Details

analyze52.0ms (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 21 to 16 computations (23.8% saved)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
5.0ms	257×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 27 computations (15.6% saved)

simplify222.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4740	16
1	4740	16

prune2.0ms (0%)

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

0.2b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize8.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 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)
0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_441`
22×	`*-un-lft-identity_binary64_419`
13×	`add-cube-cbrt_binary64_454` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
10×	`associate-l_binary64_360`
9×	`associate-r_binary64_359` `cancel-sign-sub-inv_binary64_385`
8×	`pow1_binary64_480`
6×	`difference-of-squares_binary64_388` `add-log-exp_binary64_458`
4×	`distribute-rgt-in_binary64_369` `flip3--_binary64_423` `associate-*r/_binary64_361` `distribute-lft-in_binary64_368` `flip--_binary64_394`
3×	`times-frac_binary64_425` `sub-neg_binary64_412` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `distribute-lft-out--_binary64_371` `associate-/r*_binary64_363`
2×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `difference-of-sqr-1_binary64_389` `unswap-sqr_binary64_387` `-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `div-inv_binary64_416` `frac-2neg_binary64_430` `diff-log_binary64_511` `associate-/l*_binary64_364`

Counts

4 → 96

Calls

8 calls:

12.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 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))

series448.0ms (8.4%)

Counts

4 → 45

Calls

4 calls:

180.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
136.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
97.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
36.0ms	(*.f64 m (-.f64 1 m))

Compiler

Compiled 710 to 578 computations (18.6% saved)

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4991	1752
1	4991	1752

prune168.0ms (3.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	131	10	141
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	10	142

Error

0.0b

Counts

142 → 10

Compiler

Compiled 2191 to 1398 computations (36.2% saved)

localize7.0ms (0.1%)

Local error

Found 6 expressions with local error:

0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
0.0b	(/.f64 m (/.f64 v (-.f64 1 m)))
0.0b	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
0.0b	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
0.0b	(/.f64 m (/.f64 v (-.f64 1 m)))
0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)

rewrite102.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`times-frac_binary64_425`
151×	`add-sqr-sqrt_binary64_441`
117×	`*-un-lft-identity_binary64_419`
71×	`add-cube-cbrt_binary64_454`
36×	`difference-of-squares_binary64_388`
24×	`associate-/r*_binary64_363`
14×	`distribute-lft-out--_binary64_371`
13×	`associate-l_binary64_360`
10×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
9×	`associate-/r/_binary64_365`
6×	`difference-of-sqr-1_binary64_389` `flip3--_binary64_423` `flip--_binary64_394`
5×	`add-log-exp_binary64_458` `div-inv_binary64_416` `pow1_binary64_480`
3×	`associate-r_binary64_359` `cancel-sign-sub-inv_binary64_385` `div-exp_binary64_470` `associate-/l*_binary64_364` `cbrt-undiv_binary64_453`
2×	`associate-*l/_binary64_362`
1×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `sub-neg_binary64_412` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `*-commutative_binary64_350` `frac-2neg_binary64_430` `diff-log_binary64_511`

Counts

3 → 168

Calls

6 calls:

41.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
34.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
10.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
0.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
0.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))

series410.0ms (7.7%)

Counts

3 → 39

Calls

3 calls:

174.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
136.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
100.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))

Compiler

Compiled 615 to 498 computations (19% saved)

simplify116.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4956	3975
1	4956	3975

prune195.0ms (3.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	208	9	217

Error

0.0b

Counts

217 → 9

Compiler

Compiled 3931 to 2284 computations (41.9% saved)

localize7.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b	(*.f64 m (/.f64 (-.f64 1 m) v))
0.2b	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
0.0b	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)
0.0b	(/.f64 (-.f64 1 m) v)
0.0b	(/.f64 (-.f64 1 m) v)
0.0b	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)
0.2b	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
0.3b	(*.f64 m (/.f64 (-.f64 1 m) v))

rewrite46.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64_441`
50×	`*-un-lft-identity_binary64_419`
37×	`times-frac_binary64_425`
29×	`add-cube-cbrt_binary64_454`
25×	`associate-r_binary64_359`
14×	`difference-of-squares_binary64_388`
13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`pow1_binary64_480`
7×	`distribute-lft-out--_binary64_371`
6×	`add-log-exp_binary64_458` `associate-l_binary64_360` `associate-/l*_binary64_364`
3×	`unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `flip3--_binary64_423` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385` `associate-/r*_binary64_363`
2×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `div-inv_binary64_416` `-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `associate-*r/_binary64_361` `frac-2neg_binary64_430` `diff-log_binary64_511` `div-sub_binary64_424`

Counts

4 → 117

Calls

8 calls:

11.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
11.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
8.0ms	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)
6.0ms	(/.f64 (-.f64 1 m) v)
0.0ms	(/.f64 (-.f64 1 m) v)

series469.0ms (8.8%)

Counts

4 → 48

Calls

4 calls:

175.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
126.0ms	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)
103.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
65.0ms	(/.f64 (-.f64 1 m) v)

