Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample19.0ms (0.5%)

Algorithm

1×

intervals

Results

5.0ms	156×	body	128	valid
5.0ms	58×	body	512	valid
2.0ms	34×	body	256	valid
1.0ms	8×	body	1024	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify106.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	76	16
1	76	16

prune2.0ms (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

14.1b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize6.0ms (0.2%)

Local error

Found 6 expressions with local error:

2.8b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
2.8b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

rewrite57.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64_4511`
95×	`add-sqr-sqrt_binary64_4533`
90×	`times-frac_binary64_4517`
43×	`add-cube-cbrt_binary64_4546`
30×	`distribute-lft-out--_binary64_4463`
27×	`cancel-sign-sub-inv_binary64_4477`
23×	`difference-of-squares_binary64_4480`
11×	`add-exp-log_binary64_4549` `associate-/r*_binary64_4455`
10×	`distribute-lft-out_binary64_4462`
8×	`associate-/r/_binary64_4457`
7×	`add-cbrt-cube_binary64_4547` `difference-of-sqr-1_binary64_4481` `div-inv_binary64_4508`
6×	`associate-/l*_binary64_4456`
5×	`pow1_binary64_4572` `add-log-exp_binary64_4550`
4×	`flip--_binary64_4486` `div-exp_binary64_4562`
3×	`flip3--_binary64_4515`
2×	`1-exp_binary64_4555` `flip-+_binary64_4485` `inv-pow_binary64_4596` `frac-2neg_binary64_4522` `pow-flip_binary64_4585` `rec-exp_binary64_4561` `clear-num_binary64_4510` `cbrt-undiv_binary64_4545`
1×	`flip3-+_binary64_4514` `frac-sub_binary64_4520` `diff-log_binary64_4603` `sub-neg_binary64_4504`

Counts

3 → 151

Calls

6 calls:

33.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
6.0ms	(/.f64 1 (-.f64 x 1))
5.0ms	(/.f64 1 (+.f64 x 1))
0.0ms	(/.f64 1 (+.f64 x 1))
0.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

series124.0ms (3.6%)

Counts

3 → 32

Calls

3 calls:

67.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
30.0ms	(/.f64 1 (+.f64 x 1))
27.0ms	(/.f64 1 (-.f64 x 1))

Compiler

Compiled 558 to 494 computations (11.5% saved)

simplify85.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5463	2718

prune201.0ms (5.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	182	2	184

Error

0.4b

Counts

184 → 2

Compiler

Compiled 3015 to 2432 computations (19.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.4b	(/.f64 -2 (+.f64 -1 (*.f64 x x)))
0.4b	(/.f64 -2 (+.f64 -1 (*.f64 x x)))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_4511` `add-sqr-sqrt_binary64_4533` `times-frac_binary64_4517` `add-cube-cbrt_binary64_4546`
3×	`add-cbrt-cube_binary64_4547` `associate-/l_binary64_4456` `add-exp-log_binary64_4549` `associate-/r_binary64_4455`
2×	`associate-/r/_binary64_4457`
1×	`pow1_binary64_4572` `flip-+_binary64_4485` `flip3-+_binary64_4514` `add-log-exp_binary64_4550` `div-exp_binary64_4562` `frac-2neg_binary64_4522` `clear-num_binary64_4510` `div-inv_binary64_4508` `cbrt-undiv_binary64_4545`

Counts

1 → 29

Calls

2 calls:

4.0ms	(/.f64 -2 (+.f64 -1 (*.f64 x x)))
0.0ms	(/.f64 -2 (+.f64 -1 (*.f64 x x)))

series48.0ms (1.4%)

Counts

1 → 10

Calls

1 calls:

48.0ms

(/.f64 -2 (+.f64 -1 (*.f64 x x)))

Compiler

Compiled 175 to 163 computations (6.9% saved)

simplify73.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4916	666
1	4916	666

prune51.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	37	4	41

Error

0.3b

Counts

41 → 4

Compiler

Compiled 594 to 404 computations (32% saved)

localize9.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.4b	(/.f64 -2 (+.f64 -1 (*.f64 x x)))
0.4b	(/.f64 -2 (+.f64 -1 (*.f64 x x)))
0.2b	(.f64 (cbrt.f64 (/.f64 -2 (+.f64 -1 (.f64 x x)))) (cbrt.f64 (/.f64 -2 (+.f64 -1 (*.f64 x x)))))
0.1b	(.f64 (.f64 (cbrt.f64 (/.f64 -2 (+.f64 -1 (.f64 x x)))) (cbrt.f64 (/.f64 -2 (+.f64 -1 (.f64 x x))))) (cbrt.f64 (/.f64 -2 (+.f64 -1 (*.f64 x x)))))
0.4b	(/.f64 -2 (+.f64 -1 (*.f64 x x)))
12.9b	(cbrt.f64 (/.f64 -2 (+.f64 -1 (*.f64 x x))))
12.9b	(cbrt.f64 (/.f64 -2 (+.f64 -1 (*.f64 x x))))
12.9b	(cbrt.f64 (/.f64 -2 (+.f64 -1 (*.f64 x x))))

