Details

analyze1.3s (22.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
13.2%	86.5%	0.2%	11
16.8%	83%	0.2%	12
22.7%	77.1%	0.2%	13
24.1%	74.7%	1.3%	14

Compiler

Compiled 10 to 10 computations (0% saved)

sample54.0ms (0.9%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
6.0ms	90×	body	128	invalid

Compiler

Compiled 19 to 24 computations (-26.3% saved)

simplify201.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	719	13
1	719	13

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

4.9b

Counts

2 → 1

Compiler

Compiled 18 to 18 computations (0% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 y (-.f64 z t))
0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
6.8b	(/.f64 (*.f64 y (-.f64 z t)) a)

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_7239` `add-sqr-sqrt_binary64_7261`
10×	`add-exp-log_binary64_7277` `add-cbrt-cube_binary64_7275`
9×	`add-cube-cbrt_binary64_7274`
6×	`cancel-sign-sub-inv_binary64_7205`
5×	`add-log-exp_binary64_7278` `pow1_binary64_7300` `associate-r_binary64_7179`
4×	`associate-*r/_binary64_7181` `distribute-lft-in_binary64_7188` `distribute-rgt-in_binary64_7189`
3×	`associate-/r_binary64_7183` `associate-l*_binary64_7180` `times-frac_binary64_7245`
2×	`flip3--_binary64_7243` `cbrt-unprod_binary64_7272` `flip--_binary64_7214` `associate-/l/_binary64_7186` `prod-exp_binary64_7288` `cbrt-undiv_binary64_7273` `div-exp_binary64_7290` `sub-neg_binary64_7232`
1×	`flip-+_binary64_7213` `flip3-+_binary64_7242` `pow-prod-down_binary64_7310` `frac-2neg_binary64_7250` `unswap-sqr_binary64_7207` `-commutative_binary64_7170` `associate-/l_binary64_7184` `div-inv_binary64_7236` `distribute-lft-out--_binary64_7191` `difference-of-squares_binary64_7208` `distribute-lft-out_binary64_7190` `+-commutative_binary64_7169` `sum-log_binary64_7330` `clear-num_binary64_7238`

Counts

3 → 65

Calls

3 calls:

13.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
8.0ms	(*.f64 y (-.f64 z t))
5.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

series209.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

82.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
73.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
53.0ms	(*.f64 y (-.f64 z t))

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5397	909

prune86.0ms (1.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	69	5	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	5	75

Error

0.0b

Counts

75 → 5

Compiler

Compiled 1067 to 280 computations (73.8% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
0.0b	(*.f64 y (-.f64 z t))
6.9b	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64_7277`
18×	`associate-r_binary64_7179` `add-sqr-sqrt_binary64_7261`
17×	`add-cbrt-cube_binary64_7275`
16×	`*-un-lft-identity_binary64_7239`
14×	`add-cube-cbrt_binary64_7274`
13×	`prod-exp_binary64_7288`
10×	`pow1_binary64_7300`
9×	`times-frac_binary64_7245`
7×	`associate-*r/_binary64_7181` `cbrt-unprod_binary64_7272`
6×	`cancel-sign-sub-inv_binary64_7205`
5×	`add-log-exp_binary64_7278`
4×	`distribute-lft-in_binary64_7188` `pow-prod-down_binary64_7310` `distribute-rgt-in_binary64_7189` `div-exp_binary64_7290` `associate-l_binary64_7180`
3×	`flip3--_binary64_7243` `flip--_binary64_7214`
2×	`1-exp_binary64_7283` `associate-l/_binary64_7182` `frac-times_binary64_7249` `-commutative_binary64_7170` `cbrt-undiv_binary64_7273` `rec-exp_binary64_7289` `sub-neg_binary64_7232`
1×	`flip-+_binary64_7213` `flip3-+_binary64_7242` `unswap-sqr_binary64_7207` `div-inv_binary64_7236` `un-div-inv_binary64_7237` `distribute-lft-out--_binary64_7191` `difference-of-squares_binary64_7208` `+-commutative_binary64_7169` `sum-log_binary64_7330`

