Details

analyze980.0ms (16.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1992	72
1	1992	72
0	3	3
1	3	3

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	38×	body	2048	valid
7.0ms	162×	body	128	valid
4.0ms	15×	body	4096	valid
3.0ms	21×	body	1024	valid
1.0ms	12×	body	512	valid
1.0ms	22×	body	128	nan
1.0ms	8×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune6.0ms (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: 33.9b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
22.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 86

Calls

4 calls:

17.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series248.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
64.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
61.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
31.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify81.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4916	2170
1	4916	2170

prune102.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	7	99

Merged error: 3.9b

Counts

99 → 7

Compiler

Compiled 2055 to 409 computations (80.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.6b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
7.6b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
22.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite61.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
156×	`*-un-lft-identity_binary64`
93×	`add-sqr-sqrt_binary64`
92×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
32×	`distribute-lft-out_binary64`
21×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
7×	`associate-/r*_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `div-inv_binary64` `flip-+_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64`
2×	`neg-sub0_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 217

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
9.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
6.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series444.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
146.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
55.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
51.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify114.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5421	8163

prune196.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	229	7	236

Merged error: 3.8b

Counts

236 → 7

Compiler

Compiled 6620 to 864 computations (86.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.7b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
22.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite27.0ms (0.4%)

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`
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` `cancel-sign-sub-inv_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 → 72

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
6.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series310.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

173.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
55.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
52.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
29.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify90.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4968	1696
1	4968	1696

prune68.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	84	7	91

Merged error: 3.8b

Counts

91 → 7

Compiler

Compiled 1740 to 429 computations (75.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
22.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64` `add-exp-log_binary64`
11×	`times-frac_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`cancel-sign-sub-inv_binary64` `prod-exp_binary64` `difference-of-squares_binary64`
3×	`unswap-sqr_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 87

Calls

4 calls:

16.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series244.0ms (4%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
66.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
54.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
32.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5446	1904

prune75.0ms (1.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	98	8	106

Merged error: 3.8b

Counts

106 → 8

Compiler

Compiled 1956 to 516 computations (73.6% saved)

regimes787.0ms (13%)

Compiler: Compiled 4120 to 2428 computations (41.1% saved)

bsearch103.0ms (1.7%)

Steps

Iters	Range	Point
10	1.9585105551856798e+86	1.8906084554366125e+98	1.651464782087897e+98
8	-1.1539208726064524e-307	3.181770513359429e-307	-8.744224435785807e-308
9	-1.4744807199360288e+137	-7.948036635160632e+130	-3.552145154192115e+134

Iters

Range

Point

1.9585105551856798e+86

1.8906084554366125e+98

1.651464782087897e+98

-1.1539208726064524e-307

3.181770513359429e-307

-8.744224435785807e-308

-1.4744807199360288e+137

-7.948036635160632e+130

-3.552145154192115e+134

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	79
1	102	79

end0.0ms (0%)

sample1.8s (29.5%)

Algorithm

1×

intervals

Results

239.0ms	1144×	body	2048	valid
231.0ms	5210×	body	128	valid
117.0ms	742×	body	1024	valid
102.0ms	400×	body	4096	valid
45.0ms	360×	body	512	valid
34.0ms	819×	body	128	nan
12.0ms	144×	body	256	valid
11.0ms	242×	body	128	invalid

Compiler

Compiled 1079 to 633 computations (41.3% saved)

Details

analyze980.0ms (16.2%)

sample38.0ms (0.6%)

simplify71.0ms (1.2%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite43.0ms (0.7%)

series248.0ms (4.1%)

simplify81.0ms (1.3%)

prune102.0ms (1.7%)

localize11.0ms (0.2%)

rewrite61.0ms (1%)

series444.0ms (7.4%)

simplify114.0ms (1.9%)

prune196.0ms (3.2%)

localize11.0ms (0.2%)

rewrite27.0ms (0.4%)

series310.0ms (5.1%)

simplify90.0ms (1.5%)

prune68.0ms (1.1%)

localize10.0ms (0.2%)

rewrite39.0ms (0.6%)

series244.0ms (4%)

simplify83.0ms (1.4%)

prune75.0ms (1.2%)

regimes787.0ms (13%)

bsearch103.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.8s (29.5%)

Profiling