Details

analyze453.0ms (11%)

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
21.8%	78%	0.1%	6
26.5%	73.3%	0.1%	7
32%	67.9%	0.1%	8
46.4%	52.7%	0.9%	9
50.9%	47.2%	1.9%	10
54.3%	43.3%	2.4%	11
62.1%	32.5%	5.4%	12
64.3%	28.1%	7.6%	13
66.3%	24.6%	9.2%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample19.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	29×	body	128	invalid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify242.0ms (5.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	718	15
1	718	15

prune4.0ms (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: 0.0b

Counts

2 → 2

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 4) y)
0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
3.9b	(*.f64 (/.f64 x y) z)

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_78`
25×	`add-sqr-sqrt_binary64_100`
22×	`times-frac_binary64_84`
20×	`add-cube-cbrt_binary64_113`
13×	`associate-l_binary64_19`
10×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
5×	`add-log-exp_binary64_117` `pow1_binary64_139`
4×	`associate-/l*_binary64_23` `distribute-lft-out_binary64_29`
3×	`associate-r_binary64_18` `associate-l/_binary64_21` `associate-/r_binary64_22`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `div-inv_binary64_75` `unswap-sqr_binary64_46` `associate-/l/_binary64_25`
1×	`*-commutative_binary64_9` `flip-+_binary64_52` `frac-sub_binary64_87` `flip3--_binary64_82` `diff-log_binary64_170` `frac-2neg_binary64_89` `flip--_binary64_53` `pow-prod-down_binary64_149` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `sub-div_binary64_85` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

3 → 79

Calls

3 calls:

11.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
8.0ms	(*.f64 (/.f64 x y) z)
7.0ms	(/.f64 (+.f64 x 4) y)

series171.0ms (4.2%)

Counts

3 → 9

Calls

3 calls:

85.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
48.0ms	(*.f64 (/.f64 x y) z)
38.0ms	(/.f64 (+.f64 x 4) y)

simplify78.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4982	1165
1	4982	1165

prune123.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	85	5	90

Merged error: 0b

Counts

90 → 5

Compiler

Compiled 1634 to 801 computations (51% saved)

localize17.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (/.f64 4 y) (*.f64 (/.f64 x y) (-.f64 1 z)))
3.8b	(*.f64 (/.f64 x y) (-.f64 1 z))

rewrite53.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_100`
17×	`*-un-lft-identity_binary64_78`
14×	`add-cube-cbrt_binary64_113`
13×	`associate-l_binary64_19`
12×	`cancel-sign-sub-inv_binary64_44`
10×	`times-frac_binary64_84`
8×	`distribute-lft-in_binary64_27` `associate-+r+_binary64_10` `distribute-rgt-in_binary64_28`
7×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`associate-r_binary64_18`
5×	`frac-add_binary64_86`
4×	`add-log-exp_binary64_117` `flip3--_binary64_82` `frac-times_binary64_88` `flip--_binary64_53` `associate-*r/_binary64_20` `sub-neg_binary64_71` `pow1_binary64_139`
2×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-*l/_binary64_21` `unswap-sqr_binary64_46` `difference-of-squares_binary64_47`
1×	`+-commutative_binary64_8` `*-commutative_binary64_9` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `distribute-lft-out--_binary64_30` `div-inv_binary64_75` `pow-prod-down_binary64_149` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

2 → 71

Calls

2 calls:

23.0ms	(*.f64 (/.f64 x y) (-.f64 1 z))
19.0ms	(+.f64 (/.f64 4 y) (*.f64 (/.f64 x y) (-.f64 1 z)))

series224.0ms (5.4%)

Counts

2 → 6

Calls

2 calls:

145.0ms	(*.f64 (/.f64 x y) (-.f64 1 z))
79.0ms	(+.f64 (/.f64 4 y) (*.f64 (/.f64 x y) (-.f64 1 z)))

simplify99.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5126	1213

prune86.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	77	5	82

Merged error: 0b

Counts

82 → 5

Compiler

Compiled 1480 to 818 computations (44.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.9b	(*.f64 (/.f64 x y) z)
12.3b	(cbrt.f64 (*.f64 (/.f64 x y) z))
12.3b	(cbrt.f64 (*.f64 (/.f64 x y) z))
12.3b	(cbrt.f64 (*.f64 (/.f64 x y) z))

rewrite37.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_100`
13×	`associate-l_binary64_19`
12×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
10×	`times-frac_binary64_84`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`pow1_binary64_139`
4×	`add-log-exp_binary64_117` `associate-*l/_binary64_21`
3×	`cbrt-div_binary64_110` `pow1/3_binary64_160` `associate-r_binary64_18` `cbrt-prod_binary64_109`
2×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `unswap-sqr_binary64_46`
1×	`*-commutative_binary64_9` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `div-inv_binary64_75` `pow-prod-down_binary64_149`

