Details

analyze1.0s (13.6%)

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.8%	89.9%	0.2%	11
14.1%	85.7%	0.2%	12
22.6%	77.1%	0.2%	13
23.7%	76%	0.2%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample27.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	213×	body	128	valid
2.0ms	12×	body	1024	valid
2.0ms	14×	body	512	valid
1.0ms	16×	body	256	valid
1.0ms	28×	body	128	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify181.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (174.0ms)

Iter	Nodes	Cost
0	4749	19
1	4749	19

prune2.0ms (0%)

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

Merged error: 17.4b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 z t) y)
3.4b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
11.0b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
11×	`cancel-sign-sub-inv_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `times-frac_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64`
6×	`distribute-lft-out--_binary64`
5×	`associate-/r_binary64` `pow1_binary64` `flip3--_binary64` `associate-l*_binary64` `difference-of-squares_binary64` `flip--_binary64`
4×	`associate-/r/_binary64` `associate-*l/_binary64`
3×	`associate-r_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `flip-+_binary64` `associate--l+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 80

Calls

3 calls:

13.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
10.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
8.0ms	(*.f64 (-.f64 z t) y)

series722.0ms (9.8%)

Counts

3 → 9

Calls

3 calls:

507.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
152.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
63.0ms	(*.f64 (-.f64 z t) y)

simplify44.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5395	1513

prune314.0ms (4.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	10	90

Merged error: 3.9b

Counts

90 → 10

Compiler

Compiled 6378 to 3407 computations (46.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 y (-.f64 a t))
4.9b	(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))
8.5b	(*.f64 (-.f64 z t) (/.f64 y (-.f64 a t)))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `frac-sub_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
6×	`frac-times_binary64` `associate-*l/_binary64`
5×	`flip3-+_binary64` `associate-/r_binary64` `pow1_binary64` `associate-l*_binary64` `flip-+_binary64`
4×	`associate-/r/_binary64`
3×	`associate-r/_binary64` `associate-/l_binary64`
2×	`diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `cancel-sign-sub-inv_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 107

Calls

3 calls:

15.0ms	(*.f64 (-.f64 z t) (/.f64 y (-.f64 a t)))
8.0ms	(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))
6.0ms	(/.f64 y (-.f64 a t))

series563.0ms (7.6%)

Counts

3 → 9

Calls

3 calls:

345.0ms	(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))
152.0ms	(*.f64 (-.f64 z t) (/.f64 y (-.f64 a t)))
65.0ms	(/.f64 y (-.f64 a t))

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5442	2369

prune254.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	111	5	116
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	117	9	126

Merged error: 3.9b

Counts

126 → 9

Compiler

Compiled 5737 to 2501 computations (56.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
4.2b	(.f64 (-.f64 z t) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))))
9.0b	(-.f64 (+.f64 x y) (.f64 (.f64 (-.f64 z t) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 (cbrt.f64 y) (cbrt.f64 (-.f64 a t)))))

rewrite60.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`frac-times_binary64`
22×	`add-exp-log_binary64` `frac-sub_binary64` `associate-*l/_binary64`
17×	`flip3--_binary64` `flip--_binary64`
14×	`add-cbrt-cube_binary64`
13×	`associate-r_binary64` `add-sqr-sqrt_binary64`
12×	`cbrt-div_binary64`
11×	`flip3-+_binary64` `flip-+_binary64`
10×	`*-un-lft-identity_binary64`
9×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `prod-exp_binary64`
8×	`add-cube-cbrt_binary64` `associate-/r/_binary64`
6×	`pow1_binary64` `cbrt-prod_binary64`
5×	`associate-l_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
2×	`diff-log_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `times-frac_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `cancel-sign-sub-inv_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 102

Calls

4 calls:

25.0ms	(.f64 (-.f64 z t) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))))
12.0ms	(-.f64 (+.f64 x y) (.f64 (.f64 (-.f64 z t) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 (cbrt.f64 y) (cbrt.f64 (-.f64 a t)))))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series1.3s (17.5%)

Counts

4 → 12

Calls

4 calls:

