Details

analyze250.0ms (4.1%)

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
12.5%	87.4%	0.1%	6
28.1%	71.8%	0.1%	7
42.1%	57.7%	0.1%	8
43.7%	56.2%	0.1%	9
64.4%	35.5%	0.1%	10
71.6%	28.3%	0.1%	11
72.2%	27.7%	0.1%	12
81.6%	18.2%	0.2%	13
84.9%	14.9%	0.2%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample17.0ms (0.3%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 25 to 20 computations (20% saved)

simplify250.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (154.0ms)

Iter	Nodes	Cost
0	4942	16
1	4942	16

prune5.0ms (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

0.3b

Counts

2 → 2

Compiler

Compiled 34 to 26 computations (23.5% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.3b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
0.0b	(/.f64 v (+.f64 t1 u))
0.0b	(/.f64 v (+.f64 t1 u))
1.3b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

223×	`times-frac_binary64_84`
181×	`add-sqr-sqrt_binary64_100`
174×	`*-un-lft-identity_binary64_78`
86×	`add-cube-cbrt_binary64_113`
38×	`difference-of-squares_binary64_47`
25×	`distribute-lft-out_binary64_29`
21×	`associate-/l*_binary64_23`
19×	`distribute-lft-out--_binary64_30`
18×	`associate-/r/_binary64_24`
10×	`associate-/r*_binary64_22`
9×	`add-cbrt-cube_binary64_114` `div-inv_binary64_75` `add-exp-log_binary64_116`
8×	`flip-+_binary64_52` `flip3-+_binary64_81`
4×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
2×	`add-log-exp_binary64_117` `frac-2neg_binary64_89` `clear-num_binary64_77` `pow1_binary64_139`
1×	`flip3--_binary64_82` `flip--_binary64_53` `associate-/l/_binary64_25`

Counts

2 → 182

Calls

4 calls:

16.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
5.0ms	(/.f64 v (+.f64 t1 u))
0.0ms	(/.f64 v (+.f64 t1 u))
0.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series313.0ms (5.1%)

Counts

2 → 36

Calls

2 calls:

212.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
101.0ms	(/.f64 v (+.f64 t1 u))

Compiler

Compiled 1016 to 818 computations (19.5% saved)

simplify98.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5176	6128

prune215.0ms (3.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	213	5	218
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	213	7	220

Error

0.2b

Counts

220 → 7

Compiler

Compiled 4877 to 1649 computations (66.2% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))
0.0b	(/.f64 v (+.f64 t1 u))
0.0b	(/.f64 v (+.f64 t1 u))
0.0b	(/.f64 v (+.f64 t1 u))
0.9b	(/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
14.7b	(cbrt.f64 (/.f64 v (+.f64 t1 u)))
14.7b	(cbrt.f64 (/.f64 v (+.f64 t1 u)))
14.7b	(cbrt.f64 (/.f64 v (+.f64 t1 u)))

rewrite71.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

268×	`times-frac_binary64_84`
223×	`add-sqr-sqrt_binary64_100`
217×	`*-un-lft-identity_binary64_78`
180×	`cbrt-prod_binary64_109`
113×	`add-cube-cbrt_binary64_113`
44×	`difference-of-squares_binary64_47`
30×	`distribute-lft-out_binary64_29`
22×	`distribute-lft-out--_binary64_30` `associate-/r/_binary64_24`
21×	`associate-/l*_binary64_23`
11×	`div-inv_binary64_75`
10×	`flip-+_binary64_52` `flip3-+_binary64_81`
6×	`associate-/r*_binary64_22` `add-exp-log_binary64_116`
5×	`add-cbrt-cube_binary64_114`
4×	`cbrt-div_binary64_110` `add-log-exp_binary64_117` `pow1_binary64_139`
3×	`pow1/3_binary64_160`
1×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip3--_binary64_82` `frac-2neg_binary64_89` `flip--_binary64_53` `clear-num_binary64_77` `associate-/l/_binary64_25`

Counts

4 → 249

Calls

8 calls:

20.0ms	(/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
5.0ms	(cbrt.f64 (/.f64 v (+.f64 t1 u)))
5.0ms	(cbrt.f64 (/.f64 v (+.f64 t1 u)))
5.0ms	(cbrt.f64 (/.f64 v (+.f64 t1 u)))
0.0ms	(/.f64 v (+.f64 t1 u))

series1.2s (19%)

Counts

4 → 55

Calls

4 calls:

387.0ms	(/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
263.0ms	(cbrt.f64 (/.f64 v (+.f64 t1 u)))
254.0ms	(cbrt.f64 (/.f64 v (+.f64 t1 u)))
254.0ms	(cbrt.f64 (/.f64 v (+.f64 t1 u)))

