Details

analyze435.0ms (4.3%)

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)

sample61.0ms (0.6%)

Algorithm

1×

intervals

Results

17.0ms	94×	body	256	valid
14.0ms	293×	pre	128	true
12.0ms	161×	body	128	valid
3.0ms	37×	body	128	nan
0.0ms	1×	body	512	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify374.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune7.0ms (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: 43.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.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))
39.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite45.0ms (0.4%)

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:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series733.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

266.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
222.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
164.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
81.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify94.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5031	1979

prune137.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	3	87

Merged error: 0.2b

Counts

87 → 3

Compiler

Compiled 2021 to 1195 computations (40.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.1b	(-.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)))))
0.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))

rewrite50.0ms (0.5%)

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))

series1.0s (10.1%)

Counts

4 → 12

Calls

4 calls:

429.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
326.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
181.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
88.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4960	3037
1	4960	3037

prune215.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	106	8	114

Merged error: 0b

Counts

114 → 8

Compiler

Compiled 3261 to 2013 computations (38.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.1b	(/.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))))))))
0.3b	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))

rewrite116.0ms (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:

38.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
18.0ms	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
12.0ms	(/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series1.4s (14.3%)

Counts

4 → 12

Calls

4 calls:

569.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
461.0ms	(/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))
331.0ms	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
83.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify173.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4930	10866
1	4930	10866

prune653.0ms (6.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	279	2	281
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	282	7	289

Merged error: 0b

Counts

289 → 7

Compiler

Compiled 9132 to 6040 computations (33.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_78`
20×	`add-sqr-sqrt_binary64_100`
18×	`associate-r_binary64_18`
14×	`add-cube-cbrt_binary64_113`
13×	`times-frac_binary64_84`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-log-exp_binary64_117`
7×	`pow1_binary64_139`
4×	`distribute-lft-out_binary64_29`
3×	`sqrt-prod_binary64_94` `associate-l_binary64_19`
2×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `flip3--_binary64_82` `flip--_binary64_53` `unswap-sqr_binary64_46` `sqrt-div_binary64_95` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `div-inv_binary64_75` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 76

Calls

4 calls:

14.0ms	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
13.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
9.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series909.0ms (9%)

Counts

4 → 12

Calls

4 calls:

507.0ms	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
172.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
143.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
86.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify74.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4965	1908
1	4965	1908

prune111.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	88	7	95

Merged error: 0b

Counts

95 → 7

Compiler

Compiled 2080 to 1242 computations (40.3% saved)

regimes547.0ms (5.4%)

Compiler: Compiled 5232 to 4018 computations (23.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.7s (26.9%)

Algorithm

1×

intervals

Results

379.0ms	2859×	body	256	valid
365.0ms	8939×	pre	128	true
357.0ms	5140×	body	128	valid
59.0ms	939×	body	128	nan
0.0ms	1×	body	512	valid

Compiler

Compiled 1344 to 1033 computations (23.1% saved)

Details

analyze435.0ms (4.3%)

sample61.0ms (0.6%)

simplify374.0ms (3.7%)

prune7.0ms (0.1%)

localize12.0ms (0.1%)

rewrite45.0ms (0.4%)

series733.0ms (7.3%)

simplify94.0ms (0.9%)

prune137.0ms (1.4%)

localize14.0ms (0.1%)

rewrite50.0ms (0.5%)

series1.0s (10.1%)

simplify89.0ms (0.9%)

prune215.0ms (2.1%)

localize13.0ms (0.1%)

rewrite116.0ms (1.1%)

series1.4s (14.3%)

simplify173.0ms (1.7%)

prune653.0ms (6.5%)

localize11.0ms (0.1%)

rewrite53.0ms (0.5%)

series909.0ms (9%)

simplify74.0ms (0.7%)

prune111.0ms (1.1%)

regimes547.0ms (5.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.7s (26.9%)

Profiling