0%)

sample645.0ms (19.8%)

Algorithm

1×

intervals

Results

246.0ms	7998×	body	128	valid
4.0ms	145×	body	128	nan
2.0ms	64×	body	128	invalid
0.0ms	2×	body	1024	valid

Compiler

Compiled 227 to 156 computations (31.3% saved)

Details

analyze49.0ms (1.5%)

sample15.0ms (0.4%)

simplify168.0ms (5.2%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite15.0ms (0.5%)

series100.0ms (3.1%)

simplify54.0ms (1.7%)

prune40.0ms (1.2%)

localize8.0ms (0.2%)

rewrite31.0ms (1%)

series324.0ms (9.9%)

simplify66.0ms (2%)

prune87.0ms (2.7%)

localize14.0ms (0.4%)

rewrite36.0ms (1.1%)

series737.0ms (22.6%)

simplify68.0ms (2.1%)

prune87.0ms (2.7%)

localize9.0ms (0.3%)

rewrite18.0ms (0.6%)

series464.0ms (14.2%)

simplify77.0ms (2.4%)

prune63.0ms (1.9%)

regimes76.0ms (2.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample645.0ms (19.8%)

Profiling