Details

analyze966.0ms (8.2%)

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
3.5%	96.2%	0.2%	10
9.8%	89.9%	0.2%	11
14.1%	85.7%	0.2%	12
22.6%	77.1%	0.2%	13
23.7%	76%	0.2%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample27.0ms (0.2%)

Algorithm

1×

intervals

Results

9.0ms	219×	body	128	valid
2.0ms	17×	body	1024	valid
1.0ms	14×	body	512	valid
1.0ms	26×	body	128	invalid
0.0ms	5×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify239.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	4872	19
1	4872	19

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

18.8b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

12.3b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
2.5b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
2.5b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
12.3b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_10990`
14×	`add-sqr-sqrt_binary64_11012`
11×	`cancel-sign-sub-inv_binary64_10956`
10×	`times-frac_binary64_10996`
7×	`add-log-exp_binary64_11029` `add-exp-log_binary64_11028` `add-cbrt-cube_binary64_11026`
6×	`add-cube-cbrt_binary64_11025`
5×	`distribute-lft-out--_binary64_10942` `associate-/r*_binary64_10934`
4×	`flip3--_binary64_10994` `flip--_binary64_10965` `difference-of-squares_binary64_10959` `associate-/r/_binary64_10936`
2×	`associate-/l/_binary64_10937` `pow1_binary64_11051` `frac-sub_binary64_10999` `diff-log_binary64_11082` `div-exp_binary64_11041` `div-inv_binary64_10987` `cbrt-undiv_binary64_11024` `associate-*l/_binary64_10933`
1×	`associate--l+_binary64_10927` `sum-log_binary64_11081` `prod-exp_binary64_11039` `clear-num_binary64_10989` `distribute-lft-out_binary64_10941` `associate-/l*_binary64_10935` `flip3-+_binary64_10993` `sub-neg_binary64_10983` `flip-+_binary64_10964` `cbrt-unprod_binary64_11023` `frac-2neg_binary64_11001`

Counts

2 → 58

Calls

4 calls:

13.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
11.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
0.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
0.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

series712.0ms (6.1%)

Counts

2 → 54

Calls

2 calls:

474.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
237.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

Compiler

Compiled 1677 to 1237 computations (26.2% saved)

simplify71.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5679	2192

prune149.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	106	6	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	6	113

Error

0.0b

Counts

113 → 6

Compiler

Compiled 2011 to 453 computations (77.5% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

2.4b	(*.f64 y (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))))
1.8b	(+.f64 1 (/.f64 t (-.f64 a t)))
0.0b	(/.f64 t (-.f64 a t))
0.0b	(/.f64 z (-.f64 a t))
0.0b	(/.f64 z (-.f64 a t))
0.0b	(/.f64 t (-.f64 a t))
1.8b	(+.f64 1 (/.f64 t (-.f64 a t)))
2.4b	(*.f64 y (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))))

rewrite77.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64_10990` `add-sqr-sqrt_binary64_11012`
61×	`times-frac_binary64_10996`
44×	`add-cube-cbrt_binary64_11025`
42×	`cancel-sign-sub-inv_binary64_10956`
23×	`distribute-rgt-in_binary64_10940` `distribute-lft-in_binary64_10939`
16×	`distribute-lft-out--_binary64_10942` `difference-of-squares_binary64_10959`
10×	`add-exp-log_binary64_11028` `add-cbrt-cube_binary64_11026` `associate-/r*_binary64_10934`
8×	`associate-/r/_binary64_10936`
7×	`associate-r_binary64_10930`
6×	`pow1_binary64_11051` `add-log-exp_binary64_11029` `associate-/l*_binary64_10935`
5×	`flip3--_binary64_10994` `flip--_binary64_10965`
4×	`associate-*r/_binary64_10932` `div-inv_binary64_10987`
3×	`associate-l_binary64_10931`
2×	`associate--l+_binary64_10927` `frac-sub_binary64_10999` `clear-num_binary64_10989` `distribute-lft-out_binary64_10941` `div-exp_binary64_11041` `flip3-+_binary64_10993` `sub-neg_binary64_10983` `flip-+_binary64_10964` `frac-2neg_binary64_11001` `cbrt-undiv_binary64_11024`
1×	`sum-log_binary64_11081` `prod-exp_binary64_11039` `unswap-sqr_binary64_10958` `+-commutative_binary64_10920` `cbrt-unprod_binary64_11023` `*-commutative_binary64_10921` `pow-prod-down_binary64_11061`