589.0ms	(.f64 (-.f64 z t) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))))
397.0ms	(-.f64 (+.f64 x y) (.f64 (.f64 (-.f64 z t) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 (cbrt.f64 y) (cbrt.f64 (-.f64 a t)))))
161.0ms	(cbrt.f64 y)
146.0ms	(cbrt.f64 y)

simplify95.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4928	3727
1	4928	3727

prune157.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	113	10	123

Merged error: 3.9b

Counts

123 → 10

Compiler

Compiled 4832 to 1200 computations (75.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 a t) y)
0.4b	(/.f64 1 (/.f64 (-.f64 a t) y))
6.6b	(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 1 (/.f64 (-.f64 a t) y))))
8.5b	(*.f64 (-.f64 z t) (/.f64 1 (/.f64 (-.f64 a t) y)))

rewrite93.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64`
184×	`add-sqr-sqrt_binary64`
172×	`*-un-lft-identity_binary64`
118×	`add-cube-cbrt_binary64`
62×	`associate-r_binary64`
28×	`add-exp-log_binary64`
26×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
22×	`associate-/r*_binary64`
20×	`add-cbrt-cube_binary64`
12×	`frac-sub_binary64`
10×	`div-inv_binary64`
9×	`add-log-exp_binary64` `div-exp_binary64`
8×	`flip3--_binary64` `associate-/l*_binary64` `flip--_binary64`
7×	`pow1_binary64` `cbrt-undiv_binary64`
6×	`flip3-+_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
5×	`associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
4×	`rec-exp_binary64`
3×	`cbrt-unprod_binary64` `associate-*r/_binary64` `un-div-inv_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `cancel-sign-sub-inv_binary64` `div-sub_binary64` `inv-pow_binary64` `pow-flip_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 257

Calls

4 calls:

30.0ms	(*.f64 (-.f64 z t) (/.f64 1 (/.f64 (-.f64 a t) y)))
13.0ms	(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 1 (/.f64 (-.f64 a t) y))))
10.0ms	(/.f64 1 (/.f64 (-.f64 a t) y))
7.0ms	(/.f64 (-.f64 a t) y)

series751.0ms (10.2%)

Counts

4 → 12

Calls

4 calls:

346.0ms	(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 1 (/.f64 (-.f64 a t) y))))
234.0ms	(*.f64 (-.f64 z t) (/.f64 1 (/.f64 (-.f64 a t) y)))
122.0ms	(/.f64 1 (/.f64 (-.f64 a t) y))
48.0ms	(/.f64 (-.f64 a t) y)

simplify116.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4962	5321
1	4962	5321

prune251.0ms (3.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	268	1	269
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	268	11	279

Merged error: 3.0b

Counts

279 → 11

Compiler

Compiled 6826 to 1862 computations (72.7% saved)

regimes166.0ms (2.3%)

Compiler: Compiled 1505 to 900 computations (40.2% saved)

bsearch49.0ms (0.7%)

Steps

Iters	Range		Point
9	1.7717135235096408e+193	1.6424316620783132e+200	3.799812770073835e+194
6	-1.9771059038703651e+133	-2.7380349852846582e+132	-1.2036233452053093e+133

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	229	81
1	229	81

end0.0ms (0%)

sample1.0s (14.1%)

Algorithm

1×

intervals

Results

306.0ms	6812×	body	128	valid
55.0ms	365×	body	1024	valid
50.0ms	435×	body	512	valid
38.0ms	748×	body	128	invalid
27.0ms	344×	body	256	valid
8.0ms	44×	body	2048	valid

Compiler

Compiled 441 to 249 computations (43.5% saved)

Details

analyze1.0s (13.6%)

sample27.0ms (0.4%)

simplify181.0ms (2.4%)

prune2.0ms (0%)

localize14.0ms (0.2%)

rewrite38.0ms (0.5%)

series722.0ms (9.8%)

simplify44.0ms (0.6%)

prune314.0ms (4.2%)

localize9.0ms (0.1%)

rewrite41.0ms (0.6%)

series563.0ms (7.6%)

simplify68.0ms (0.9%)

prune254.0ms (3.4%)

localize18.0ms (0.2%)

rewrite60.0ms (0.8%)

series1.3s (17.5%)

simplify95.0ms (1.3%)

prune157.0ms (2.1%)

localize11.0ms (0.1%)

rewrite93.0ms (1.3%)

series751.0ms (10.2%)

simplify116.0ms (1.6%)

prune251.0ms (3.4%)

regimes166.0ms (2.3%)

bsearch49.0ms (0.7%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample1.0s (14.1%)

Profiling