Counts

4 → 62

Calls

4 calls:

14.0ms	(*.f64 (/.f64 x y) z)
8.0ms	(cbrt.f64 (*.f64 (/.f64 x y) z))
5.0ms	(cbrt.f64 (*.f64 (/.f64 x y) z))
4.0ms	(cbrt.f64 (*.f64 (/.f64 x y) z))

series609.0ms (14.8%)

Counts

4 → 12

Calls

4 calls:

225.0ms	(cbrt.f64 (*.f64 (/.f64 x y) z))
173.0ms	(cbrt.f64 (*.f64 (/.f64 x y) z))
169.0ms	(cbrt.f64 (*.f64 (/.f64 x y) z))
42.0ms	(*.f64 (/.f64 x y) z)

simplify97.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4932	761
1	4932	761

prune112.0ms (2.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	74	5	79

Merged error: 0b

Counts

79 → 5

Compiler

Compiled 2348 to 677 computations (71.2% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (+.f64 x 4) (*.f64 x z))
3.4b	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
9×	`times-frac_binary64_84`
7×	`add-log-exp_binary64_117`
4×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
3×	`associate-/l_binary64_23` `associate-/r_binary64_22`
2×	`flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `associate-/l/_binary64_25` `pow1_binary64_139`
1×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `frac-2neg_binary64_89` `associate--l+_binary64_15` `div-inv_binary64_75` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `div-sub_binary64_83` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

2 → 44

Calls

2 calls:

8.0ms	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)
7.0ms	(-.f64 (+.f64 x 4) (*.f64 x z))

series165.0ms (4%)

Counts

2 → 6

Calls

2 calls:

124.0ms	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)
40.0ms	(-.f64 (+.f64 x 4) (*.f64 x z))

simplify69.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5065	938

prune50.0ms (1.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	50	5	55

Merged error: 0b

Counts

55 → 5

Compiler

Compiled 864 to 464 computations (46.3% saved)

regimes298.0ms (7.2%)

Compiler: Compiled 1172 to 886 computations (24.4% saved)

bsearch64.0ms (1.6%)

Steps

Iters	Range	Point
5	1.5026492204542855e+136	4.5062924545700535e+136	1.532546704293406e+136
7	-2.4915747764694524e-282	-9.732291266439374e-284	-2.2732327689230565e-282
8	-1.3542318939205016e+150	-6.457034359171956e+145	-8.278448837687982e+145

Iters

Range

Point

1.5026492204542855e+136

4.5062924545700535e+136

1.532546704293406e+136

-2.4915747764694524e-282

-9.732291266439374e-284

-2.2732327689230565e-282

-1.3542318939205016e+150

-6.457034359171956e+145

-8.278448837687982e+145

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	84	87
1	84	87

end0.0ms (0%)

sample956.0ms (23.2%)

Algorithm

1×

intervals

Results

377.0ms	8000×	body	128	valid
57.0ms	1197×	body	128	invalid

Compiler

Compiled 295 to 218 computations (26.1% saved)

Details

analyze453.0ms (11%)

sample19.0ms (0.5%)

simplify242.0ms (5.9%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

rewrite41.0ms (1%)

series171.0ms (4.2%)

simplify78.0ms (1.9%)

prune123.0ms (3%)

localize17.0ms (0.4%)

rewrite53.0ms (1.3%)

series224.0ms (5.4%)

simplify99.0ms (2.4%)

prune86.0ms (2.1%)

localize14.0ms (0.3%)

rewrite37.0ms (0.9%)

series609.0ms (14.8%)

simplify97.0ms (2.3%)

prune112.0ms (2.7%)

localize9.0ms (0.2%)

rewrite19.0ms (0.5%)

series165.0ms (4%)

simplify69.0ms (1.7%)

prune50.0ms (1.2%)

regimes298.0ms (7.2%)

bsearch64.0ms (1.6%)

simplify7.0ms (0.2%)

end0.0ms (0%)

sample956.0ms (23.2%)

Profiling