Details

analyze43.0ms (1%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
50%	50%	0.1%	6
68.7%	31.2%	0.1%	7
81.2%	18.7%	0.1%	8
89%	10.9%	0.1%	9
92.1%	7.8%	0.1%	10
95.6%	4.3%	0.1%	11
96.4%	3.5%	0.1%	12
98%	1.9%	0.1%	13
98.2%	1.7%	0.1%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample15.0ms (0.3%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify227.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (136.0ms)

Iter	Nodes	Cost
0	4853	13
1	4853	13

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

11.9b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

11.6b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))
11.6b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64_15118` `add-exp-log_binary64_15120`
7×	`*-un-lft-identity_binary64_15082` `add-sqr-sqrt_binary64_15104`
5×	`times-frac_binary64_15088` `associate-/r*_binary64_15026`
3×	`div-exp_binary64_15133` `prod-exp_binary64_15131` `add-cube-cbrt_binary64_15117` `cbrt-unprod_binary64_15115` `cbrt-undiv_binary64_15116`
2×	`distribute-lft-out--_binary64_15034` `difference-of-squares_binary64_15051` `associate-/r/_binary64_15028`
1×	`frac-2neg_binary64_15093` `flip3--_binary64_15086` `clear-num_binary64_15081` `pow1_binary64_15143` `add-log-exp_binary64_15121` `div-inv_binary64_15079` `flip--_binary64_15057` `associate-/l*_binary64_15027`

Counts

1 → 29

Calls

2 calls:

9.0ms	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))
0.0ms	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

series104.0ms (2.3%)

Counts

1 → 21

Calls

1 calls:

104.0ms

(/.f64 (*.f64 (*.f64 x 2) y) (-.f64 x y))

Compiler

Compiled 405 to 357 computations (11.9% saved)

simplify53.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5029	817

prune49.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	47	4	51

Error

0.0b

Counts

51 → 4

Compiler

Compiled 666 to 320 computations (52% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
0.0b	(-.f64 (/.f64 1/2 y) (/.f64 1/2 x))
0.0b	(-.f64 (/.f64 1/2 y) (/.f64 1/2 x))
0.2b	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))

rewrite43.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-sqr-sqrt_binary64_15104`
95×	`times-frac_binary64_15088`
76×	`*-un-lft-identity_binary64_15082`
36×	`add-cube-cbrt_binary64_15117`
25×	`distribute-lft-out--_binary64_15034`
20×	`difference-of-squares_binary64_15051`
13×	`cancel-sign-sub-inv_binary64_15048`
12×	`div-inv_binary64_15079` `associate-/r*_binary64_15026`
6×	`add-exp-log_binary64_15120`
4×	`add-cbrt-cube_binary64_15118` `add-log-exp_binary64_15121`
3×	`pow1_binary64_15143` `associate-/r/_binary64_15028` `associate-/l*_binary64_15027`
2×	`div-exp_binary64_15133` `frac-sub_binary64_15091` `flip3--_binary64_15086` `flip--_binary64_15057`
1×	`inv-pow_binary64_15167` `frac-2neg_binary64_15093` `clear-num_binary64_15081` `cbrt-undiv_binary64_15116` `sub-neg_binary64_15075` `diff-log_binary64_15174` `1-exp_binary64_15126` `rec-exp_binary64_15132` `pow-flip_binary64_15156`

Counts

2 → 104

Calls

4 calls:

16.0ms	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
15.0ms	(-.f64 (/.f64 1/2 y) (/.f64 1/2 x))
0.0ms	(-.f64 (/.f64 1/2 y) (/.f64 1/2 x))
0.0ms	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))

series216.0ms (4.8%)

Counts

2 → 33

Calls

2 calls:

113.0ms	(-.f64 (/.f64 1/2 y) (/.f64 1/2 x))
103.0ms	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))

