Details

analyze259.0ms (3.2%)

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)

sample35.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	248×	body	128	valid
11.0ms	290×	pre	128	true
2.0ms	34×	body	128	nan
1.0ms	8×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify228.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune8.0ms (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

Merged error: 29.0b

Counts

2 → 2

Compiler

Compiled 82 to 67 computations (18.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
28.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_79`
10×	`add-log-exp_binary64_118`
9×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
8×	`add-sqr-sqrt_binary64_101`
7×	`add-cube-cbrt_binary64_114`
6×	`distribute-lft-out_binary64_30`
5×	`times-frac_binary64_85` `associate-/l*_binary64_24` `pow1_binary64_140`
3×	`sqrt-prod_binary64_95` `distribute-rgt-neg-in_binary64_37`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `neg-sub0_binary64_74` `flip-+_binary64_53` `sum-log_binary64_170` `associate-+l-_binary64_14` `flip--_binary64_54` `sqrt-div_binary64_96` `flip3--_binary64_83` `associate-/l/_binary64_26` `flip3-+_binary64_82`
1×	`associate-/r*_binary64_23` `div-sub_binary64_84` `div-inv_binary64_76` `neg-log_binary64_172` `+-commutative_binary64_9` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `diff-log_binary64_171` `clear-num_binary64_78` `pow1/2_binary64_159` `cancel-sign-sub-inv_binary64_45` `sub-neg_binary64_72` `frac-2neg_binary64_90`

Counts

4 → 70

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
10.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series538.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
137.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
128.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify58.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5290	1826

prune173.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	79	5	84

Merged error: 0.3b

Counts

84 → 5

Compiler

Compiled 3544 to 2350 computations (33.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.2b	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite70.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
34×	`times-frac_binary64_85`
32×	`add-sqr-sqrt_binary64_101` `*-un-lft-identity_binary64_79`
17×	`cbrt-undiv_binary64_113` `div-exp_binary64_130`
14×	`associate-/l*_binary64_24`
13×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128`
12×	`add-cube-cbrt_binary64_114`
10×	`distribute-lft-out--_binary64_31` `difference-of-squares_binary64_48` `add-log-exp_binary64_118`
8×	`sqrt-prod_binary64_95` `associate-/r*_binary64_23`
7×	`cancel-sign-sub-inv_binary64_45`
6×	`associate-/r/_binary64_25`
5×	`flip--_binary64_54` `distribute-rgt-neg-in_binary64_37` `flip3--_binary64_83`
4×	`div-inv_binary64_76` `pow1_binary64_140`
3×	`diff-log_binary64_171`
2×	`clear-num_binary64_78` `sub-neg_binary64_72` `frac-2neg_binary64_90`
1×	`associate--l-_binary64_17` `neg-sub0_binary64_74` `neg-log_binary64_172` `associate-/l/_binary64_26`

Counts

4 → 122

Calls

4 calls:

22.0ms	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
16.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series940.0ms (11.7%)

Counts

4 → 12

Calls

4 calls:

405.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
332.0ms	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
141.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
61.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify81.0ms (1%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4950	4144
1	4950	4144

prune564.0ms (7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	123	11	134
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	128	11	139

Merged error: 0.0b

Counts

139 → 11

Compiler

Compiled 12217 to 8247 computations (32.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite75.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64_101` `*-un-lft-identity_binary64_79`
45×	`times-frac_binary64_85`
36×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
29×	`add-cube-cbrt_binary64_114`
27×	`associate-r_binary64_19`
14×	`distribute-lft-out--_binary64_31` `difference-of-squares_binary64_48`
12×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128`
10×	`associate-/r*_binary64_23` `cbrt-undiv_binary64_113` `div-exp_binary64_130`
9×	`pow1_binary64_140`
7×	`sqrt-prod_binary64_95` `distribute-rgt-neg-in_binary64_37`
6×	`add-log-exp_binary64_118`
4×	`associate-/l*_binary64_24` `associate-/r/_binary64_25`
3×	`div-inv_binary64_76` `flip--_binary64_54` `pow-prod-down_binary64_150` `flip3--_binary64_83`
2×	`associate-*r/_binary64_21` `clear-num_binary64_78` `frac-2neg_binary64_90`
1×	`associate-l_binary64_20` `*-commutative_binary64_10` `diff-log_binary64_171` `cancel-sign-sub-inv_binary64_45` `associate-/l/_binary64_26` `sub-neg_binary64_72`

