Details

analyze587.0ms (12.8%)

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
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample65.0ms (1.4%)

Algorithm

1×

intervals

Results

25.0ms	47×	body	1280	valid
12.0ms	40×	body	640	valid
7.0ms	137×	body	80	valid
4.0ms	21×	body	320	valid
2.0ms	9×	body	640	invalid
2.0ms	5×	body	1280	invalid
1.0ms	11×	body	160	valid
1.0ms	5×	body	320	invalid
0.0ms	7×	body	80	nan
0.0ms	5×	body	80	invalid
0.0ms	1×	body	160	invalid

Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify68.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4987	13
1	4987	13

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 10.1b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x y))
0.0b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
3.9b	(pow.f64 (/.f64 x (+.f64 x y)) x)

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
118×	`*-un-lft-identity_binary64`
90×	`unpow-prod-down_binary64`
80×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
25×	`associate-/l*_binary64`
19×	`distribute-lft-out_binary64`
16×	`add-exp-log_binary64`
12×	`associate-/r/_binary64`
7×	`associate-/r*_binary64` `add-cbrt-cube_binary64` `div-inv_binary64` `div-exp_binary64`
6×	`flip3-+_binary64` `flip-+_binary64`
5×	`sqr-pow_binary64`
4×	`pow1_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64` `add-log-exp_binary64`
2×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64`

Counts

3 → 172

Calls

3 calls:

11.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
7.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
5.0ms	(/.f64 x (+.f64 x y))

series75.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

35.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
34.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
6.0ms	(/.f64 x (+.f64 x y))

simplify98.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4953	4029
1	4953	4029

prune98.0ms (2.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	177	4	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	178	4	182

Merged error: 0.5b

Counts

182 → 4

Compiler

Compiled 3426 to 687 computations (79.9% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.7b	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
1.2b	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`unpow-prod-down_binary64`
51×	`cbrt-prod_binary64`
48×	`*-un-lft-identity_binary64`
43×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
20×	`add-exp-log_binary64`
14×	`cbrt-div_binary64`
10×	`associate-/r/_binary64`
7×	`flip3-+_binary64` `flip-+_binary64` `pow-exp_binary64`
6×	`pow-unpow_binary64` `pow1_binary64` `distribute-lft-out_binary64`
5×	`div-exp_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `prod-exp_binary64` `frac-times_binary64`
2×	`pow-to-exp_binary64` `associate-r/_binary64` `pow1/3_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-inv_binary64` `associate-l/_binary64`

Counts

4 → 116

Calls

4 calls:

16.0ms	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)
11.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series138.0ms (3%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)
49.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
16.0ms	(cbrt.f64 x)
14.0ms	(cbrt.f64 x)

simplify91.0ms (2%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5564	3131

prune79.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	128	4	132

Merged error: 0.0b

Counts

132 → 4

Compiler

Compiled 4763 to 944 computations (80.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.7b	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
2.2b	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`cbrt-prod_binary64`
85×	`*-un-lft-identity_binary64`
84×	`times-frac_binary64`
61×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
48×	`log-prod_binary64` `unpow-prod-down_binary64`
12×	`distribute-lft-out_binary64`
10×	`add-exp-log_binary64`
6×	`pow1_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
3×	`pow-unpow_binary64`
2×	`flip3-+_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow-pow_binary64` `log-pow_binary64` `sqr-pow_binary64` `log-div_binary64`

Counts

4 → 144

Calls

4 calls:

13.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
8.0ms	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series102.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
19.0ms	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))
18.0ms	(cbrt.f64 x)
15.0ms	(cbrt.f64 x)

simplify120.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4902	3711
1	4902	3711

prune110.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	156	4	160

Merged error: 0.0b

Counts

160 → 4

Compiler

Compiled 5317 to 1606 computations (69.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x))
3.9b	(pow.f64 (/.f64 x (+.f64 x y)) x)
3.9b	(pow.f64 (/.f64 x (+.f64 x y)) x)
3.9b	(pow.f64 (/.f64 x (+.f64 x y)) x)

rewrite46.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
117×	`*-un-lft-identity_binary64`
108×	`unpow-prod-down_binary64`
81×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
70×	`cbrt-prod_binary64`
18×	`distribute-lft-out_binary64`
13×	`add-exp-log_binary64`
12×	`associate-/r/_binary64`
9×	`pow-unpow_binary64`
7×	`pow1_binary64` `div-inv_binary64`
6×	`flip3-+_binary64` `sqr-pow_binary64` `flip-+_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow-to-exp_binary64` `pow-pow_binary64` `div-exp_binary64`
1×	`cbrt-div_binary64` `pow1/3_binary64`

Counts

4 → 178

Calls

4 calls:

11.0ms	(cbrt.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x))
7.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
7.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
7.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

series193.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x))
37.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
35.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
34.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

simplify107.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4984	4987
1	4984	4987

prune92.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	190	4	194

Merged error: 0.0b

Counts

194 → 4

Compiler

Compiled 8019 to 979 computations (87.8% saved)

regimes70.0ms (1.5%)

Compiler: Compiled 164 to 86 computations (47.6% saved)

bsearch74.0ms (1.6%)

Steps

Iters	Range		Point
11	0.44195685534953083	7.474014145689251e+19	187990.0439940413
9	-2.4245165398332455e+73	-1.641892610892636e+67	-1.6688752800430258e+67

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	62
1	39	62

end0.0ms (0%)

sample2.2s (48.2%)

Algorithm

1×

intervals

Results

699.0ms	1423×	body	1280	valid
344.0ms	1168×	body	640	valid
236.0ms	4374×	body	80	valid
135.0ms	668×	body	320	valid
71.0ms	250×	body	640	invalid
47.0ms	367×	body	160	valid
46.0ms	107×	body	1280	invalid
30.0ms	151×	body	320	invalid
12.0ms	98×	body	160	invalid
10.0ms	174×	body	80	invalid
8.0ms	206×	body	80	nan

Compiler

Compiled 175 to 99 computations (43.4% saved)

Details

analyze587.0ms (12.8%)

sample65.0ms (1.4%)

simplify68.0ms (1.5%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

rewrite32.0ms (0.7%)

series75.0ms (1.6%)

simplify98.0ms (2.1%)

prune98.0ms (2.1%)

localize15.0ms (0.3%)

rewrite35.0ms (0.8%)

series138.0ms (3%)

simplify91.0ms (2%)

prune79.0ms (1.7%)

localize15.0ms (0.3%)

rewrite32.0ms (0.7%)

series102.0ms (2.2%)

simplify120.0ms (2.6%)

prune110.0ms (2.4%)

localize11.0ms (0.2%)

rewrite46.0ms (1%)

series193.0ms (4.2%)

simplify107.0ms (2.3%)

prune92.0ms (2%)

regimes70.0ms (1.5%)

bsearch74.0ms (1.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (48.2%)

Profiling