Details

analyze229.0ms (3.7%)

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
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

Compiler

Compiled 30 to 26 computations (13.3% saved)

sample71.0ms (1.1%)

Algorithm

1×

intervals

Results

30.0ms	69×	body	1024	valid
10.0ms	130×	body	128	valid
10.0ms	9×	body	2048	valid
9.0ms	32×	body	512	valid
3.0ms	16×	body	256	valid
1.0ms	8×	body	128	invalid
1.0ms	7×	body	128	overflowed

Compiler

Compiled 59 to 53 computations (10.2% saved)

simplify225.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4933	41
1	4933	41

prune7.0ms (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: 31.4b

Counts

2 → 1

Compiler

Compiled 112 to 96 computations (14.3% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
0.0b	(*.f64 (+.f64 1 eps) x)
0.0b	(*.f64 (-.f64 1 eps) x)
2.4b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite88.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64_88`
76×	`exp-neg_binary64_126` `frac-times_binary64_89`
57×	`exp-diff_binary64_127` `neg-sub0_binary64_74`
42×	`associate-*l/_binary64_22`
38×	`associate-*r/_binary64_21`
31×	`flip-+_binary64_53` `flip3-+_binary64_82`
29×	`flip--_binary64_54` `flip3--_binary64_83`
19×	`un-div-inv_binary64_77` `add-sqr-sqrt_binary64_101`
18×	`*-un-lft-identity_binary64_79`
15×	`associate-l_binary64_20`
10×	`add-cbrt-cube_binary64_115` `add-cube-cbrt_binary64_114` `pow1_binary64_140`
9×	`add-exp-log_binary64_117` `associate-r_binary64_19`
6×	`add-log-exp_binary64_118`
3×	`unswap-sqr_binary64_47` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `*-commutative_binary64_10` `pow-prod-down_binary64_150` `distribute-lft-out_binary64_30`
2×	`difference-of-squares_binary64_48`
1×	`distribute-lft-out--_binary64_31` `div-inv_binary64_76` `diff-log_binary64_171` `cancel-sign-sub-inv_binary64_45` `sub-neg_binary64_72`

Counts

4 → 166

Calls

4 calls:

21.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
17.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
8.0ms	(*.f64 (-.f64 1 eps) x)
7.0ms	(*.f64 (+.f64 1 eps) x)

series388.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
55.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
38.0ms	(*.f64 (-.f64 1 eps) x)
33.0ms	(*.f64 (+.f64 1 eps) x)

simplify129.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4980	8781
1	4980	8781

prune1.3s (20.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	177	2	179

Merged error: 0.6b

Counts

179 → 2

Compiler

Compiled 24673 to 19788 computations (19.8% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
5.6b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_101`
12×	`associate-l_binary64_20`
7×	`add-exp-log_binary64_117` `add-log-exp_binary64_118`
6×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
4×	`add-cbrt-cube_binary64_115` `unswap-sqr_binary64_47` `unpow-prod-down_binary64_158` `cube-prod_binary64_107`
3×	`prod-exp_binary64_128` `associate-r_binary64_19`
2×	`sqr-pow_binary64_51` `diff-log_binary64_171` `pow1_binary64_140`
1×	`pow-exp_binary64_147` `pow-to-exp_binary64_148` `associate--l+_binary64_16` `sum-log_binary64_170` `flip--_binary64_54` `cube-mult_binary64_109` `cbrt-unprod_binary64_112` `*-commutative_binary64_10` `difference-of-squares_binary64_48` `flip3--_binary64_83` `cancel-sign-sub-inv_binary64_45` `sub-neg_binary64_72` `unpow3_binary64_145`

Counts

2 → 46

Calls

2 calls:

9.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
7.0ms	(*.f64 (pow.f64 x 3) 2/3)

series80.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

46.0ms	(*.f64 (pow.f64 x 3) 2/3)
34.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5056	681

prune81.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	50	4	54

Merged error: 0.6b

Counts

54 → 4

Compiler

Compiled 1441 to 1110 computations (23% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
5.6b	(-.f64 (+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (.f64 x 2/3)) 2) (.f64 x x))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_101`
22×	`cbrt-prod_binary64_110`
14×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
11×	`pow1_binary64_140`
9×	`add-log-exp_binary64_118`
8×	`pow1/3_binary64_161`
6×	`add-exp-log_binary64_117` `associate-l_binary64_20` `swap-sqr_binary64_46` `associate-r_binary64_19`
4×	`add-cbrt-cube_binary64_115` `unswap-sqr_binary64_47`
2×	`pow-prod-up_binary64_149` `pow-sqr_binary64_52` `pow-prod-down_binary64_150` `diff-log_binary64_171`
1×	`associate--l+_binary64_16` `sum-log_binary64_170` `flip--_binary64_54` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `*-commutative_binary64_10` `difference-of-squares_binary64_48` `flip3--_binary64_83` `cancel-sign-sub-inv_binary64_45` `pow-plus_binary64_142` `sub-neg_binary64_72` `pow2_binary64_160`

