Details

analyze674.0ms (14.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
9.4%	90.4%	0.2%	8
9.4%	90.4%	0.2%	9
10.9%	88.9%	0.2%	10
25.9%	73.9%	0.2%	11
47.1%	52.7%	0.2%	12
55.3%	44.5%	0.2%	13
59.2%	40.6%	0.2%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample21.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

valid

Compiler

Compiled 35 to 33 computations (5.7% saved)

simplify144.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4793	19
1	4793	19

prune8.0ms (0.2%)

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: 2.2b

Counts

2 → 2

Compiler

Compiled 43 to 36 computations (16.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
4.9b	(/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
5.3b	(/.f64 (.f64 y t) (.f64 2 z))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
17×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`
3×	`pow1_binary64` `insert-posit16`
2×	`associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 73

Calls

3 calls:

17.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
12.0ms	(/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
8.0ms	(/.f64 (.f64 y t) (.f64 2 z))

series301.0ms (6.6%)

Counts

3 → 9

Calls

3 calls:

137.0ms	(/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
114.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
49.0ms	(/.f64 (.f64 y t) (.f64 2 z))

simplify100.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5156	1632

prune84.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	80	4	84

Merged error: 0.3b

Counts

84 → 4

Compiler

Compiled 1625 to 835 computations (48.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z)))
0.7b	(/.f64 2 (/.f64 t z))
4.9b	(/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z))
5.0b	(/.f64 y (/.f64 2 (/.f64 t z)))

rewrite160.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

519×	`times-frac_binary64`
300×	`add-sqr-sqrt_binary64`
254×	`*-un-lft-identity_binary64`
244×	`add-cube-cbrt_binary64`
65×	`associate-/r*_binary64`
23×	`div-inv_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`difference-of-squares_binary64`
10×	`cbrt-undiv_binary64` `div-exp_binary64`
9×	`associate-/l*_binary64`
8×	`associate-/r/_binary64`
6×	`add-log-exp_binary64`
4×	`pow1_binary64` `distribute-lft-out--_binary64` `insert-posit16`
3×	`clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 331

Calls

4 calls:

54.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z)))
48.0ms	(/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z))
15.0ms	(/.f64 y (/.f64 2 (/.f64 t z)))
12.0ms	(/.f64 2 (/.f64 t z))

series340.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

136.0ms	(/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z))
116.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z)))
52.0ms	(/.f64 y (/.f64 2 (/.f64 t z)))
36.0ms	(/.f64 2 (/.f64 t z))

simplify216.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

343 → 343

Iterations

Useful iterations: 0 (131.0ms)

Iter	Nodes	Cost
0	5009	8077

prune354.0ms (7.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	341	2	343
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	342	5	347

Merged error: 0.2b

Counts

347 → 5

Compiler

Compiled 8034 to 3680 computations (54.2% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
1.1b	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))
20.4b	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64` `pow1_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `times-frac_binary64` `div-exp_binary64` `insert-posit16` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`

Counts

3 → 52

Calls

3 calls:

13.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))
12.0ms	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
7.0ms	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))

series500.0ms (11%)

Counts

3 → 9

Calls

3 calls:

248.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))
183.0ms	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
69.0ms	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))

simplify172.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	5005	1408

prune67.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	2	0	2
Picked	0	1	1
Done	0	2	2
Total	62	4	66

Merged error: 0b

Counts

66 → 4

Compiler

Compiled 1364 to 756 computations (44.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (/.f64 z y) 1) (.f64 (/.f64 t z) -1/2))
0.0b	(*.f64 (/.f64 t z) -1/2)
0.0b	(-.f64 x (/.f64 1 (+.f64 (.f64 (/.f64 z y) 1) (.f64 (/.f64 t z) -1/2))))
1.1b	(/.f64 1 (+.f64 (.f64 (/.f64 z y) 1) (.f64 (/.f64 t z) -1/2)))

rewrite50.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `associate-l_binary64`
11×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
5×	`associate-*l/_binary64`
4×	`insert-posit16`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-flip_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

19.0ms	(-.f64 x (/.f64 1 (+.f64 (.f64 (/.f64 z y) 1) (.f64 (/.f64 t z) -1/2))))
11.0ms	(/.f64 1 (+.f64 (.f64 (/.f64 z y) 1) (.f64 (/.f64 t z) -1/2)))
8.0ms	(+.f64 (.f64 (/.f64 z y) 1) (.f64 (/.f64 t z) -1/2))
8.0ms	(*.f64 (/.f64 t z) -1/2)

series198.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(-.f64 x (/.f64 1 (+.f64 (.f64 (/.f64 z y) 1) (.f64 (/.f64 t z) -1/2))))
57.0ms	(/.f64 1 (+.f64 (.f64 (/.f64 z y) 1) (.f64 (/.f64 t z) -1/2)))
45.0ms	(+.f64 (.f64 (/.f64 z y) 1) (.f64 (/.f64 t z) -1/2))
25.0ms	(*.f64 (/.f64 t z) -1/2)

simplify137.0ms (3%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4906	1964
1	4906	1964

prune109.0ms (2.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	110	4	114

Merged error: 0b

Counts

114 → 4

Compiler

Compiled 2222 to 1177 computations (47% saved)

regimes76.0ms (1.7%)

Compiler: Compiled 420 to 386 computations (8.1% saved)

bsearch0.0ms (0%)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	39	19
1	39	19

end0.0ms (0%)

sample725.0ms (15.9%)

Algorithm

1×

intervals

Results

396.0ms

8000×

body

valid

Compiler

Compiled 102 to 93 computations (8.8% saved)

Details

analyze674.0ms (14.8%)

sample21.0ms (0.5%)

simplify144.0ms (3.2%)

prune8.0ms (0.2%)

localize9.0ms (0.2%)

rewrite40.0ms (0.9%)

series301.0ms (6.6%)

simplify100.0ms (2.2%)

prune84.0ms (1.8%)

localize11.0ms (0.2%)

rewrite160.0ms (3.5%)

series340.0ms (7.5%)

simplify216.0ms (4.7%)

prune354.0ms (7.8%)

localize11.0ms (0.2%)

rewrite34.0ms (0.8%)

series500.0ms (11%)

simplify172.0ms (3.8%)

prune67.0ms (1.5%)

localize11.0ms (0.2%)

rewrite50.0ms (1.1%)

series198.0ms (4.4%)

simplify137.0ms (3%)

prune109.0ms (2.4%)

regimes76.0ms (1.7%)

bsearch0.0ms (0%)

simplify7.0ms (0.2%)

end0.0ms (0%)

sample725.0ms (15.9%)

Profiling