Counts

4 → 132

Calls

4 calls:

20.0ms	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
18.0ms	(/.f64 (.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))) a)
12.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

series1.2s (14.4%)

Counts

4 → 12

Calls

4 calls:

407.0ms	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
349.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
335.0ms	(/.f64 (.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))) a)
65.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4983	4089
1	4983	4089

prune371.0ms (4.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	145	10	155

Merged error: 0.0b

Counts

155 → 10

Compiler

Compiled 8380 to 5305 computations (36.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite123.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

330×	`times-frac_binary64_85`
249×	`add-sqr-sqrt_binary64_101` `*-un-lft-identity_binary64_79`
149×	`add-cube-cbrt_binary64_114`
85×	`associate-r_binary64_19`
50×	`distribute-lft-out--_binary64_31` `difference-of-squares_binary64_48`
32×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
30×	`associate-/l*_binary64_24`
25×	`sqrt-prod_binary64_95` `distribute-rgt-neg-in_binary64_37`
16×	`associate-/r/_binary64_25`
10×	`associate-/r*_binary64_23` `cbrt-undiv_binary64_113` `div-exp_binary64_130` `div-inv_binary64_76`
9×	`flip--_binary64_54` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `flip3--_binary64_83` `pow1_binary64_140`
6×	`add-log-exp_binary64_118`
3×	`pow-prod-down_binary64_150`
2×	`clear-num_binary64_78` `frac-2neg_binary64_90`
1×	`associate-l_binary64_20` `associate-r/_binary64_21` `-commutative_binary64_10` `diff-log_binary64_171` `cancel-sign-sub-inv_binary64_45` `associate-/l/_binary64_26` `sub-neg_binary64_72`

Counts

4 → 292

Calls

4 calls:

34.0ms	(.f64 (.f64 a 2) (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) a))
18.0ms	(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) a)
12.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

series1.2s (14.9%)

Counts

4 → 12

Calls

4 calls:

466.0ms	(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) a)
351.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
315.0ms	(.f64 (.f64 a 2) (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) a))
67.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

simplify140.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4967	11298
1	4967	11298

prune602.0ms (7.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	301	3	304
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	304	10	314

Merged error: 0b

Counts

314 → 10

Compiler

Compiled 12412 to 6520 computations (47.5% saved)

regimes78.0ms (1%)

Compiler: Compiled 786 to 603 computations (23.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	32
1	85	32

end0.0ms (0%)

sample1.2s (14.6%)

Algorithm

1×

intervals

Results

384.0ms	7686×	body	128	valid
265.0ms	8828×	pre	128	true
38.0ms	828×	body	128	nan
30.0ms	314×	body	256	valid

Compiler

Compiled 311 to 238 computations (23.5% saved)

Details

analyze259.0ms (3.2%)

sample35.0ms (0.4%)

simplify228.0ms (2.8%)

prune8.0ms (0.1%)

localize11.0ms (0.1%)

rewrite39.0ms (0.5%)

series538.0ms (6.7%)

simplify58.0ms (0.7%)

prune173.0ms (2.2%)

localize13.0ms (0.2%)

rewrite70.0ms (0.9%)

series940.0ms (11.7%)

simplify81.0ms (1%)

prune564.0ms (7%)

localize14.0ms (0.2%)

rewrite75.0ms (0.9%)

series1.2s (14.4%)

simplify83.0ms (1%)

prune371.0ms (4.6%)

localize16.0ms (0.2%)

rewrite123.0ms (1.5%)

series1.2s (14.9%)

simplify140.0ms (1.7%)

prune602.0ms (7.5%)

regimes78.0ms (1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.2s (14.6%)

Profiling