Details

analyze626.0ms (9%)

Algorithm

1×

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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	175×	body	128	valid
6.0ms	21×	body	4096	valid
5.0ms	23×	body	2048	valid
4.0ms	20×	body	1024	valid
2.0ms	13×	body	512	valid
1.0ms	17×	body	128	nan
0.0ms	4×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify170.0ms (2.4%)

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: 34.4b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize10.0ms (0.1%)

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)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite39.0ms (0.6%)

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:

11.0ms	(/.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))

series598.0ms (8.6%)

Counts

4 → 69

Calls

4 calls:

170.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
152.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
149.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
127.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 1839 to 1501 computations (18.4% saved)

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5234	3018

prune168.0ms (2.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	136	19	155
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	137	19	156

Merged error: 12.9b

Counts

156 → 19

Compiler

Compiled 2983 to 776 computations (74% saved)

localize19.0ms (0.3%)

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))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite44.0ms (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)
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series580.0ms (8.3%)

Counts

4 → 69

Calls

4 calls:

160.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
149.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
143.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
127.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 1999 to 1661 computations (16.9% saved)

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5020	2770

prune131.0ms (1.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	6	12	18
Picked	1	0	1
Done	0	0	0
Total	159	16	175

Merged error: 12.9b

Counts

175 → 16

Compiler

Compiled 3003 to 1030 computations (65.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 a)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64` `sqrt-prod_binary64`
3×	`flip3--_binary64` `flip--_binary64` `cbrt-prod_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64`

Counts

4 → 55

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.0ms	(cbrt.f64 a)

series522.0ms (7.5%)

Counts

4 → 57

Calls

4 calls:

152.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
143.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
136.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
92.0ms	(cbrt.f64 a)

Compiler

Compiled 2279 to 1651 computations (27.6% saved)

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4947	1632
1	4947	1632

prune118.0ms (1.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	106	6	112
Fresh	0	15	15
Picked	1	0	1
Done	0	0	0
Total	107	21	128

Merged error: 12.9b

Counts

128 → 21

Compiler

Compiled 3051 to 1023 computations (66.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
10.8b	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) b_2)
25.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
25.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64` `sqrt-prod_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`difference-of-squares_binary64`

Counts

4 → 57

Calls

4 calls:

16.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.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	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series571.0ms (8.2%)

Counts

4 → 73

Calls

4 calls:

150.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) b_2)
142.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
142.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
137.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2928 to 2157 computations (26.3% saved)

simplify42.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5342	2062

prune109.0ms (1.6%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	20	20
Picked	0	1	1
Done	0	0	0
Total	130	21	151

Merged error: 12.9b

Counts

151 → 21

Compiler

Compiled 3213 to 760 computations (76.3% saved)

regimes907.0ms (13%)

Compiler: Compiled 4196 to 2670 computations (36.4% saved)

bsearch62.0ms (0.9%)

Steps

Iters	Range		Point
8	1.908893459727095e-38	1.3134165204498558e-34	1.9966424328827729e-38
9	-1.5400601507326208e+159	-5.5788539022192515e+149	-1.3308472529742322e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	67
1	68	67

end0.0ms (0%)

sample1.9s (27.3%)

Algorithm

1×

intervals

Results

242.0ms	5236×	body	128	valid
241.0ms	1109×	body	2048	valid
118.0ms	695×	body	1024	valid
110.0ms	422×	body	4096	valid
44.0ms	360×	body	512	valid
34.0ms	807×	body	128	nan
15.0ms	178×	body	256	valid
11.0ms	244×	body	128	invalid

Compiler

Compiled 1099 to 700 computations (36.3% saved)

Details

analyze626.0ms (9%)

sample39.0ms (0.6%)

simplify170.0ms (2.4%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

rewrite39.0ms (0.6%)

series598.0ms (8.6%)

simplify72.0ms (1%)

prune168.0ms (2.4%)

localize19.0ms (0.3%)

rewrite44.0ms (0.6%)

series580.0ms (8.3%)

simplify71.0ms (1%)

prune131.0ms (1.9%)

localize14.0ms (0.2%)

rewrite22.0ms (0.3%)

series522.0ms (7.5%)

simplify72.0ms (1%)

prune118.0ms (1.7%)

localize10.0ms (0.1%)

rewrite36.0ms (0.5%)

series571.0ms (8.2%)

simplify42.0ms (0.6%)

prune109.0ms (1.6%)

regimes907.0ms (13%)

bsearch62.0ms (0.9%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.9s (27.3%)

Profiling