Counts

3 → 83

Calls

3 calls:

11.0ms	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))
7.0ms	(*.f64 y (-.f64 z t))
5.0ms	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))

series172.0ms (3%)

Counts

3 → 9

Calls

3 calls:

66.0ms	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
64.0ms	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))
42.0ms	(*.f64 y (-.f64 z t))

simplify41.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5062	1164

prune116.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	92	5	97

Error

0.0b

Counts

97 → 5

Compiler

Compiled 1412 to 473 computations (66.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 y (-.f64 z t))
0.0b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
0.7b	(/.f64 1 (/.f64 a (*.f64 y (-.f64 z t))))
6.8b	(/.f64 a (*.f64 y (-.f64 z t)))

rewrite59.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64_7245`
33×	`*-un-lft-identity_binary64_7239`
32×	`add-exp-log_binary64_7277` `add-sqr-sqrt_binary64_7261`
28×	`add-cube-cbrt_binary64_7274`
20×	`add-cbrt-cube_binary64_7275`
14×	`div-exp_binary64_7290`
12×	`associate-*r/_binary64_7181`
11×	`associate-/r/_binary64_7185`
10×	`associate-/r*_binary64_7183`
7×	`div-inv_binary64_7236` `cbrt-undiv_binary64_7273` `pow1_binary64_7300`
6×	`flip3--_binary64_7243` `add-log-exp_binary64_7278` `flip--_binary64_7214` `associate-/l*_binary64_7184` `cancel-sign-sub-inv_binary64_7205`
5×	`prod-exp_binary64_7288` `associate-r_binary64_7179`
4×	`distribute-lft-in_binary64_7188` `distribute-rgt-in_binary64_7189`
3×	`1-exp_binary64_7283` `cbrt-unprod_binary64_7272` `rec-exp_binary64_7289` `associate-l_binary64_7180`
2×	`frac-2neg_binary64_7250` `distribute-lft-out_binary64_7190` `sub-neg_binary64_7232` `clear-num_binary64_7238`
1×	`flip-+_binary64_7213` `flip3-+_binary64_7242` `pow-prod-down_binary64_7310` `pow-flip_binary64_7313` `inv-pow_binary64_7324` `unswap-sqr_binary64_7207` `*-commutative_binary64_7170` `distribute-lft-out--_binary64_7191` `difference-of-squares_binary64_7208` `+-commutative_binary64_7169` `sum-log_binary64_7330`

Counts

4 → 130

Calls

4 calls:

14.0ms	(/.f64 1 (/.f64 a (*.f64 y (-.f64 z t))))
11.0ms	(/.f64 a (*.f64 y (-.f64 z t)))
11.0ms	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
7.0ms	(*.f64 y (-.f64 z t))

series260.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

87.0ms	(/.f64 a (*.f64 y (-.f64 z t)))
76.0ms	(/.f64 1 (/.f64 a (*.f64 y (-.f64 z t))))
62.0ms	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
35.0ms	(*.f64 y (-.f64 z t))

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5046	2049

prune114.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	141	6	147

Error

Counts

147 → 6

Compiler

Compiled 2255 to 722 computations (68% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 y (-.f64 z t))
0.0b	(+.f64 x (/.f64 (/.f64 1 a) (/.f64 1 (*.f64 y (-.f64 z t)))))
0.3b	(/.f64 1 (*.f64 y (-.f64 z t)))
6.9b	(/.f64 (/.f64 1 a) (/.f64 1 (*.f64 y (-.f64 z t))))