Compiler

Compiled 591 to 549 computations (7.1% saved)

simplify76.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4907	2412
1	4907	2412

prune127.0ms (2.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	136	5	141

Error

Counts

141 → 5

Compiler

Compiled 2080 to 1575 computations (24.3% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.0b	(.f64 (.f64 x 2) (/.f64 y (-.f64 x y)))
0.0b	(/.f64 y (-.f64 x y))
0.0b	(/.f64 y (-.f64 x y))
8.0b	(.f64 (.f64 x 2) (/.f64 y (-.f64 x y)))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64_15082` `add-sqr-sqrt_binary64_15104`
30×	`times-frac_binary64_15088`
21×	`add-cube-cbrt_binary64_15117` `associate-r_binary64_15022`
16×	`add-cbrt-cube_binary64_15118` `add-exp-log_binary64_15120`
7×	`distribute-lft-out--_binary64_15034` `difference-of-squares_binary64_15051` `pow1_binary64_15143`
6×	`prod-exp_binary64_15131` `cbrt-unprod_binary64_15115`
5×	`associate-/r*_binary64_15026`
4×	`associate-/r/_binary64_15028`
3×	`pow-prod-down_binary64_15153` `div-exp_binary64_15133` `cbrt-undiv_binary64_15116` `associate-/l*_binary64_15027`
2×	`flip3--_binary64_15086` `add-log-exp_binary64_15121` `div-inv_binary64_15079` `flip--_binary64_15057`
1×	`frac-2neg_binary64_15093` `clear-num_binary64_15081` `associate-l_binary64_15023` `-commutative_binary64_15013` `associate-r/_binary64_15024`

Counts

2 → 78

Calls

4 calls:

11.0ms	(.f64 (.f64 x 2) (/.f64 y (-.f64 x y)))
6.0ms	(/.f64 y (-.f64 x y))
0.0ms	(/.f64 y (-.f64 x y))
0.0ms	(.f64 (.f64 x 2) (/.f64 y (-.f64 x y)))

series180.0ms (4%)

Counts

2 → 42

Calls

2 calls:

102.0ms	(.f64 (.f64 x 2) (/.f64 y (-.f64 x y)))
77.0ms	(/.f64 y (-.f64 x y))

Compiler

Compiled 810 to 690 computations (14.8% saved)

simplify65.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5320	1783

prune86.0ms (1.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	120	5	125

Error

Counts

125 → 5

Compiler

Compiled 1750 to 686 computations (60.8% saved)

localize10.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (/.f64 1/2 y) (/.f64 1/2 x))
0.0b	(-.f64 (/.f64 1/2 y) (/.f64 1/2 x))
0.0b	(sqrt.f64 (/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x))))
0.0b	(sqrt.f64 (/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x))))
0.0b	(-.f64 (/.f64 1/2 y) (/.f64 1/2 x))
0.2b	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
0.2b	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))) (sqrt.f64 (/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))))

rewrite197.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Rules

467×	`times-frac_binary64_15088`
463×	`add-sqr-sqrt_binary64_15104`
357×	`*-un-lft-identity_binary64_15082`
214×	`sqrt-prod_binary64_15098`
159×	`add-cube-cbrt_binary64_15117`
111×	`distribute-lft-out--_binary64_15034`
84×	`difference-of-squares_binary64_15051`
56×	`swap-sqr_binary64_15049`
51×	`div-inv_binary64_15079`
46×	`associate-l_binary64_15023` `associate-r_binary64_15022`
29×	`pow1_binary64_15143`
24×	`sqrt-pow1_binary64_15100` `associate-/r*_binary64_15026`
18×	`associate-/r/_binary64_15028`
16×	`unswap-sqr_binary64_15050`
14×	`add-exp-log_binary64_15120`
13×	`cancel-sign-sub-inv_binary64_15048`
10×	`inv-pow_binary64_15167` `add-cbrt-cube_binary64_15118` `pow-flip_binary64_15156`
9×	`pow-prod-up_binary64_15152`
8×	`pow1/2_binary64_15162`
7×	`frac-sub_binary64_15091` `flip3--_binary64_15086` `flip--_binary64_15057`
6×	`rem-sqrt-square_binary64_15095` `add-log-exp_binary64_15121` `associate-/l*_binary64_15027`
5×	`pow-prod-down_binary64_15153` `pow-sqr_binary64_15055`
4×	`div-exp_binary64_15133` `sqrt-div_binary64_15099`
3×	`sqr-abs_binary64_15097`
2×	`frac-2neg_binary64_15093` `clear-num_binary64_15081` `cbrt-undiv_binary64_15116` `1-exp_binary64_15126` `rec-exp_binary64_15132`
1×	`rem-square-sqrt_binary64_15094` `frac-times_binary64_15092` `prod-exp_binary64_15131` `pow2_binary64_15163` `cbrt-unprod_binary64_15115` `sub-neg_binary64_15075` `sqrt-unprod_binary64_15102` `-commutative_binary64_15013` `diff-log_binary64_15174` `associate-l/_binary64_15025` `associate-*r/_binary64_15024` `pow-plus_binary64_15145`

