Details

analyze272.0ms (4.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 23 to 18 computations (21.7% saved)

sample27.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
6.0ms	257×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify205.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4924	19
1	4924	19

prune4.0ms (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

Error

0.1b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.0b	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
0.0b	(*.f64 m (-.f64 1 m))
0.0b	(*.f64 m (-.f64 1 m))
0.0b	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

rewrite61.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-r_binary64`
10×	`associate-l_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`pow1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64`
6×	`add-log-exp_binary64` `associate-*r/_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-out--_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 113

Calls

8 calls:

19.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
8.0ms	(*.f64 m (-.f64 1 m))
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.0ms	(*.f64 m (-.f64 1 m))

series432.0ms (6.6%)

Counts

4 → 48

Calls

4 calls:

149.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
139.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
104.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
39.0ms	(*.f64 m (-.f64 1 m))

Compiler

Compiled 890 to 737 computations (17.2% saved)

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4990	2592
1	4990	2592

prune228.0ms (3.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	157	4	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	158	4	162

Error

0.0b

Counts

162 → 4

Compiler

Compiled 2916 to 1922 computations (34.1% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b	(-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (.f64 2 (.f64 (/.f64 m v) m))))
0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (.f64 2 (.f64 (/.f64 m v) m)))) (/.f64 (pow.f64 m 3) v))
0.0b	(.f64 2 (.f64 (/.f64 m v) m))
0.0b	(+.f64 m (/.f64 m v))
0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (.f64 2 (.f64 (/.f64 m v) m)))) (/.f64 (pow.f64 m 3) v))
0.1b	(-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (.f64 2 (.f64 (/.f64 m v) m))))
0.2b	(*.f64 (/.f64 m v) m)
7.8b	(/.f64 (pow.f64 m 3) v)

rewrite72.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
46×	`add-sqr-sqrt_binary64` `times-frac_binary64`
39×	`add-cube-cbrt_binary64`
34×	`add-log-exp_binary64`
14×	`add-exp-log_binary64`
13×	`associate-l_binary64` `sum-log_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64` `associate-/l*_binary64`
11×	`add-cbrt-cube_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`diff-log_binary64` `frac-sub_binary64`
6×	`pow1_binary64` `frac-add_binary64` `cancel-sign-sub-inv_binary64`
5×	`distribute-lft-out_binary64` `associate-+l+_binary64`
4×	`sqr-pow_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`associate-/r_binary64` `associate-r*_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `flip--_binary64` `associate--l+_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `associate--r+_binary64` `associate-+l-_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `pow-exp_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 153

Calls

8 calls:

31.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (.f64 2 (.f64 (/.f64 m v) m)))) (/.f64 (pow.f64 m 3) v))
12.0ms	(-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (.f64 2 (.f64 (/.f64 m v) m))))
7.0ms	(*.f64 (/.f64 m v) m)
5.0ms	(/.f64 (pow.f64 m 3) v)
0.0ms	(+.f64 m (/.f64 m v))

series489.0ms (7.4%)

Counts

4 → 45

Calls

4 calls:

180.0ms	(-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (.f64 2 (.f64 (/.f64 m v) m))))
160.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (.f64 2 (.f64 (/.f64 m v) m)))) (/.f64 (pow.f64 m 3) v))
89.0ms	(/.f64 (pow.f64 m 3) v)
60.0ms	(*.f64 (/.f64 m v) m)

Compiler

Compiled 1178 to 891 computations (24.4% saved)

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4971	4376
1	4971	4376

prune232.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	198	4	202

Error

0.0b

Counts

202 → 4

Compiler

Compiled 5479 to 2475 computations (54.8% saved)

localize9.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (-.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1) (-.f64 1 m))
0.0b	(/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v))
0.0b	(-.f64 (/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v)) 1)
0.0b	(-.f64 (*.f64 m m) m)
0.0b	(-.f64 (*.f64 m m) m)
0.0b	(-.f64 (/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v)) 1)
0.0b	(/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v))
0.1b	(.f64 (-.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1) (-.f64 1 m))

rewrite83.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64`
62×	`*-un-lft-identity_binary64`
56×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
22×	`difference-of-squares_binary64`
18×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
12×	`distribute-rgt-out--_binary64` `cancel-sign-sub-inv_binary64`
10×	`associate-/r_binary64` `associate-l*_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64` `associate-r_binary64` `neg-mul-1_binary64`
5×	`associate-/l*_binary64`
4×	`sub-neg_binary64` `difference-of-sqr-1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `frac-times_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `associate-r/_binary64` `div-sub_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

4 → 162

Calls

8 calls:

30.0ms	(.f64 (-.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1) (-.f64 1 m))
26.0ms	(-.f64 (/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v)) 1)
8.0ms	(/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v))
4.0ms	(-.f64 (*.f64 m m) m)
0.0ms	(-.f64 (*.f64 m m) m)

series430.0ms (6.5%)

Counts

4 → 48

Calls

4 calls:

138.0ms	(-.f64 (/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v)) 1)
135.0ms	(.f64 (-.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1) (-.f64 1 m))
119.0ms	(/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v))
37.0ms	(-.f64 (*.f64 m m) m)