Counts

4 → 77

Calls

4 calls:

11.0ms	(-.f64 (+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (.f64 x 2/3)) 2) (.f64 x x))
7.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series523.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

164.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
149.0ms	(cbrt.f64 x)
147.0ms	(cbrt.f64 x)
63.0ms	(-.f64 (+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (.f64 x 2/3)) 2) (.f64 x x))

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5100	884

prune121.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 0.6b

Counts

93 → 5

Compiler

Compiled 2354 to 1558 computations (33.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 x 2/3)
0.5b	(pow.f64 (cbrt.f64 x) 2)
0.6b	(cbrt.f64 x)
5.6b	(-.f64 (+.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3) (.f64 x 2/3)) 2) (*.f64 x x))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_101`
10×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
9×	`add-log-exp_binary64_118`
7×	`add-exp-log_binary64_117` `pow1_binary64_140`
6×	`add-cbrt-cube_binary64_115` `unpow-prod-down_binary64_158` `cbrt-prod_binary64_110`
3×	`associate-l_binary64_20` `pow-unpow_binary64_156` `associate-r_binary64_19`
2×	`pow-pow_binary64_151` `diff-log_binary64_171` `pow1/3_binary64_161`
1×	`pow-exp_binary64_147` `pow-to-exp_binary64_148` `associate--l+_binary64_16` `unpow2_binary64_144` `sqr-pow_binary64_51` `sum-log_binary64_170` `flip--_binary64_54` `unswap-sqr_binary64_47` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `*-commutative_binary64_10` `pow-prod-down_binary64_150` `difference-of-squares_binary64_48` `flip3--_binary64_83` `cancel-sign-sub-inv_binary64_45` `sub-neg_binary64_72`

Counts

4 → 66

Calls

4 calls:

15.0ms	(-.f64 (+.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3) (.f64 x 2/3)) 2) (*.f64 x x))
4.0ms	(*.f64 x 2/3)
3.0ms	(pow.f64 (cbrt.f64 x) 2)
1.0ms	(cbrt.f64 x)

series406.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

173.0ms	(pow.f64 (cbrt.f64 x) 2)
149.0ms	(cbrt.f64 x)
61.0ms	(-.f64 (+.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3) (.f64 x 2/3)) 2) (*.f64 x x))
21.0ms	(*.f64 x 2/3)

simplify84.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4878	763
1	4878	763

prune81.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	78	5	83

Merged error: 0.6b

Counts

83 → 5

Compiler

Compiled 1622 to 1128 computations (30.5% saved)

regimes46.0ms (0.7%)

Compiler: Compiled 220 to 196 computations (10.9% saved)

bsearch75.0ms (1.2%)

Steps

Iters	Range		Point
9	22.498808965744637	1845318018.2096539	368.7430660701782

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	160	71
1	160	71

end0.0ms (0%)

sample2.1s (33.5%)

Algorithm

1×

intervals

Results

851.0ms	1953×	body	1024	valid
352.0ms	4331×	body	128	valid
249.0ms	980×	body	512	valid
159.0ms	224×	body	2048	valid
84.0ms	512×	body	256	valid
20.0ms	228×	body	128	invalid
13.0ms	175×	body	128	overflowed
8.0ms	18×	body	1024	invalid
1.0ms	4×	body	512	invalid
1.0ms	5×	body	256	invalid

Compiler

Compiled 185 to 161 computations (13% saved)

Details

analyze229.0ms (3.7%)

sample71.0ms (1.1%)

simplify225.0ms (3.6%)

prune7.0ms (0.1%)

localize18.0ms (0.3%)

rewrite88.0ms (1.4%)

series388.0ms (6.2%)

simplify129.0ms (2.1%)

prune1.3s (20.3%)

localize8.0ms (0.1%)

rewrite20.0ms (0.3%)

series80.0ms (1.3%)

simplify54.0ms (0.9%)

prune81.0ms (1.3%)

localize13.0ms (0.2%)

rewrite28.0ms (0.4%)

series523.0ms (8.4%)

simplify66.0ms (1.1%)

prune121.0ms (1.9%)

localize13.0ms (0.2%)

rewrite29.0ms (0.5%)

series406.0ms (6.5%)

simplify84.0ms (1.3%)

prune81.0ms (1.3%)

regimes46.0ms (0.7%)

bsearch75.0ms (1.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.1s (33.5%)

Profiling