Details

analyze260.0ms (4.5%)

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)

sample52.0ms (0.9%)

Algorithm

1×

intervals

Results

18.0ms	117×	body	320	valid
9.0ms	93×	body	160	valid
9.0ms	285×	pre	80	true
3.0ms	16×	body	640	valid
1.0ms	30×	body	80	valid
1.0ms	29×	body	80	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify111.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	928	24
1	928	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: 52.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
25.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `insert-posit16` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 74

Calls

4 calls:

17.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
10.0ms	(-.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)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series512.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

206.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
130.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify134.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	6773	2041

prune105.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Merged error: 0.1b

Counts

87 → 4

Compiler

Compiled 2072 to 1233 computations (40.5% saved)

localize17.0ms (0.3%)

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

rewrite50.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`associate-/l*_binary64`
10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `insert-posit16` `flip-+_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 102

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
14.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
8.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series844.0ms (14.5%)

Counts

4 → 12

Calls

4 calls:

361.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
294.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
118.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
69.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify123.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4929	3120
1	4929	3120

prune157.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	112	6	118

Merged error: 0b

Counts

118 → 6

Compiler

Compiled 3231 to 1987 computations (38.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64` `insert-posit16`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 75

Calls

4 calls:

10.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
8.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
6.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series637.0ms (11%)

Counts

4 → 12

Calls

4 calls:

328.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
119.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
73.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify152.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	4914	2037
1	4914	2037

prune115.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	88	5	93

Merged error: 0b

Counts

93 → 5

Compiler

Compiled 2305 to 1435 computations (37.7% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
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)

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `cbrt-prod_binary64`
10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`unpow-prod-down_binary64` `cube-prod_binary64`
5×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`cube-div_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `flip3--_binary64` `flip--_binary64`
2×	`cbrt-div_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 75

Calls

4 calls:

12.0ms	(+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))))
7.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)
7.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))
6.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series438.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

177.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)
127.0ms	(+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))))
68.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))
66.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify132.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4925	1820
1	4925	1820

prune108.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	87	5	92

Merged error: 0b

Counts

92 → 5

Compiler

Compiled 2310 to 1501 computations (35% saved)

regimes47.0ms (0.8%)

Compiler: Compiled 396 to 321 computations (18.9% saved)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	67	29
1	67	29

end0.0ms (0%)

sample1.7s (28.5%)

Algorithm

1×

intervals

Results

515.0ms	3645×	body	320	valid
282.0ms	3013×	body	160	valid
275.0ms	8833×	pre	80	true
91.0ms	475×	body	640	valid
43.0ms	867×	body	80	valid
40.0ms	833×	body	80	nan

Compiler

Compiled 179 to 144 computations (19.6% saved)

Details

analyze260.0ms (4.5%)

sample52.0ms (0.9%)

simplify111.0ms (1.9%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite40.0ms (0.7%)

series512.0ms (8.8%)

simplify134.0ms (2.3%)

prune105.0ms (1.8%)

localize17.0ms (0.3%)

rewrite50.0ms (0.9%)

series844.0ms (14.5%)

simplify123.0ms (2.1%)

prune157.0ms (2.7%)

localize12.0ms (0.2%)

rewrite31.0ms (0.5%)

series637.0ms (11%)

simplify152.0ms (2.6%)

prune115.0ms (2%)

localize16.0ms (0.3%)

rewrite34.0ms (0.6%)

series438.0ms (7.6%)

simplify132.0ms (2.3%)

prune108.0ms (1.9%)

regimes47.0ms (0.8%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample1.7s (28.5%)

Profiling