Details

analyze29.0ms (0.7%)

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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
62.4%	37.5%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample12.0ms (0.3%)

Algorithm

1×

intervals

Results

6.0ms

256×

body

128

valid

Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify154.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	782	10
1	782	10

prune2.0ms (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

0.0b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64_15764`
22×	`add-sqr-sqrt_binary64_15786`
20×	`times-frac_binary64_15770`
12×	`add-cube-cbrt_binary64_15799`
6×	`distribute-lft-out_binary64_15715`
5×	`distribute-lft-out--_binary64_15716` `difference-of-squares_binary64_15733` `associate-/r*_binary64_15708`
4×	`associate-/l*_binary64_15709`
3×	`add-cbrt-cube_binary64_15800` `add-exp-log_binary64_15802`
2×	`associate-/l/_binary64_15711` `associate-/r/_binary64_15710`
1×	`add-log-exp_binary64_15803` `cbrt-undiv_binary64_15798` `flip3-+_binary64_15767` `div-inv_binary64_15761` `frac-2neg_binary64_15775` `flip--_binary64_15739` `clear-num_binary64_15763` `flip-+_binary64_15738` `flip3--_binary64_15768` `pow1_binary64_15825` `div-exp_binary64_15815`

Counts

1 → 45

Calls

2 calls:

10.0ms	(/.f64 (+.f64 x y) (-.f64 x y))
0.0ms	(/.f64 (+.f64 x y) (-.f64 x y))

series86.0ms (2.2%)

Counts

1 → 21

Calls

1 calls:

86.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

Compiler

Compiled 321 to 297 computations (7.5% saved)

simplify65.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5508	1063

prune69.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	5	67

Error

Counts

67 → 5

Compiler

Compiled 911 to 271 computations (70.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

178×	`times-frac_binary64_15770`
174×	`*-un-lft-identity_binary64_15764`
122×	`add-sqr-sqrt_binary64_15786`
80×	`add-cube-cbrt_binary64_15799`
30×	`associate-/r*_binary64_15708`
26×	`distribute-lft-out_binary64_15715`
21×	`distribute-lft-out--_binary64_15716` `difference-of-squares_binary64_15733`
15×	`add-exp-log_binary64_15802`
11×	`associate-/r/_binary64_15710`
9×	`add-cbrt-cube_binary64_15800`
8×	`associate-/l*_binary64_15709` `div-exp_binary64_15815`
6×	`div-inv_binary64_15761`
5×	`flip3-+_binary64_15767` `flip-+_binary64_15738`
4×	`cbrt-undiv_binary64_15798`
3×	`pow1_binary64_15825`
2×	`add-log-exp_binary64_15803` `frac-2neg_binary64_15775` `associate-/l/_binary64_15711` `clear-num_binary64_15763` `rec-exp_binary64_15814` `1-exp_binary64_15808`
1×	`inv-pow_binary64_15849` `pow-flip_binary64_15838` `flip--_binary64_15739` `div-sub_binary64_15769` `flip3--_binary64_15768`

Counts

2 → 174

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 (-.f64 x y) (+.f64 x y)))
8.0ms	(/.f64 (-.f64 x y) (+.f64 x y))
0.0ms	(/.f64 1 (/.f64 (-.f64 x y) (+.f64 x y)))
0.0ms	(/.f64 (-.f64 x y) (+.f64 x y))

series163.0ms (4.2%)

Counts

2 → 42

Calls

2 calls:

85.0ms	(/.f64 (-.f64 x y) (+.f64 x y))
78.0ms	(/.f64 1 (/.f64 (-.f64 x y) (+.f64 x y)))

Compiler

Compiled 681 to 633 computations (7% saved)

simplify115.0ms (3%)

Algorithm

1×	egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5982	4198

prune142.0ms (3.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	216	5	221

Error

Counts

221 → 5

Compiler

Compiled 3475 to 980 computations (71.8% saved)

localize10.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
0.0b	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
0.0b	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
0.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
0.0b	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
0.0b	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
0.0b	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
0.0b	(*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