Counts

4 → 158

Calls

8 calls:

36.0ms	(*.f64 y (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))))
11.0ms	(+.f64 1 (/.f64 t (-.f64 a t)))
7.0ms	(/.f64 t (-.f64 a t))
6.0ms	(/.f64 z (-.f64 a t))
0.0ms	(/.f64 z (-.f64 a t))

series570.0ms (4.9%)

Counts

4 → 65

Calls

4 calls:

341.0ms	(*.f64 y (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))))
120.0ms	(/.f64 z (-.f64 a t))
57.0ms	(+.f64 1 (/.f64 t (-.f64 a t)))
51.0ms	(/.f64 t (-.f64 a t))

Compiler

Compiled 2245 to 1759 computations (21.6% saved)

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5172	4224

prune190.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	221	2	223
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	223	6	229

Error

0.0b

Counts

229 → 6

Compiler

Compiled 5146 to 1604 computations (68.8% saved)

localize12.0ms (0.1%)

Local error

Found 6 expressions with local error:

9.6b	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))
3.7b	(-.f64 (+.f64 x y) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
0.0b	(/.f64 (-.f64 a t) y)
0.0b	(/.f64 (-.f64 a t) y)
3.7b	(-.f64 (+.f64 x y) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
9.6b	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))

rewrite109.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

373×	`times-frac_binary64_10996`
313×	`add-sqr-sqrt_binary64_11012`
309×	`*-un-lft-identity_binary64_10990`
152×	`add-cube-cbrt_binary64_11025`
100×	`cancel-sign-sub-inv_binary64_10956`
79×	`difference-of-squares_binary64_10959`
78×	`distribute-lft-out--_binary64_10942`
22×	`associate-/r*_binary64_10934`
14×	`div-inv_binary64_10987`
10×	`add-exp-log_binary64_11028` `associate-/l*_binary64_10935` `add-cbrt-cube_binary64_11026`
8×	`add-log-exp_binary64_11029`
4×	`associate-/l/_binary64_10937` `div-exp_binary64_11041` `cbrt-undiv_binary64_11024`
3×	`flip3--_binary64_10994` `div-sub_binary64_10995` `flip--_binary64_10965` `pow1_binary64_11051`
2×	`frac-sub_binary64_10999` `clear-num_binary64_10989` `diff-log_binary64_11082` `associate-/r/_binary64_10936` `frac-2neg_binary64_11001`
1×	`associate--l+_binary64_10927` `sum-log_binary64_11081` `distribute-lft-out_binary64_10941` `flip3-+_binary64_10993` `sub-neg_binary64_10983` `flip-+_binary64_10964` `associate--r-_binary64_10929`

Counts

3 → 296

Calls

6 calls:

46.0ms	(-.f64 (+.f64 x y) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
14.0ms	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))
7.0ms	(/.f64 (-.f64 a t) y)
0.0ms	(/.f64 (-.f64 a t) y)
0.0ms	(-.f64 (+.f64 x y) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))

series827.0ms (7%)

Counts

3 → 69

Calls

3 calls:

477.0ms	(-.f64 (+.f64 x y) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
238.0ms	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))
111.0ms	(/.f64 (-.f64 a t) y)

Compiler

Compiled 2011 to 1517 computations (24.6% saved)

simplify111.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

365 → 365

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5158	9763

prune260.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	365	0	365
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	365	6	371

Error

0.0b

Counts

371 → 6

Compiler

Compiled 8299 to 1037 computations (87.5% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.3b	(/.f64 y (/.f64 t (-.f64 z a)))
0.0b	(/.f64 t (-.f64 z a))
0.0b	(/.f64 t (-.f64 z a))
4.3b	(/.f64 y (/.f64 t (-.f64 z a)))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_10996`
102×	`*-un-lft-identity_binary64_10990` `add-sqr-sqrt_binary64_11012`
70×	`add-cube-cbrt_binary64_11025`
26×	`associate-/r*_binary64_10934`
16×	`distribute-lft-out--_binary64_10942` `difference-of-squares_binary64_10959`
11×	`associate-/r/_binary64_10936`
9×	`add-exp-log_binary64_11028` `add-cbrt-cube_binary64_11026`
6×	`associate-/l*_binary64_10935` `div-inv_binary64_10987`
5×	`flip3--_binary64_10994` `flip--_binary64_10965`
4×	`div-exp_binary64_11041` `cbrt-undiv_binary64_11024`
2×	`pow1_binary64_11051` `add-log-exp_binary64_11029` `clear-num_binary64_10989` `frac-2neg_binary64_11001`