rewrite27.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`cbrt-prod_binary64_4542`
36×	`times-frac_binary64_4517`
33×	`*-un-lft-identity_binary64_4511` `add-sqr-sqrt_binary64_4533` `add-cube-cbrt_binary64_4546`
8×	`associate-/r/_binary64_4457`
6×	`add-cbrt-cube_binary64_4547` `add-exp-log_binary64_4549`
4×	`pow1_binary64_4572` `flip-+_binary64_4485` `flip3-+_binary64_4514` `add-log-exp_binary64_4550` `div-inv_binary64_4508`
3×	`associate-/l_binary64_4456` `pow1/3_binary64_4593` `cbrt-div_binary64_4543` `associate-/r_binary64_4455`
1×	`div-exp_binary64_4562` `frac-2neg_binary64_4522` `clear-num_binary64_4510` `cbrt-undiv_binary64_4545`

Counts

4 → 101

Calls

8 calls:

4.0ms	(/.f64 -2 (+.f64 -1 (*.f64 x x)))
4.0ms	(cbrt.f64 (/.f64 -2 (+.f64 -1 (*.f64 x x))))
4.0ms	(cbrt.f64 (/.f64 -2 (+.f64 -1 (*.f64 x x))))
4.0ms	(cbrt.f64 (/.f64 -2 (+.f64 -1 (*.f64 x x))))
0.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 -2 (+.f64 -1 (.f64 x x)))) (cbrt.f64 (/.f64 -2 (+.f64 -1 (.f64 x x))))) (cbrt.f64 (/.f64 -2 (+.f64 -1 (*.f64 x x)))))

series485.0ms (13.9%)

Counts

4 → 37

Calls

4 calls:

150.0ms	(cbrt.f64 (/.f64 -2 (+.f64 -1 (*.f64 x x))))
145.0ms	(cbrt.f64 (/.f64 -2 (+.f64 -1 (*.f64 x x))))
136.0ms	(cbrt.f64 (/.f64 -2 (+.f64 -1 (*.f64 x x))))
53.0ms	(/.f64 -2 (+.f64 -1 (*.f64 x x)))

Compiler

Compiled 1707 to 1457 computations (14.6% saved)

simplify83.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5066	3151

prune271.0ms (7.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	138	4	142

Error

0.3b

Counts

142 → 4

Compiler

Compiled 4836 to 3369 computations (30.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

19.6b	(.f64 (/.f64 -2 (-.f64 1 (pow.f64 x 4))) (-.f64 -1 (.f64 x x)))
0.1b	(/.f64 -2 (-.f64 1 (pow.f64 x 4)))
0.1b	(/.f64 -2 (-.f64 1 (pow.f64 x 4)))
19.6b	(.f64 (/.f64 -2 (-.f64 1 (pow.f64 x 4))) (-.f64 -1 (.f64 x x)))

rewrite38.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`add-sqr-sqrt_binary64_4533`
67×	`*-un-lft-identity_binary64_4511`
61×	`times-frac_binary64_4517`
43×	`difference-of-squares_binary64_4480`
36×	`associate-l_binary64_4452`
32×	`add-cube-cbrt_binary64_4546`
14×	`sqr-pow_binary64_4483` `unpow-prod-down_binary64_4590`
10×	`associate-/r*_binary64_4455`
9×	`add-cbrt-cube_binary64_4547` `add-exp-log_binary64_4549`
7×	`distribute-lft-out--_binary64_4463`
4×	`flip--_binary64_4486` `pow1_binary64_4572` `flip3--_binary64_4515` `associate-r_binary64_4451` `associate-/r/_binary64_4457`
3×	`associate-/l*_binary64_4456`
2×	`unswap-sqr_binary64_4479` `distribute-lft-in_binary64_4460` `add-log-exp_binary64_4550` `associate-*r/_binary64_4453` `prod-exp_binary64_4560` `cbrt-unprod_binary64_4544` `div-exp_binary64_4562` `distribute-rgt-in_binary64_4461` `cancel-sign-sub-inv_binary64_4477` `sub-neg_binary64_4504` `frac-times_binary64_4521` `div-inv_binary64_4508` `cbrt-undiv_binary64_4545`
1×	`frac-2neg_binary64_4522` `pow-prod-down_binary64_4582` `-commutative_binary64_4442` `associate-l/_binary64_4454` `clear-num_binary64_4510`