rewrite106.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

306×	`*-un-lft-identity_binary64_15764`
238×	`cbrt-prod_binary64_15795`
190×	`times-frac_binary64_15770`
174×	`add-sqr-sqrt_binary64_15786`
86×	`add-cube-cbrt_binary64_15799`
53×	`distribute-lft-out_binary64_15715`
51×	`swap-sqr_binary64_15731`
44×	`distribute-lft-out--_binary64_15716`
32×	`difference-of-squares_binary64_15733`
29×	`associate-l_binary64_15705` `associate-r_binary64_15704`
14×	`associate-/r/_binary64_15710`
11×	`pow1_binary64_15825`
9×	`unswap-sqr_binary64_15732` `pow1/3_binary64_15846`
7×	`div-inv_binary64_15761` `cbrt-div_binary64_15796` `flip--_binary64_15739` `flip3--_binary64_15768`
6×	`add-exp-log_binary64_15802`
4×	`add-log-exp_binary64_15803` `add-cbrt-cube_binary64_15800`
2×	`pow-sqr_binary64_15737` `pow-prod-up_binary64_15834` `pow-prod-down_binary64_15835`
1×	`associate-l/_binary64_15707` `pow2_binary64_15845` `associate-r/_binary64_15706` `pow-plus_binary64_15827` `cbrt-unprod_binary64_15797` `frac-times_binary64_15774` `prod-exp_binary64_15813` `*-commutative_binary64_15695`

Counts

4 → 244

Calls

8 calls:

45.0ms	(*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
8.0ms	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
7.0ms	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
7.0ms	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
0.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

series397.0ms (10.3%)

Counts

4 → 57

Calls

4 calls:

172.0ms	(*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
77.0ms	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
76.0ms	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
72.0ms	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))

Compiler

Compiled 1965 to 1269 computations (35.4% saved)

simplify156.0ms (4%)

Algorithm

1×	egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4909	7805
1	4909	7805

prune264.0ms (6.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	301	0	301
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	301	5	306

Error

Counts

306 → 5

Compiler

Compiled 9986 to 1562 computations (84.4% saved)

localize11.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (/.f64 y x) y)
0.1b	(.f64 (+.f64 (/.f64 y x) 1) (.f64 (/.f64 y x) y))
0.0b	(+.f64 (/.f64 y x) 1)
0.0b	(+.f64 1 (.f64 (/.f64 2 x) (+.f64 y (.f64 (+.f64 (/.f64 y x) 1) (*.f64 (/.f64 y x) y)))))
0.0b	(+.f64 1 (.f64 (/.f64 2 x) (+.f64 y (.f64 (+.f64 (/.f64 y x) 1) (*.f64 (/.f64 y x) y)))))
0.1b	(.f64 (+.f64 (/.f64 y x) 1) (.f64 (/.f64 y x) y))
0.2b	(*.f64 (/.f64 y x) y)
0.6b	(.f64 (/.f64 2 x) (+.f64 y (.f64 (+.f64 (/.f64 y x) 1) (*.f64 (/.f64 y x) y))))

rewrite49.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_15786`
30×	`associate-l_binary64_15705`
23×	`add-cbrt-cube_binary64_15800` `add-exp-log_binary64_15802` `*-un-lft-identity_binary64_15764`
21×	`add-cube-cbrt_binary64_15799`
20×	`times-frac_binary64_15770`
13×	`pow1_binary64_15825`
9×	`cbrt-unprod_binary64_15797` `prod-exp_binary64_15813`
7×	`associate-l/_binary64_15707` `associate-r*_binary64_15704`
6×	`add-log-exp_binary64_15803`
5×	`flip3-+_binary64_15767` `flip-+_binary64_15738` `pow-prod-down_binary64_15835`
4×	`frac-times_binary64_15774` `unswap-sqr_binary64_15732`
3×	`cbrt-undiv_binary64_15798` `associate-r/_binary64_15706` `-commutative_binary64_15695` `div-exp_binary64_15815`
2×	`distribute-lft-in_binary64_15713` `div-inv_binary64_15761` `distribute-rgt-in_binary64_15714` `associate-+r+_binary64_15696`
1×	`distribute-lft-out_binary64_15715` `sum-log_binary64_15855` `+-commutative_binary64_15694`

Counts

4 → 109

Calls

8 calls:

19.0ms	(.f64 (+.f64 (/.f64 y x) 1) (.f64 (/.f64 y x) y))
9.0ms	(.f64 (/.f64 2 x) (+.f64 y (.f64 (+.f64 (/.f64 y x) 1) (*.f64 (/.f64 y x) y))))
7.0ms	(*.f64 (/.f64 y x) y)
3.0ms	(+.f64 1 (.f64 (/.f64 2 x) (+.f64 y (.f64 (+.f64 (/.f64 y x) 1) (*.f64 (/.f64 y x) y)))))
0.0ms	(+.f64 1 (.f64 (/.f64 2 x) (+.f64 y (.f64 (+.f64 (/.f64 y x) 1) (*.f64 (/.f64 y x) y)))))

series516.0ms (13.3%)

Counts

4 → 54

Calls

4 calls:

182.0ms	(.f64 (/.f64 2 x) (+.f64 y (.f64 (+.f64 (/.f64 y x) 1) (*.f64 (/.f64 y x) y))))
152.0ms	(.f64 (+.f64 (/.f64 y x) 1) (.f64 (/.f64 y x) y))
119.0ms	(+.f64 1 (.f64 (/.f64 2 x) (+.f64 y (.f64 (+.f64 (/.f64 y x) 1) (*.f64 (/.f64 y x) y)))))
62.0ms	(*.f64 (/.f64 y x) y)

Compiler

Compiled 1290 to 1104 computations (14.4% saved)

simplify98.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5026	3222

prune155.0ms (4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	163	5	168

Error

Counts

168 → 5

Compiler

Compiled 3707 to 1860 computations (49.8% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	165	460
1	165	460

regimes101.0ms (2.6%)

Compiler: Compiled 994 to 588 computations (40.8% saved)

bsearch0.0ms (0%)

regimes31.0ms (0.8%)

Compiler: Compiled 90 to 102 computations (-13.3% saved)

bsearch0.0ms (0%)

regimes63.0ms (1.6%)

Compiler: Compiled 38 to 54 computations (-42.1% saved)

bsearch47.0ms (1.2%)

Steps

Iters	Range		Point
7	1.5707465168723226e-18	9.582814385231955e-17	1.5476769801282746e-17
9	-4.1276384639791836e-153	-3.144070743768402e-161	-4.0647988135274745e-153
7	-9.0023014773824e-85	-4.0512097831317006e-86	-4.107632137092257e-86
10	-1.2322661262005462e+97	-1.6483013458971535e+84	-4.442686845312879e+90

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes59.0ms (1.5%)

Compiler: Compiled 24 to 40 computations (-66.7% saved)

bsearch45.0ms (1.1%)

Steps

Iters	Range		Point
7	1.5707465168723226e-18	9.582814385231955e-17	3.013434194537718e-17
9	-4.1276384639791836e-153	-3.144070743768402e-161	-4.0647988135274745e-153
7	-9.0023014773824e-85	-4.0512097831317006e-86	-5.300995057569918e-85
10	-1.2322661262005462e+97	-1.6483013458971535e+84	-1.6685747854616791e+84

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes50.0ms (1.3%)

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

bsearch43.0ms (1.1%)

Steps

Iters	Range		Point
7	1.5707465168723226e-18	9.582814385231955e-17	2.885165728068953e-17
9	-4.1276384639791836e-153	-3.144070743768402e-161	-3.059364406300126e-153
7	-9.0023014773824e-85	-4.0512097831317006e-86	-6.0259921717511666e-86
10	-1.2322661262005462e+97	-1.6483013458971535e+84	-1.6685747854616791e+84

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes14.0ms (0.4%)

Accuracy

Total 0.0b remaining (92.3%)

Threshold costs 0.0b (92.3%)

Compiler

Compiled 8 to 20 computations (-150% saved)

bsearch6.0ms (0.2%)

Compiler: Compiled 122 to 96 computations (21.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	144	139
1	144	139

end0.0ms (0%)

sample737.0ms (19%)

Algorithm

1×

intervals

Results

180.0ms

8000×

body

128

valid

Compiler

Compiled 420 to 275 computations (34.5% saved)

Pareto

0.2425647646259801

Details

analyze29.0ms (0.7%)

sample12.0ms (0.3%)

simplify154.0ms (4%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite14.0ms (0.4%)

series86.0ms (2.2%)

simplify65.0ms (1.7%)

prune69.0ms (1.8%)

localize8.0ms (0.2%)

rewrite38.0ms (1%)

series163.0ms (4.2%)

simplify115.0ms (3%)

prune142.0ms (3.7%)

localize10.0ms (0.3%)

rewrite106.0ms (2.7%)

series397.0ms (10.3%)

simplify156.0ms (4%)

prune264.0ms (6.8%)

localize11.0ms (0.3%)

rewrite49.0ms (1.3%)

series516.0ms (13.3%)

simplify98.0ms (2.5%)

prune155.0ms (4%)

simplify10.0ms (0.2%)

regimes101.0ms (2.6%)

bsearch0.0ms (0%)

regimes31.0ms (0.8%)

bsearch0.0ms (0%)

regimes63.0ms (1.6%)

bsearch47.0ms (1.2%)

regimes59.0ms (1.5%)

bsearch45.0ms (1.1%)

regimes50.0ms (1.3%)

bsearch43.0ms (1.1%)

regimes14.0ms (0.4%)

bsearch6.0ms (0.2%)

simplify7.0ms (0.2%)

end0.0ms (0%)

sample737.0ms (19%)

Profiling