Counts

2 → 139

Calls

4 calls:

10.0ms	(/.f64 y (/.f64 t (-.f64 z a)))
6.0ms	(/.f64 t (-.f64 z a))
0.0ms	(/.f64 t (-.f64 z a))
0.0ms	(/.f64 y (/.f64 t (-.f64 z a)))

series331.0ms (2.8%)

Counts

2 → 42

Calls

2 calls:

202.0ms	(/.f64 y (/.f64 t (-.f64 z a)))
128.0ms	(/.f64 t (-.f64 z a))

Compiler

Compiled 885 to 779 computations (12% saved)

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4973	3383
1	4973	3383

prune128.0ms (1.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	181	6	187

Error

0.0b

Counts

187 → 6

Compiler

Compiled 3048 to 603 computations (80.2% saved)

simplify155.0ms (1.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (140.0ms)

Iter	Nodes	Cost
0	3847	1261
1	3847	1261

regimes437.0ms (3.7%)

Compiler: Compiled 4265 to 3365 computations (21.1% saved)

bsearch0.0ms (0%)

regimes573.0ms (4.9%)

Compiler: Compiled 1520 to 1620 computations (-6.6% saved)

bsearch87.0ms (0.7%)

Steps

Iters	Range		Point
10	5.2319529242399576e+135	1.7201774682424886e+146	7.921218364600235e+135
5	-2.1172760617743151e+49	-8.132405057136235e+48	-1.9875888461327692e+49
7	-1.1988611412940193e+141	-1.0106240280586121e+139	-1.0555721836227872e+141
8	-2.7188738162876495e+196	-3.4348635850603555e+193	-3.468984774702244e+193

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes489.0ms (4.2%)

Compiler: Compiled 1165 to 1320 computations (-13.3% saved)

bsearch83.0ms (0.7%)

Steps

Iters	Range		Point
10	5.2319529242399576e+135	1.7201774682424886e+146	1.0258657210943311e+141
5	-2.1172760617743151e+49	-8.132405057136235e+48	-1.9875888461327692e+49
7	-1.1988611412940193e+141	-1.0106240280586121e+139	-5.436989244625463e+139
7	-2.078811671276147e+175	-9.835525955186611e+172	-3.837304396320661e+173

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes406.0ms (3.5%)

Compiler: Compiled 1100 to 1265 computations (-15% saved)

bsearch86.0ms (0.7%)

Steps

Iters	Range		Point
8	2.2973489671601615e+69	1.1598170306329588e+73	2.0925975603621751e+71
5	86982.03912130732	197819.99057816356	93033.91069691468
8	1.5388719632705386e-62	2.0373203778486197e-59	1.7173201819750254e-62
9	-0.11905078355326623	-4.507548683800103e-08	-1.276293961224281e-06

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes375.0ms (3.2%)

Compiler: Compiled 1035 to 1210 computations (-16.9% saved)

bsearch42.0ms (0.4%)

Steps

Iters	Range		Point
10	5.2319529242399576e+135	1.7201774682424886e+146	8.714435894414823e+135
5	-2.1172760617743151e+49	-8.132405057136235e+48	-1.6763395285930586e+49

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes364.0ms (3.1%)

Compiler: Compiled 870 to 1055 computations (-21.3% saved)

bsearch53.0ms (0.4%)

Steps

Iters	Range		Point
8	2.2973489671601615e+69	1.1598170306329588e+73	2.4217990137655632e+69
9	-0.11905078355326623	-4.507548683800103e-08	-0.0759632044576224

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes276.0ms (2.3%)

Compiler: Compiled 505 to 705 computations (-39.6% saved)

bsearch21.0ms (0.2%)

Steps

Iters	Range		Point
0	6.814343587842381e+92	6.83579204903071e+92	6.825067818436545e+92
8	-2.211001577175341e+66	-2.558935043014995e+63	-3.394760557120719e+63

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes323.0ms (2.7%)

Compiler: Compiled 415 to 615 computations (-48.2% saved)

bsearch109.0ms (0.9%)