Counts

4 → 377

Calls

8 calls:

82.0ms	(*.f64 (sqrt.f64 (/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))) (sqrt.f64 (/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))))
17.0ms	(-.f64 (/.f64 1/2 y) (/.f64 1/2 x))
17.0ms	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
16.0ms	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
0.0ms	(sqrt.f64 (/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x))))

series431.0ms (9.6%)

Counts

4 → 63

Calls

4 calls:

133.0ms	(*.f64 (sqrt.f64 (/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))) (sqrt.f64 (/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))))
117.0ms	(-.f64 (/.f64 1/2 y) (/.f64 1/2 x))
93.0ms	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
88.0ms	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))

Compiler

Compiled 1944 to 1716 computations (11.7% saved)

simplify171.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

440 → 440

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4893	9789
1	4893	9789

prune1.0s (22.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	440	0	440
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	440	5	445

Error

Counts

445 → 5

Compiler

Compiled 11273 to 9009 computations (20.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	279
1	75	279

regimes94.0ms (2.1%)

Compiler: Compiled 672 to 536 computations (20.2% saved)

bsearch0.0ms (0%)

regimes117.0ms (2.6%)

Compiler: Compiled 133 to 145 computations (-9% saved)

bsearch1.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

regimes50.0ms (1.1%)

Compiler: Compiled 40 to 56 computations (-40% saved)

bsearch22.0ms (0.5%)

Steps

Iters	Range		Point
7	1.2463260213552496e+137	1.0474430707392218e+139	1.0026498818947338e+139
7	-3.0399864347553708e+177	-5.0772557633666874e+175	-1.109646578913455e+177

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes86.0ms (1.9%)

Compiler: Compiled 22 to 42 computations (-90.9% saved)

bsearch73.0ms (1.6%)

Steps

Iters	Range		Point
9	4.372073121076635e+70	1.2430539840618463e+79	3.3521562902045345e+75
7	824774.8097494192	56344691.204104096	3456615.4289567317
7	2.353091830464471e-39	8.315823845240522e-38	8.031107239722553e-38
7	-2.7471247689241686e-87	-1.6164114508215236e-89	-1.4280374223387492e-87
8	-1.024909052974981e-56	-2.1034644235848792e-59	-1.3784118628517233e-58
9	-1.982307286577987e+25	-5.39461787143076e+18	-1.4561056209255127e+24

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes20.0ms (0.5%)

Compiler: Compiled 16 to 34 computations (-112.5% saved)

bsearch0.0ms (0%)

regimes17.0ms (0.4%)

Accuracy

Total 0.2b remaining (99%)

Threshold costs 0.2b (99%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch7.0ms (0.2%)

Compiler: Compiled 175 to 119 computations (32% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	139	202
1	139	202

end0.0ms (0%)

sample798.0ms (17.9%)

Algorithm

1×

intervals

Results

239.0ms

8000×

body

128

valid

Compiler

Compiled 370 to 284 computations (23.2% saved)

Pareto

0.6624026395385063

Details

analyze43.0ms (1%)

sample15.0ms (0.3%)

simplify227.0ms (5.1%)

prune2.0ms (0.1%)

localize10.0ms (0.2%)

rewrite11.0ms (0.3%)

series104.0ms (2.3%)

simplify53.0ms (1.2%)

prune49.0ms (1.1%)

localize6.0ms (0.1%)

rewrite43.0ms (1%)

series216.0ms (4.8%)

simplify76.0ms (1.7%)

prune127.0ms (2.8%)

localize6.0ms (0.1%)

rewrite26.0ms (0.6%)

series180.0ms (4%)

simplify65.0ms (1.5%)

prune86.0ms (1.9%)

localize10.0ms (0.2%)

rewrite197.0ms (4.4%)

series431.0ms (9.6%)

simplify171.0ms (3.8%)

prune1.0s (22.8%)

simplify5.0ms (0.1%)

regimes94.0ms (2.1%)

bsearch0.0ms (0%)

regimes117.0ms (2.6%)

bsearch1.0ms (0%)

regimes50.0ms (1.1%)

bsearch22.0ms (0.5%)

regimes86.0ms (1.9%)

bsearch73.0ms (1.6%)

regimes20.0ms (0.5%)

bsearch0.0ms (0%)

regimes17.0ms (0.4%)

bsearch7.0ms (0.2%)

simplify8.0ms (0.2%)

end0.0ms (0%)

sample798.0ms (17.9%)

Profiling