Details

analyze266.0ms (3.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample36.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	243×	body	128	valid
9.0ms	287×	pre	128	true
1.0ms	31×	body	128	nan
1.0ms	13×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify396.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (303.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 29.6b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
29.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_100`
14×	`*-un-lft-identity_binary64_78`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-log-exp_binary64_117` `add-cube-cbrt_binary64_113`
6×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/l*_binary64_23` `difference-of-squares_binary64_47`
5×	`pow1_binary64_139`
4×	`flip3--_binary64_82` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44`
3×	`distribute-lft-out--_binary64_30`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `diff-log_binary64_170` `sqrt-div_binary64_95` `associate-/l/_binary64_25` `sub-neg_binary64_71`
1×	`sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/r*_binary64_22` `clear-num_binary64_77` `div-sub_binary64_83` `pow1/2_binary64_158`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series261.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
65.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify90.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune104.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	7	87

Merged error: 0.4b

Counts

87 → 7

Compiler

Compiled 2144 to 1283 computations (40.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
22×	`times-frac_binary64_84`
20×	`*-un-lft-identity_binary64_78`
17×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
13×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
11×	`associate-/l*_binary64_23`
10×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
8×	`add-log-exp_binary64_117`
6×	`associate-/r/_binary64_24`
5×	`associate-/r*_binary64_22` `distribute-lft-out_binary64_29`
4×	`flip-+_binary64_52` `div-inv_binary64_75` `pow1_binary64_139` `flip3-+_binary64_81`
2×	`frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`+-commutative_binary64_8` `flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44` `associate-/l/_binary64_25` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 99

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series449.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

195.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
152.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
68.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify63.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune170.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	108	10	118

Merged error: 0.0b

Counts

118 → 10

Compiler

Compiled 3345 to 2073 computations (38% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
0.3b	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))

rewrite84.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

323×	`times-frac_binary64_84`
165×	`*-un-lft-identity_binary64_78`
129×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
52×	`add-exp-log_binary64_116`
49×	`associate-/r*_binary64_22`
40×	`associate-/r/_binary64_24`
32×	`add-cbrt-cube_binary64_114`
30×	`div-exp_binary64_129`
23×	`div-inv_binary64_75`
18×	`distribute-lft-out_binary64_29`
17×	`flip-+_binary64_52` `flip3-+_binary64_81`
16×	`cbrt-undiv_binary64_112`
7×	`associate-/l*_binary64_23`
6×	`add-log-exp_binary64_117`
5×	`prod-exp_binary64_127` `pow1_binary64_139`
4×	`1-exp_binary64_122` `rec-exp_binary64_128`
3×	`cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`inv-pow_binary64_163` `flip3--_binary64_82` `diff-log_binary64_170` `pow-flip_binary64_152` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71`

Counts

4 → 269

Calls

4 calls:

19.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
12.0ms	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
10.0ms	(/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series516.0ms (7%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
180.0ms	(/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))
108.0ms	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
36.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify131.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5098	10866

prune559.0ms (7.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	278	3	281
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	282	9	291

Merged error: 0b

Counts

291 → 9

Compiler

Compiled 9173 to 6078 computations (33.7% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3))))))
0.3b	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3)))))))
0.5b	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))
0.7b	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)

rewrite94.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

319×	`times-frac_binary64_84`
165×	`*-un-lft-identity_binary64_78`
133×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
48×	`add-exp-log_binary64_116`
45×	`associate-/r*_binary64_22`
38×	`associate-/r/_binary64_24`
28×	`add-cbrt-cube_binary64_114` `div-exp_binary64_129`
22×	`div-inv_binary64_75`
16×	`flip-+_binary64_52` `distribute-lft-out_binary64_29` `flip3-+_binary64_81`
14×	`cbrt-undiv_binary64_112`
12×	`cbrt-prod_binary64_109`
6×	`unpow-prod-down_binary64_157` `associate-/l*_binary64_23` `cube-prod_binary64_106` `pow1_binary64_139`
4×	`add-log-exp_binary64_117` `prod-exp_binary64_127` `cube-div_binary64_107` `1-exp_binary64_122` `rec-exp_binary64_128`
3×	`pow-unpow_binary64_155`
2×	`cube-mult_binary64_108` `cbrt-div_binary64_110` `cbrt-unprod_binary64_111` `flip3--_binary64_82` `frac-2neg_binary64_89` `sqr-pow_binary64_50` `flip--_binary64_53` `clear-num_binary64_77` `unpow3_binary64_144`
1×	`rem-cube-cbrt_binary64_101` `rem-cbrt-cube_binary64_102` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `inv-pow_binary64_163` `pow1/3_binary64_160` `pow-flip_binary64_152` `pow-pow_binary64_150`

Counts

4 → 280

Calls

4 calls:

22.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3)))))))
16.0ms	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3))))))
6.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)
5.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))

series413.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3)))))))
110.0ms	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3))))))
85.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)
33.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))

simplify138.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4975	11064
1	4975	11064

prune537.0ms (7.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	292	9	301

Merged error: 0b

Counts

301 → 9

Compiler

Compiled 9595 to 6399 computations (33.3% saved)

regimes543.0ms (7.4%)

Compiler: Compiled 7468 to 5698 computations (23.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	29
1	63	29

end0.0ms (0%)

sample2.4s (32.2%)

Algorithm

1×

intervals

Results

390.0ms	7684×	body	128	valid
276.0ms	8846×	pre	128	true
39.0ms	846×	body	128	nan
30.0ms	316×	body	256	valid

Compiler

Compiled 1906 to 1456 computations (23.6% saved)

Details

analyze266.0ms (3.6%)

sample36.0ms (0.5%)

simplify396.0ms (5.4%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite34.0ms (0.5%)

series261.0ms (3.5%)

simplify90.0ms (1.2%)

prune104.0ms (1.4%)

localize14.0ms (0.2%)

rewrite48.0ms (0.7%)

series449.0ms (6.1%)

simplify63.0ms (0.9%)

prune170.0ms (2.3%)

localize13.0ms (0.2%)

rewrite84.0ms (1.1%)

series516.0ms (7%)

simplify131.0ms (1.8%)

prune559.0ms (7.6%)

localize20.0ms (0.3%)

rewrite94.0ms (1.3%)

series413.0ms (5.6%)

simplify138.0ms (1.9%)

prune537.0ms (7.3%)

regimes543.0ms (7.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.4s (32.2%)

Profiling