Compiler

Compiled 3935 to 2707 computations (31.2% saved)

simplify124.0ms (2%)

Algorithm

1×	egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5037	9089

prune328.0ms (5.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	304	0	304
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	304	7	311

Error

0.2b

Counts

311 → 7

Compiler

Compiled 11449 to 2784 computations (75.7% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.1b	(/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))
0.1b	(*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1)))
0.1b	(*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1)))
3.1b	(/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_100`
26×	`cancel-sign-sub-inv_binary64_44`
24×	`*-un-lft-identity_binary64_78`
22×	`times-frac_binary64_84`
20×	`add-cube-cbrt_binary64_113`
14×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`frac-times_binary64_88` `associate-/r/_binary64_24`
6×	`flip-+_binary64_52` `flip3--_binary64_82` `associate-r_binary64_18` `flip--_binary64_53` `flip3-+_binary64_81`
4×	`associate-l_binary64_19` `associate-l/_binary64_21` `associate-r/_binary64_20` `pow1_binary64_139`
3×	`div-inv_binary64_75` `associate-/l*_binary64_23`
2×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `difference-of-squares_binary64_47` `sub-neg_binary64_71`
1×	`-commutative_binary64_9` `distribute-lft-out--_binary64_30` `frac-2neg_binary64_89` `associate-/r_binary64_22` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `clear-num_binary64_77` `distribute-lft-out_binary64_29`

Counts

2 → 87

Calls

4 calls:

14.0ms	(*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1)))
12.0ms	(/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))
0.0ms	(*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1)))
0.0ms	(/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))

series372.0ms (6.1%)

Counts

2 → 36

Calls

2 calls:

211.0ms	(/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))
161.0ms	(*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1)))

Compiler

Compiled 791 to 683 computations (13.7% saved)

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5116	2299

prune90.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	124	6	130

Error

0.2b

Counts

130 → 6

Compiler

Compiled 2134 to 756 computations (64.6% saved)

localize9.0ms (0.1%)

Local error

Found 6 expressions with local error:

2.0b	(/.f64 v (-.f64 -1 (/.f64 u t1)))
1.2b	(*.f64 (/.f64 1 (+.f64 t1 u)) (/.f64 v (-.f64 -1 (/.f64 u t1))))
0.0b	(/.f64 1 (+.f64 t1 u))
0.0b	(/.f64 1 (+.f64 t1 u))
1.2b	(*.f64 (/.f64 1 (+.f64 t1 u)) (/.f64 v (-.f64 -1 (/.f64 u t1))))
2.0b	(/.f64 v (-.f64 -1 (/.f64 u t1)))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`add-sqr-sqrt_binary64_100`
74×	`times-frac_binary64_84`
71×	`*-un-lft-identity_binary64_78`
41×	`add-cube-cbrt_binary64_113`
31×	`add-exp-log_binary64_116`
24×	`associate-r_binary64_18`
19×	`add-cbrt-cube_binary64_114`
18×	`associate-l_binary64_19`
14×	`difference-of-squares_binary64_47`
11×	`div-exp_binary64_129`
10×	`associate-/r*_binary64_22`
8×	`prod-exp_binary64_127` `associate-/r/_binary64_24`
7×	`distribute-lft-out--_binary64_30` `distribute-lft-out_binary64_29`
6×	`cbrt-undiv_binary64_112` `associate-/l*_binary64_23` `unswap-sqr_binary64_46` `pow1_binary64_139`
4×	`cbrt-unprod_binary64_111` `div-inv_binary64_75`
3×	`add-log-exp_binary64_117` `1-exp_binary64_122` `rec-exp_binary64_128`
2×	`flip-+_binary64_52` `flip3--_binary64_82` `frac-2neg_binary64_89` `flip--_binary64_53` `clear-num_binary64_77` `flip3-+_binary64_81`
1×	`-commutative_binary64_9` `inv-pow_binary64_163` `frac-times_binary64_88` `pow-flip_binary64_152` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-*r/_binary64_20`

Counts

3 → 150

Calls

6 calls:

24.0ms	(*.f64 (/.f64 1 (+.f64 t1 u)) (/.f64 v (-.f64 -1 (/.f64 u t1))))
8.0ms	(/.f64 v (-.f64 -1 (/.f64 u t1)))
5.0ms	(/.f64 1 (+.f64 t1 u))
0.0ms	(/.f64 1 (+.f64 t1 u))
0.0ms	(*.f64 (/.f64 1 (+.f64 t1 u)) (/.f64 v (-.f64 -1 (/.f64 u t1))))

series408.0ms (6.7%)

