Details

analyze533.0ms (8.6%)

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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample41.0ms (0.7%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
3.0ms	33×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify255.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	1224	54
1	1224	54

prune8.0ms (0.1%)

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: 20.6b

Counts

2 → 1

Compiler

Compiled 148 to 102 computations (31.1% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_79`
14×	`add-sqr-sqrt_binary64_101`
12×	`add-log-exp_binary64_118`
10×	`sqrt-prod_binary64_95`
8×	`add-cube-cbrt_binary64_114`
6×	`cancel-sign-sub-inv_binary64_45` `pow1_binary64_140`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `sqrt-div_binary64_96`
3×	`flip--_binary64_54` `flip3--_binary64_83`
2×	`neg-sub0_binary64_74` `distribute-lft-out--_binary64_31` `sum-log_binary64_170` `neg-log_binary64_172` `rem-sqrt-square_binary64_92` `distribute-rgt-neg-in_binary64_37` `sqrt-pow1_binary64_97` `difference-of-squares_binary64_48` `diff-log_binary64_171` `pow1/2_binary64_159` `distribute-lft-out_binary64_30`
1×	`associate--l-_binary64_17` `flip-+_binary64_53` `associate-+l-_binary64_14` `+-commutative_binary64_9` `flip3-+_binary64_82` `sub-neg_binary64_72`

Counts

4 → 68

Calls

4 calls:

11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
10.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series486.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

132.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
118.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify100.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4860	1694
1	4860	1694

prune426.0ms (6.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	74	6	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	7	81

Merged error: 8.1b

Counts

81 → 7

Compiler

Compiled 10193 to 6570 computations (35.5% saved)

localize30.0ms (0.5%)

Local error

Found 4 expressions with local error:

5.0b	(+.f64 (neg.f64 b) (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.0b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_101`
8×	`add-log-exp_binary64_118`
7×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
6×	`sqrt-prod_binary64_95` `pow1_binary64_140`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `sqrt-div_binary64_96`
3×	`flip--_binary64_54` `cbrt-prod_binary64_110` `flip3--_binary64_83`
2×	`sum-log_binary64_170` `cbrt-div_binary64_111` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `pow1/2_binary64_159`
1×	`neg-sub0_binary64_74` `flip-+_binary64_53` `neg-log_binary64_172` `associate-+l-_binary64_14` `+-commutative_binary64_9` `pow1/3_binary64_161` `flip3-+_binary64_82`

Counts

4 → 56

Calls

4 calls:

5.0ms	(+.f64 (neg.f64 b) (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series529.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
119.0ms	(+.f64 (neg.f64 b) (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify89.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4856	1381
1	4856	1381

prune150.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	68	7	75

Merged error: 8.1b

Counts

75 → 7

Compiler

Compiled 3881 to 2253 computations (41.9% saved)

localize30.0ms (0.5%)

Local error

Found 4 expressions with local error:

22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_95` `add-sqr-sqrt_binary64_101`
8×	`add-cube-cbrt_binary64_114` `sqrt-div_binary64_96` `pow1_binary64_140` `*-un-lft-identity_binary64_79`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `flip--_binary64_54` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `add-log-exp_binary64_118` `pow1/2_binary64_159` `flip3--_binary64_83`

Counts

4 → 60

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series465.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4932	1404
1	4932	1404

prune222.0ms (3.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	72	7	79

Merged error: 8.1b

Counts

79 → 7

Compiler

Compiled 5591 to 3155 computations (43.6% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.2b	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 a c) b) b)) (*.f64 2 a))
5.5b	(/.f64 (*.f64 a c) b)
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
11×	`*-un-lft-identity_binary64_79`
8×	`add-sqr-sqrt_binary64_101` `add-log-exp_binary64_118`
7×	`add-cube-cbrt_binary64_114`
6×	`cbrt-undiv_binary64_113` `div-exp_binary64_130`
5×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128` `pow1_binary64_140`
4×	`associate-/r*_binary64_23` `times-frac_binary64_85`
3×	`sqrt-prod_binary64_95`
2×	`div-inv_binary64_76` `sum-log_binary64_170` `associate-/l_binary64_24` `flip--_binary64_54` `associate-r/_binary64_21` `sqrt-div_binary64_96` `clear-num_binary64_78` `flip3--_binary64_83` `associate-/l/_binary64_26` `distribute-lft-out_binary64_30` `frac-2neg_binary64_90`
1×	`neg-sub0_binary64_74` `flip-+_binary64_53` `neg-log_binary64_172` `associate-+l-_binary64_14` `+-commutative_binary64_9` `rem-sqrt-square_binary64_92` `distribute-rgt-neg-in_binary64_37` `sqrt-pow1_binary64_97` `pow1/2_binary64_159` `flip3-+_binary64_82`

Counts

4 → 74

Calls

4 calls:

14.0ms	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 a c) b) b)) (*.f64 2 a))
10.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(/.f64 (*.f64 a c) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series357.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
113.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
91.0ms	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 a c) b) b)) (*.f64 2 a))
33.0ms	(/.f64 (*.f64 a c) b)

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5289	1355

prune440.0ms (7.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	3	3
Picked	1	0	1
Done	0	3	3
Total	83	10	93

Merged error: 7.1b

Counts

93 → 10

Compiler

Compiled 10761 to 6771 computations (37.1% saved)

regimes233.0ms (3.8%)

Compiler: Compiled 1734 to 1202 computations (30.7% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	132	487
1	132	487

end0.0ms (0%)

sample1.5s (24.6%)

Algorithm

1×

intervals

Results

756.0ms	8000×	body	128	valid
58.0ms	657×	body	128	nan
37.0ms	411×	body	128	invalid

Compiler

Compiled 774 to 503 computations (35% saved)

Details

analyze533.0ms (8.6%)

sample41.0ms (0.7%)

simplify255.0ms (4.1%)

prune8.0ms (0.1%)

localize23.0ms (0.4%)

rewrite32.0ms (0.5%)

series486.0ms (7.8%)

simplify100.0ms (1.6%)

prune426.0ms (6.9%)

localize30.0ms (0.5%)

rewrite21.0ms (0.3%)

series529.0ms (8.5%)

simplify89.0ms (1.4%)

prune150.0ms (2.4%)

localize30.0ms (0.5%)

rewrite21.0ms (0.3%)

series465.0ms (7.5%)

simplify67.0ms (1.1%)

prune222.0ms (3.6%)

localize25.0ms (0.4%)

rewrite36.0ms (0.6%)

series357.0ms (5.7%)

simplify58.0ms (0.9%)

prune440.0ms (7.1%)

regimes233.0ms (3.8%)

bsearch3.0ms (0.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.5s (24.6%)

Profiling