Details

analyze662.0ms (11.8%)

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)

sample41.0ms (0.7%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
3.0ms	41×	body	128	invalid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify252.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	738	15
1	738	15

prune7.0ms (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)

localize17.0ms (0.3%)

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))
3.3b	(*.f64 (/.f64 x y) z)

rewrite60.0ms (1.1%)

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:

20.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
14.0ms	(*.f64 (/.f64 x y) z)
11.0ms	(/.f64 (+.f64 x 4) y)

series135.0ms (2.4%)

Counts

3 → 9

Calls

3 calls:

63.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
38.0ms	(*.f64 (/.f64 x y) z)
34.0ms	(/.f64 (+.f64 x 4) y)

simplify147.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4926	1165
1	4926	1165

prune155.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	85	5	90

Merged error: 0.0b

Counts

90 → 5

Compiler

Compiled 1614 to 794 computations (50.8% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)
1.2b	(*.f64 z (/.f64 (cbrt.f64 x) y))
2.4b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 z (/.f64 (cbrt.f64 x) y)))

rewrite69.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`add-exp-log_binary64_116`
35×	`add-cbrt-cube_binary64_114`
33×	`prod-exp_binary64_127`
30×	`add-sqr-sqrt_binary64_100`
23×	`times-frac_binary64_84` `associate-r_binary64_18`
22×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
20×	`cbrt-unprod_binary64_111`
18×	`div-exp_binary64_129`
16×	`cbrt-prod_binary64_109`
11×	`pow1_binary64_139`
10×	`associate-l_binary64_19` `cbrt-undiv_binary64_112`
6×	`1-exp_binary64_122`
4×	`add-log-exp_binary64_117` `pow-prod-down_binary64_149` `associate-*r/_binary64_20`
3×	`unswap-sqr_binary64_46`
2×	`*-commutative_binary64_9` `pow1/3_binary64_160` `div-inv_binary64_75`
1×	`frac-times_binary64_88` `associate-*l/_binary64_21`

Counts

4 → 109

Calls

4 calls:

25.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 z (/.f64 (cbrt.f64 x) y)))
19.0ms	(*.f64 z (/.f64 (cbrt.f64 x) y))
2.0ms	(cbrt.f64 x)
2.0ms	(cbrt.f64 x)

series557.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt.f64 x)
155.0ms	(cbrt.f64 x)
146.0ms	(*.f64 z (/.f64 (cbrt.f64 x) y))
82.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 z (/.f64 (cbrt.f64 x) y)))

simplify143.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4951	1179
1	4951	1179

prune216.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	120	6	126

Merged error: 0b

Counts

126 → 6

Compiler

Compiled 2737 to 1217 computations (55.5% saved)

localize15.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (+.f64 x 4) (*.f64 x z))
2.7b	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)

rewrite34.0ms (0.6%)

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:

15.0ms	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)
13.0ms	(-.f64 (+.f64 x 4) (*.f64 x z))

series109.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

81.0ms	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)
28.0ms	(-.f64 (+.f64 x 4) (*.f64 x z))

simplify113.0ms (2%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4966	938
1	4966	938

prune89.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	51	5	56

Merged error: 0b

Counts

56 → 5

Compiler

Compiled 906 to 499 computations (44.9% saved)

localize18.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (+.f64 x 4) (*.f64 x z))
0.1b	(/.f64 1 (/.f64 y (-.f64 (+.f64 x 4) (*.f64 x z))))
2.7b	(/.f64 y (-.f64 (+.f64 x 4) (*.f64 x z)))

rewrite74.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64_84`
55×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
18×	`associate-/r*_binary64_22`
16×	`add-exp-log_binary64_116`
11×	`associate-/r/_binary64_24`
10×	`add-cbrt-cube_binary64_114`
8×	`add-log-exp_binary64_117` `div-exp_binary64_129`
6×	`flip3--_binary64_82` `div-inv_binary64_75` `flip--_binary64_53` `associate-/l*_binary64_23`
4×	`cbrt-undiv_binary64_112` `pow1_binary64_139`
2×	`diff-log_binary64_170` `frac-2neg_binary64_89` `1-exp_binary64_122` `rec-exp_binary64_128` `clear-num_binary64_77`
1×	`inv-pow_binary64_163` `associate--l+_binary64_15` `pow-flip_binary64_152` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

3 → 127

Calls

3 calls:

21.0ms	(/.f64 1 (/.f64 y (-.f64 (+.f64 x 4) (*.f64 x z))))
15.0ms	(/.f64 y (-.f64 (+.f64 x 4) (*.f64 x z)))
12.0ms	(-.f64 (+.f64 x 4) (*.f64 x z))

series233.0ms (4.1%)

Counts

3 → 9

Calls

3 calls:

126.0ms	(/.f64 y (-.f64 (+.f64 x 4) (*.f64 x z)))
78.0ms	(/.f64 1 (/.f64 y (-.f64 (+.f64 x 4) (*.f64 x z))))
28.0ms	(-.f64 (+.f64 x 4) (*.f64 x z))

simplify169.0ms (3%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	5478	3310

prune262.0ms (4.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	136	5	141

Merged error: 0b

Counts

141 → 5

Compiler

Compiled 2912 to 1677 computations (42.4% saved)

regimes370.0ms (6.6%)

Compiler: Compiled 1352 to 1001 computations (26% saved)

bsearch68.0ms (1.2%)

Steps

Iters	Range		Point
7	5.525308498023065e-78	2.1612977340322427e-76	8.445136388882722e-77
9	-2.675550763182555e-39	-1.0064484611189599e-47	-2.3799731064557978e-40

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	73	47
1	73	47

end0.0ms (0%)

sample1.6s (28.2%)

Algorithm

1×

intervals

Results

585.0ms	8000×	body	128	valid
84.0ms	1174×	body	128	invalid

Compiler

Compiled 304 to 226 computations (25.7% saved)

Details

analyze662.0ms (11.8%)

sample41.0ms (0.7%)

simplify252.0ms (4.5%)

prune7.0ms (0.1%)

localize17.0ms (0.3%)

rewrite60.0ms (1.1%)

series135.0ms (2.4%)

simplify147.0ms (2.6%)

prune155.0ms (2.7%)

localize27.0ms (0.5%)

rewrite69.0ms (1.2%)

series557.0ms (9.9%)

simplify143.0ms (2.5%)

prune216.0ms (3.8%)

localize15.0ms (0.3%)

rewrite34.0ms (0.6%)

series109.0ms (1.9%)

simplify113.0ms (2%)

prune89.0ms (1.6%)

localize18.0ms (0.3%)

rewrite74.0ms (1.3%)

series233.0ms (4.1%)

simplify169.0ms (3%)

prune262.0ms (4.6%)

regimes370.0ms (6.6%)

bsearch68.0ms (1.2%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.6s (28.2%)

Profiling