Counts

2 → 121

Calls

4 calls:

18.0ms	(.f64 (/.f64 -2 (-.f64 1 (pow.f64 x 4))) (-.f64 -1 (.f64 x x)))
8.0ms	(/.f64 -2 (-.f64 1 (pow.f64 x 4)))
0.0ms	(/.f64 -2 (-.f64 1 (pow.f64 x 4)))
0.0ms	(.f64 (/.f64 -2 (-.f64 1 (pow.f64 x 4))) (-.f64 -1 (.f64 x x)))

series166.0ms (4.8%)

Counts

2 → 19

Calls

2 calls:

96.0ms	(/.f64 -2 (-.f64 1 (pow.f64 x 4)))
70.0ms	(.f64 (/.f64 -2 (-.f64 1 (pow.f64 x 4))) (-.f64 -1 (.f64 x x)))

Compiler

Compiled 392 to 349 computations (11% saved)

simplify75.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5053	2798

prune169.0ms (4.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	139	5	144

Error

0.3b

Counts

144 → 5

Compiler

Compiled 2939 to 2166 computations (26.3% saved)

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	260	683
1	260	683

regimes49.0ms (1.4%)

Compiler: Compiled 428 to 345 computations (19.4% saved)

bsearch0.0ms (0%)

regimes22.0ms (0.6%)

Compiler: Compiled 18 to 20 computations (-11.1% saved)

bsearch32.0ms (0.9%)

Steps

Iters	Range		Point
11	2.307904188735251e-08	144708799448604.4	1.0121555451085444
9	-3.221532685900676	-5.458083995085865e-08	-1.0247328982238428

Compiler

Compiled 1 to 1 computations (0% saved)

regimes20.0ms (0.6%)

Compiler: Compiled 11 to 14 computations (-27.3% saved)

bsearch31.0ms (0.9%)

Steps

Iters	Range		Point
11	2.307904188735251e-08	144708799448604.4	1.0121555451085444
9	-3.221532685900676	-5.458083995085865e-08	-1.0247328982238428

Compiler

Compiled 1 to 1 computations (0% saved)

regimes18.0ms (0.5%)

Compiler: Compiled 6 to 10 computations (-66.7% saved)

bsearch29.0ms (0.8%)

Steps

Iters	Range		Point
11	2.307904188735251e-08	144708799448604.4	1.0121555451085444
9	-3.221532685900676	-5.458083995085865e-08	-1.0247328982238428

Compiler

Compiled 1 to 1 computations (0% saved)

regimes16.0ms (0.5%)

Accuracy

Total 0.1b remaining (12.8%)

Threshold costs 0.1b (12.8%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch33.0ms (0.9%)

Steps

Iters	Range		Point
11	2.307904188735251e-08	144708799448604.4	1.0121555451085444
9	-3.221532685900676	-5.458083995085865e-08	-1.0247328982238428

Compiler

Compiled 75 to 58 computations (22.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	94
1	35	94

end0.0ms (0%)

sample1.1s (31.4%)

Algorithm

1×

intervals

Results

165.0ms	1945×	body	512	valid
144.0ms	4626×	body	128	valid
59.0ms	988×	body	256	valid
50.0ms	441×	body	1024	valid

Compiler

Compiled 504 to 410 computations (18.7% saved)

Pareto

0.36159092085772276

Details

analyze4.0ms (0.1%)

sample19.0ms (0.5%)

simplify106.0ms (3.1%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite57.0ms (1.6%)

series124.0ms (3.6%)

simplify85.0ms (2.5%)

prune201.0ms (5.8%)

localize4.0ms (0.1%)

rewrite7.0ms (0.2%)

series48.0ms (1.4%)

simplify73.0ms (2.1%)

prune51.0ms (1.5%)

localize9.0ms (0.3%)

rewrite27.0ms (0.8%)

series485.0ms (13.9%)

simplify83.0ms (2.4%)

prune271.0ms (7.8%)

localize8.0ms (0.2%)

rewrite38.0ms (1.1%)

series166.0ms (4.8%)

simplify75.0ms (2.2%)

prune169.0ms (4.9%)

simplify14.0ms (0.4%)

regimes49.0ms (1.4%)

bsearch0.0ms (0%)

regimes22.0ms (0.6%)

bsearch32.0ms (0.9%)

regimes20.0ms (0.6%)

bsearch31.0ms (0.9%)

regimes18.0ms (0.5%)

bsearch29.0ms (0.8%)

regimes16.0ms (0.5%)

bsearch33.0ms (0.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (31.4%)

Profiling