Details

analyze273.0ms (7.3%)

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%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
31.2%	68.6%	0.1%	9
43.3%	49.9%	6.8%	10
49.7%	40.8%	9.5%	11
55.7%	34%	10.3%	12
61.3%	24.4%	14.3%	13
65%	19.8%	15.3%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample14.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	80	valid
0.0ms	13×	body	80	invalid

Compiler

Compiled 15 to 16 computations (-6.7% saved)

simplify43.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	275	10
1	275	10

prune2.0ms (0%)

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: 0.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 (-.f64 y x) z))
0.0b	(*.f64 (-.f64 y x) z)

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64`
2×	`insert-posit16` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 35

Calls

2 calls:

8.0ms	(*.f64 (-.f64 y x) z)
4.0ms	(+.f64 x (*.f64 (-.f64 y x) z))

series119.0ms (3.2%)

Counts

2 → 6

Calls

2 calls:

64.0ms	(*.f64 (-.f64 y x) z)
55.0ms	(+.f64 x (*.f64 (-.f64 y x) z))

simplify126.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4808	469
1	4808	469

prune30.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	4	42

Merged error: 0.0b

Counts

42 → 4

Compiler

Compiled 542 to 163 computations (69.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 (-.f64 y x) z)) (cbrt.f64 (*.f64 (-.f64 y x) z)))
3.9b	(cbrt.f64 (*.f64 (-.f64 y x) z))
3.9b	(cbrt.f64 (*.f64 (-.f64 y x) z))
3.9b	(cbrt.f64 (*.f64 (-.f64 y x) z))

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`associate-*l/_binary64`
18×	`cbrt-div_binary64`
11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`flip3--_binary64` `pow1/3_binary64` `flip--_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`cbrt-prod_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `insert-posit16` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-*r/_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 76

Calls

4 calls:

10.0ms	(.f64 (cbrt.f64 (.f64 (-.f64 y x) z)) (cbrt.f64 (*.f64 (-.f64 y x) z)))
7.0ms	(cbrt.f64 (*.f64 (-.f64 y x) z))
7.0ms	(cbrt.f64 (*.f64 (-.f64 y x) z))
6.0ms	(cbrt.f64 (*.f64 (-.f64 y x) z))

series1.1s (30.6%)

Counts

4 → 12

Calls

4 calls:

347.0ms	(.f64 (cbrt.f64 (.f64 (-.f64 y x) z)) (cbrt.f64 (*.f64 (-.f64 y x) z)))
268.0ms	(cbrt.f64 (*.f64 (-.f64 y x) z))
267.0ms	(cbrt.f64 (*.f64 (-.f64 y x) z))
257.0ms	(cbrt.f64 (*.f64 (-.f64 y x) z))

simplify120.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4927	1420
1	4927	1420

prune87.0ms (2.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	87	5	92

Merged error: 0.0b

Counts

92 → 5

Compiler

Compiled 2400 to 593 computations (75.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x)))
1.7b	(-.f64 (.f64 y y) (.f64 x x))
8.8b	(.f64 z (-.f64 (.f64 y y) (*.f64 x x)))
18.4b	(/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x))

rewrite39.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64`
4×	`associate-/r_binary64` `associate-r_binary64` `associate-r/_binary64` `times-frac_binary64` `insert-posit16`
3×	`sub-neg_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 78

Calls

4 calls:

13.0ms	(/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x))
10.0ms	(+.f64 x (/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x)))
9.0ms	(.f64 z (-.f64 (.f64 y y) (*.f64 x x)))
5.0ms	(-.f64 (.f64 y y) (.f64 x x))

series444.0ms (11.9%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x))
119.0ms	(.f64 z (-.f64 (.f64 y y) (*.f64 x x)))
104.0ms	(+.f64 x (/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x)))
45.0ms	(-.f64 (.f64 y y) (.f64 x x))

simplify108.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4956	1263
1	4956	1263

prune66.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	91	4	95

Merged error: 0b

Counts

95 → 4

Compiler

Compiled 1582 to 364 computations (77% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 z (/.f64 1 (-.f64 y x))))
0.0b	(/.f64 1 (-.f64 y x))
0.2b	(/.f64 z (/.f64 1 (-.f64 y x)))

rewrite53.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
105×	`*-un-lft-identity_binary64`
103×	`add-sqr-sqrt_binary64`
71×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`
16×	`add-exp-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
11×	`associate-/r/_binary64`
10×	`add-cbrt-cube_binary64`
8×	`div-exp_binary64`
6×	`associate-/l*_binary64` `div-inv_binary64`
5×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
4×	`pow1_binary64` `cbrt-undiv_binary64`
3×	`insert-posit16`
2×	`1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `inv-pow_binary64` `+-commutative_binary64` `pow-flip_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 160

Calls

3 calls:

24.0ms	(+.f64 x (/.f64 z (/.f64 1 (-.f64 y x))))
12.0ms	(/.f64 z (/.f64 1 (-.f64 y x)))
8.0ms	(/.f64 1 (-.f64 y x))

series171.0ms (4.6%)

Counts

3 → 9

Calls

3 calls:

67.0ms	(/.f64 z (/.f64 1 (-.f64 y x)))
53.0ms	(/.f64 1 (-.f64 y x))
51.0ms	(+.f64 x (/.f64 z (/.f64 1 (-.f64 y x))))

simplify150.0ms (4%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	5277	2771

prune120.0ms (3.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	169	4	173

Merged error: 0b

Counts

173 → 4

Compiler

Compiled 2619 to 914 computations (65.1% saved)

regimes47.0ms (1.3%)

Compiler: Compiled 232 to 162 computations (30.2% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms (0%)

sample493.0ms (13.2%)

Algorithm

1×

intervals

Results

209.0ms	8000×	body	80	valid
14.0ms	585×	body	80	invalid

Compiler

Compiled 68 to 49 computations (27.9% saved)

Details

analyze273.0ms (7.3%)

sample14.0ms (0.4%)

simplify43.0ms (1.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite14.0ms (0.4%)

series119.0ms (3.2%)

simplify126.0ms (3.4%)

prune30.0ms (0.8%)

localize11.0ms (0.3%)

rewrite32.0ms (0.9%)

series1.1s (30.6%)

simplify120.0ms (3.2%)

prune87.0ms (2.3%)

localize10.0ms (0.3%)

rewrite39.0ms (1.1%)

series444.0ms (11.9%)

simplify108.0ms (2.9%)

prune66.0ms (1.8%)

localize6.0ms (0.2%)

rewrite53.0ms (1.4%)

series171.0ms (4.6%)

simplify150.0ms (4%)

prune120.0ms (3.2%)

regimes47.0ms (1.3%)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

end0.0ms (0%)

sample493.0ms (13.2%)

Profiling