Compiler

Compiled 901 to 748 computations (17% saved)

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5092	4040

prune193.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	210	4	214

Error

0.0b

Counts

214 → 4

Compiler

Compiled 4181 to 2034 computations (51.4% saved)

localize14.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
0.0b	(*.f64 m (-.f64 1 m))
0.0b	(*.f64 m (-.f64 1 m))
0.0b	(*.f64 m (-.f64 1 m))
0.3b	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
0.3b	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
0.3b	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
0.3b	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))

rewrite69.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`cbrt-prod_binary64`
55×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64`
18×	`cbrt-div_binary64`
16×	`difference-of-squares_binary64`
15×	`add-cube-cbrt_binary64`
14×	`swap-sqr_binary64`
11×	`pow1_binary64`
10×	`associate-r_binary64` `associate-l_binary64`
9×	`flip3--_binary64` `pow1/3_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 115

Calls

8 calls:

24.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
9.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
8.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
8.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
0.0ms	(*.f64 m (-.f64 1 m))

series847.0ms (12.9%)

Counts

4 → 48

Calls

4 calls:

459.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
134.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
128.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
125.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))

Compiler

Compiled 3995 to 3210 computations (19.6% saved)

simplify122.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4964	6182
1	4964	6182

prune432.0ms (6.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	163	4	167

Error

0.0b

Counts

167 → 4

Compiler

Compiled 7953 to 5685 computations (28.5% saved)

simplify140.0ms (2.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	2723	1215
1	2723	1215

regimes145.0ms (2.2%)

Compiler: Compiled 1604 to 1240 computations (22.7% saved)

bsearch0.0ms (0%)

regimes90.0ms (1.4%)

Compiler: Compiled 854 to 666 computations (22% saved)

bsearch0.0ms (0%)

regimes34.0ms (0.5%)

Compiler: Compiled 176 to 158 computations (10.2% saved)

bsearch0.0ms (0%)

regimes60.0ms (0.9%)

Compiler: Compiled 150 to 138 computations (8% saved)

bsearch16.0ms (0.2%)

Steps

Iters	Range		Point
8	1.8476922047977924e-12	1.3265106416288759e-08	3.577168187192135e-11

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes44.0ms (0.7%)

Compiler: Compiled 84 to 86 computations (-2.4% saved)

bsearch14.0ms (0.2%)

Steps

Iters	Range		Point
8	1.8476922047977924e-12	1.3265106416288759e-08	3.1628156974903413e-12

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes29.0ms (0.4%)

Compiler: Compiled 62 to 68 computations (-9.7% saved)

bsearch11.0ms (0.2%)

Steps

Iters	Range		Point
6	0.4460450998243931	2.9472869234977117	2.90526406314691

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes19.0ms (0.3%)

Compiler: Compiled 24 to 38 computations (-58.3% saved)

bsearch0.0ms (0%)

regimes17.0ms (0.3%)

Compiler: Compiled 10 to 26 computations (-160% saved)

bsearch0.0ms (0%)

regimes13.0ms (0.2%)

Accuracy

Total 0.1b remaining (96.7%)

Threshold costs 0.1b (96.7%)

Compiler

Compiled 8 to 20 computations (-150% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 120 to 91 computations (24.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	116	174
1	116	174

end0.0ms (0%)

sample1.5s (22.5%)

Algorithm

1×

intervals

Results

287.0ms	8000×	body	128	valid
163.0ms	8064×	pre	128	true
2.0ms	64×	body	128	invalid

Compiler

Compiled 943 to 727 computations (22.9% saved)

Pareto

0.92922611896841

Details

analyze272.0ms (4.1%)

sample27.0ms (0.4%)

simplify205.0ms (3.1%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

rewrite61.0ms (0.9%)

series432.0ms (6.6%)

simplify77.0ms (1.2%)

prune228.0ms (3.5%)

localize13.0ms (0.2%)

rewrite72.0ms (1.1%)

series489.0ms (7.4%)

simplify75.0ms (1.1%)

prune232.0ms (3.5%)

localize9.0ms (0.1%)

rewrite83.0ms (1.3%)

series430.0ms (6.5%)

simplify66.0ms (1%)

prune193.0ms (2.9%)

localize14.0ms (0.2%)

rewrite69.0ms (1%)

series847.0ms (12.9%)

simplify122.0ms (1.9%)

prune432.0ms (6.6%)

simplify140.0ms (2.1%)

regimes145.0ms (2.2%)

bsearch0.0ms (0%)

regimes90.0ms (1.4%)

bsearch0.0ms (0%)

regimes34.0ms (0.5%)

bsearch0.0ms (0%)

regimes60.0ms (0.9%)

bsearch16.0ms (0.2%)

regimes44.0ms (0.7%)

bsearch14.0ms (0.2%)

regimes29.0ms (0.4%)

bsearch11.0ms (0.2%)

regimes19.0ms (0.3%)

bsearch0.0ms (0%)

regimes17.0ms (0.3%)

bsearch0.0ms (0%)

regimes13.0ms (0.2%)

bsearch7.0ms (0.1%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.5s (22.5%)

Profiling