Counts

3 → 51

Calls

3 calls:

202.0ms	(*.f64 (/.f64 1 (+.f64 t1 u)) (/.f64 v (-.f64 -1 (/.f64 u t1))))
145.0ms	(/.f64 v (-.f64 -1 (/.f64 u t1)))
60.0ms	(/.f64 1 (+.f64 t1 u))

Compiler

Compiled 1481 to 1205 computations (18.6% saved)

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5043	3483

prune170.0ms (2.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	201	6	207

Error

0.2b

Counts

207 → 6

Compiler

Compiled 3766 to 1693 computations (55% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	219	742
1	219	742

regimes151.0ms (2.5%)

Compiler: Compiled 1488 to 1077 computations (27.6% saved)

bsearch0.0ms (0%)

regimes46.0ms (0.8%)

Compiler: Compiled 189 to 213 computations (-12.7% saved)

bsearch0.0ms (0%)

regimes110.0ms (1.8%)

Compiler: Compiled 156 to 186 computations (-19.2% saved)

bsearch38.0ms (0.6%)

Steps

Iters	Range		Point
10	2.2429623354556628e-135	1.9719356529200544e-123	1.825414605180934e-123
9	-2638.9784618703015	-1.1325315815149874e-06	-0.0007085118757943032

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes96.0ms (1.6%)

Compiler: Compiled 96 to 132 computations (-37.5% saved)

bsearch30.0ms (0.5%)

Steps

Iters	Range		Point
7	3.5851749028325866e-116	7.872980757453358e-114	1.901358804695172e-114
9	-2638.9784618703015	-1.1325315815149874e-06	-1.6279607611381128

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes106.0ms (1.7%)

Compiler: Compiled 72 to 111 computations (-54.2% saved)

bsearch36.0ms (0.6%)

Steps

Iters	Range		Point
9	1.091017357409398e-97	3.9756948554788977e-88	2.4916353317115206e-89
9	-2638.9784618703015	-1.1325315815149874e-06	-0.2140300373321104

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes59.0ms (1%)

Compiler: Compiled 48 to 90 computations (-87.5% saved)

bsearch26.0ms (0.4%)

Steps

Iters	Range		Point
7	8.862097312374607e-211	1.4972199967924396e-209	1.4778993763372515e-209
8	-1.1118702121739113e-173	-1.7455976129605223e-177	-1.0132433850623741e-175

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes66.0ms (1.1%)

Compiler: Compiled 27 to 69 computations (-155.6% saved)

bsearch28.0ms (0.5%)

Steps

Iters	Range		Point
9	7.537188061329055e+130	2.20949605896149e+138	1.758383268694475e+131
8	-10445.509635664921	-29.602837703586957	-10310.711087361351

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes25.0ms (0.4%)

Accuracy

Total 1.2b remaining (91.4%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 152 to 121 computations (20.4% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	132	188
1	132	188

end0.0ms (0%)

sample1.1s (17.5%)

Algorithm

1×

intervals

Results

261.0ms	8000×	body	128	valid
9.0ms	277×	body	128	invalid

Compiler

Compiled 635 to 474 computations (25.4% saved)

Pareto

0.12353606135533758

Details

analyze250.0ms (4.1%)

sample17.0ms (0.3%)

simplify250.0ms (4.1%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

rewrite42.0ms (0.7%)

series313.0ms (5.1%)

simplify98.0ms (1.6%)

prune215.0ms (3.5%)

localize13.0ms (0.2%)

rewrite71.0ms (1.2%)

series1.2s (19%)

simplify124.0ms (2%)

prune328.0ms (5.4%)

localize7.0ms (0.1%)

rewrite34.0ms (0.6%)

series372.0ms (6.1%)

simplify68.0ms (1.1%)

prune90.0ms (1.5%)

localize9.0ms (0.1%)

rewrite51.0ms (0.8%)

series408.0ms (6.7%)

simplify74.0ms (1.2%)

prune170.0ms (2.8%)

simplify11.0ms (0.2%)

regimes151.0ms (2.5%)

bsearch0.0ms (0%)

regimes46.0ms (0.8%)

bsearch0.0ms (0%)

regimes110.0ms (1.8%)

bsearch38.0ms (0.6%)

regimes96.0ms (1.6%)

bsearch30.0ms (0.5%)

regimes106.0ms (1.7%)

bsearch36.0ms (0.6%)

regimes59.0ms (1%)

bsearch26.0ms (0.4%)

regimes66.0ms (1.1%)

bsearch28.0ms (0.5%)

regimes25.0ms (0.4%)

bsearch8.0ms (0.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.1s (17.5%)

Profiling