Compiler

Compiled 794 to 642 computations (19.1% saved)

simplify75.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5598	2164

prune142.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	165	9	174

Error

0.0b

Counts

174 → 9

Compiler

Compiled 2652 to 1671 computations (37% saved)

localize12.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(/.f64 (-.f64 1 m) (sqrt.f64 v))
0.3b	(/.f64 m (sqrt.f64 v))
0.2b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
0.0b	(-.f64 (*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1)
0.2b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
0.3b	(/.f64 m (sqrt.f64 v))
0.3b	(/.f64 (-.f64 1 m) (sqrt.f64 v))
0.4b	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))

rewrite84.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

145×	`add-sqr-sqrt_binary64_441`
120×	`times-frac_binary64_425`
113×	`*-un-lft-identity_binary64_419`
74×	`add-cube-cbrt_binary64_454`
66×	`sqrt-prod_binary64_435`
43×	`associate-r_binary64_359`
26×	`difference-of-squares_binary64_388`
25×	`associate-l_binary64_360`
22×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
13×	`distribute-lft-out--_binary64_371`
12×	`associate-/r*_binary64_363`
10×	`unswap-sqr_binary64_387`
9×	`associate-/l*_binary64_364`
8×	`pow1_binary64_480`
6×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
5×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
4×	`add-log-exp_binary64_458` `div-inv_binary64_416`
3×	`associate-*l/_binary64_362`
2×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `flip3--_binary64_423` `*-commutative_binary64_350` `frac-2neg_binary64_430` `flip--_binary64_394` `associate-/l/_binary64_366`
1×	`frac-times_binary64_429` `associate-*r/_binary64_361` `div-sub_binary64_424`

Counts

4 → 213

Calls

8 calls:

30.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
15.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
8.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
4.0ms	(/.f64 m (sqrt.f64 v))
0.0ms	(-.f64 (*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1)

series423.0ms (7.9%)

Counts

4 → 38

Calls

4 calls:

171.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
96.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
91.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
64.0ms	(/.f64 m (sqrt.f64 v))

Compiler

Compiled 948 to 761 computations (19.7% saved)

simplify106.0ms (2%)

Algorithm

1×	egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4976	4162
1	4976	4162

prune237.0ms (4.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	250	1	251
Fresh	1	5	6
Picked	0	1	1
Done	1	1	2
Total	252	8	260

Error

0.0b

Counts

260 → 8

Compiler

Compiled 5149 to 2451 computations (52.4% saved)

simplify17.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	340	1027
1	340	1027

regimes144.0ms (2.7%)

Compiler: Compiled 1380 to 1078 computations (21.9% saved)

bsearch0.0ms (0%)

regimes44.0ms (0.8%)

Compiler: Compiled 198 to 172 computations (13.1% saved)

bsearch0.0ms (0%)

regimes75.0ms (1.4%)

Compiler: Compiled 176 to 154 computations (12.5% saved)

bsearch14.0ms (0.3%)

Steps

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

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes38.0ms (0.7%)

Compiler: Compiled 86 to 86 computations (0% saved)

bsearch11.0ms (0.2%)

Steps

Iters	Range		Point
6	0.4460450998243931	2.9472869234977117	1.0658776399970118

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes27.0ms (0.5%)

Compiler: Compiled 70 to 74 computations (-5.7% saved)

bsearch0.0ms (0%)

regimes21.0ms (0.4%)

Compiler: Compiled 28 to 42 computations (-50% saved)

bsearch0.0ms (0%)

regimes19.0ms (0.3%)

Compiler: Compiled 14 to 32 computations (-128.6% saved)

bsearch0.0ms (0%)

regimes16.0ms (0.3%)

Accuracy

Total 0.2b remaining (98.3%)

Threshold costs 0.2b (98.3%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 79 to 62 computations (21.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	114
1	79	114

end0.0ms (0%)

sample1.4s (27.1%)

Algorithm

1×

intervals

Results

266.0ms	8000×	body	128	valid
170.0ms	8064×	pre	128	true
2.0ms	64×	body	128	invalid

Compiler

Compiled 788 to 615 computations (22% saved)

Pareto

0.5269093016188522

Details

analyze52.0ms (1%)

sample22.0ms (0.4%)

simplify222.0ms (4.2%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite44.0ms (0.8%)

series448.0ms (8.4%)

simplify63.0ms (1.2%)

prune168.0ms (3.1%)

localize7.0ms (0.1%)

rewrite102.0ms (1.9%)

series410.0ms (7.7%)

simplify116.0ms (2.2%)

prune195.0ms (3.6%)

localize7.0ms (0.1%)

rewrite46.0ms (0.9%)

series469.0ms (8.8%)

simplify75.0ms (1.4%)

prune142.0ms (2.7%)

localize12.0ms (0.2%)

rewrite84.0ms (1.6%)

series423.0ms (7.9%)

simplify106.0ms (2%)

prune237.0ms (4.4%)

simplify17.0ms (0.3%)

regimes144.0ms (2.7%)

bsearch0.0ms (0%)

regimes44.0ms (0.8%)

bsearch0.0ms (0%)

regimes75.0ms (1.4%)

bsearch14.0ms (0.3%)

regimes38.0ms (0.7%)

bsearch11.0ms (0.2%)

regimes27.0ms (0.5%)

bsearch0.0ms (0%)

regimes21.0ms (0.4%)

bsearch0.0ms (0%)

regimes19.0ms (0.3%)

bsearch0.0ms (0%)

regimes16.0ms (0.3%)

bsearch6.0ms (0.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (27.1%)

Profiling