rewrite97.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

252×	`times-frac_binary64_7245`
112×	`*-un-lft-identity_binary64_7239` `add-sqr-sqrt_binary64_7261`
108×	`add-cube-cbrt_binary64_7274`
100×	`add-exp-log_binary64_7277`
62×	`div-exp_binary64_7290`
32×	`associate-*r/_binary64_7181` `add-cbrt-cube_binary64_7275`
31×	`associate-/r/_binary64_7185`
26×	`div-inv_binary64_7236`
17×	`1-exp_binary64_7283` `rec-exp_binary64_7289`
16×	`flip3--_binary64_7243` `flip--_binary64_7214` `prod-exp_binary64_7288` `associate-/l*_binary64_7184`
15×	`cbrt-undiv_binary64_7273`
10×	`associate-/r*_binary64_7183`
9×	`pow1_binary64_7300`
6×	`add-log-exp_binary64_7278` `cancel-sign-sub-inv_binary64_7205`
5×	`associate-r_binary64_7179`
4×	`distribute-lft-in_binary64_7188` `cbrt-unprod_binary64_7272` `distribute-rgt-in_binary64_7189`
3×	`associate-l_binary64_7180`
2×	`pow-prod-down_binary64_7310` `pow-flip_binary64_7313` `frac-2neg_binary64_7250` `sub-neg_binary64_7232` `clear-num_binary64_7238`
1×	`flip-+_binary64_7213` `flip3-+_binary64_7242` `inv-pow_binary64_7324` `unswap-sqr_binary64_7207` `associate-/l/_binary64_7186` `*-commutative_binary64_7170` `distribute-lft-out--_binary64_7191` `difference-of-squares_binary64_7208` `distribute-lft-out_binary64_7190` `+-commutative_binary64_7169` `sum-log_binary64_7330`

Counts

4 → 257

Calls

4 calls:

32.0ms	(+.f64 x (/.f64 (/.f64 1 a) (/.f64 1 (*.f64 y (-.f64 z t)))))
17.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (*.f64 y (-.f64 z t))))
7.0ms	(*.f64 y (-.f64 z t))
7.0ms	(/.f64 1 (*.f64 y (-.f64 z t)))

series249.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (*.f64 y (-.f64 z t))))
73.0ms	(+.f64 x (/.f64 (/.f64 1 a) (/.f64 1 (*.f64 y (-.f64 z t)))))
60.0ms	(*.f64 y (-.f64 z t))
27.0ms	(/.f64 1 (*.f64 y (-.f64 z t)))

simplify151.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5494	5386

prune596.0ms (10.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	269	6	275

Error

Counts

275 → 6

Compiler

Compiled 4989 to 2022 computations (59.5% saved)

regimes424.0ms (7.3%)

Accuracy

Total 0.9b remaining (98.8%)

Threshold costs 0.9b (98.8%)

Compiler

Compiled 1603 to 1343 computations (16.2% saved)

bsearch48.0ms (0.8%)

Steps

Iters	Range		Point
9	3.3269747207606073e-136	7.248989302577038e-127	5.346561464685811e-127
10	-6.872080776233599e+31	-4.925635416490372e+19	-2.5257589444242445e+21

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	51
1	38	51

end0.0ms (0%)

sample1.3s (22.5%)

Algorithm

1×

intervals

Results

401.0ms	8000×	body	128	valid
119.0ms	2577×	body	128	invalid

Compiler

Compiled 232 to 178 computations (23.3% saved)

Details

analyze1.3s (22.7%)

sample54.0ms (0.9%)

simplify201.0ms (3.5%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite30.0ms (0.5%)

series209.0ms (3.6%)

simplify83.0ms (1.4%)

prune86.0ms (1.5%)

localize11.0ms (0.2%)

rewrite36.0ms (0.6%)

series172.0ms (3%)

simplify41.0ms (0.7%)

prune116.0ms (2%)

localize16.0ms (0.3%)

rewrite59.0ms (1%)

series260.0ms (4.5%)

simplify93.0ms (1.6%)

prune114.0ms (2%)

localize9.0ms (0.2%)

rewrite97.0ms (1.7%)

series249.0ms (4.3%)

simplify151.0ms (2.6%)

prune596.0ms (10.3%)

regimes424.0ms (7.3%)

bsearch48.0ms (0.8%)

simplify9.0ms (0.1%)

end0.0ms (0%)

sample1.3s (22.5%)

Profiling