Steps

Iters	Range		Point
9	264729009546.1871	5.0654496233882586e+17	775814873614.9922
5	86982.03912130732	197819.99057816356	156667.26386403333
8	1.5388719632705386e-62	2.0373203778486197e-59	3.388916562014322e-61
10	-4.507548683800103e-08	-3.1617480287840637e-21	-6.242253695008518e-18
8	-1.322734048362542e+238	-1.8255088719327543e+235	-7.500629331326737e+236

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes250.0ms (2.1%)

Compiler: Compiled 370 to 570 computations (-54.1% saved)

bsearch46.0ms (0.4%)

Steps

Iters	Range		Point
8	1.5388719632705386e-62	2.0373203778486197e-59	1.9128254245190953e-59
10	-4.507548683800103e-08	-3.1617480287840637e-21	-1.4624546912627737e-16

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes153.0ms (1.3%)

Compiler: Compiled 105 to 270 computations (-157.1% saved)

bsearch47.0ms (0.4%)

Steps

Iters	Range		Point
8	1.5388719632705386e-62	2.0373203778486197e-59	7.639369142200596e-60
8	-3.1617480287840637e-21	-6.790653546376402e-26	-9.612938949830728e-22

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes92.0ms (0.8%)

Compiler: Compiled 70 to 230 computations (-228.6% saved)

bsearch37.0ms (0.3%)

Steps

Iters	Range		Point
7	27.818774907627667	2439.716269231201	498.68364292446523
8	-5.205818343439722e-100	-9.967201267879474e-105	-5.941352493305822e-101

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes52.0ms (0.4%)

Compiler: Compiled 30 to 165 computations (-450% saved)

bsearch0.0ms (0%)

regimes46.0ms (0.4%)

Accuracy

Total 4.3b remaining (99.3%)

Threshold costs 0b (0%)

Compiler

Compiled 25 to 140 computations (-460% saved)

bsearch17.0ms (0.1%)

Compiler: Compiled 434 to 256 computations (41% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	375	611
1	375	611

end0.0ms (0%)

sample2.1s (17.5%)

Algorithm

1×

intervals

Results

281.0ms	6803×	body	128	valid
57.0ms	463×	body	512	valid
50.0ms	354×	body	1024	valid
29.0ms	752×	body	128	invalid
27.0ms	325×	body	256	valid
10.0ms	55×	body	2048	valid

Compiler

Compiled 1358 to 970 computations (28.6% saved)

Pareto

0.580924697801358

Details

analyze966.0ms (8.2%)

sample27.0ms (0.2%)

simplify239.0ms (2%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite29.0ms (0.2%)

series712.0ms (6.1%)

simplify71.0ms (0.6%)

prune149.0ms (1.3%)

localize11.0ms (0.1%)

rewrite77.0ms (0.7%)

series570.0ms (4.9%)

simplify96.0ms (0.8%)

prune190.0ms (1.6%)

localize12.0ms (0.1%)

rewrite109.0ms (0.9%)

series827.0ms (7%)

simplify111.0ms (0.9%)

prune260.0ms (2.2%)

localize7.0ms (0.1%)

rewrite34.0ms (0.3%)

series331.0ms (2.8%)

simplify85.0ms (0.7%)

prune128.0ms (1.1%)

simplify155.0ms (1.3%)

regimes437.0ms (3.7%)

bsearch0.0ms (0%)

regimes573.0ms (4.9%)

bsearch87.0ms (0.7%)

regimes489.0ms (4.2%)

bsearch83.0ms (0.7%)

regimes406.0ms (3.5%)

bsearch86.0ms (0.7%)

regimes375.0ms (3.2%)

bsearch42.0ms (0.4%)

regimes364.0ms (3.1%)

bsearch53.0ms (0.4%)

regimes276.0ms (2.3%)

bsearch21.0ms (0.2%)

regimes323.0ms (2.7%)

bsearch109.0ms (0.9%)

regimes250.0ms (2.1%)

bsearch46.0ms (0.4%)

regimes153.0ms (1.3%)

bsearch47.0ms (0.4%)

regimes92.0ms (0.8%)

bsearch37.0ms (0.3%)

regimes52.0ms (0.4%)

bsearch0.0ms (0%)

regimes46.0ms (0.4%)

bsearch17.0ms (0.1%)

simplify14.0ms (0.1%)

end0.0ms (0%)

sample2.1s (17.5%)

Profiling