Details

analyze12.0ms (0.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 23 to 15 computations (34.8% saved)

sample22.0ms (1%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify240.0ms (10.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5184	22

prune2.0ms (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: 22.9b

Counts

2 → 1

Compiler

Compiled 30 to 18 computations (40% saved)

localize9.0ms (0.4%)

Local error

Found 1 expressions with local error:

22.6b

(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))

rewrite18.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64_1058`
6×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
4×	`flip-+_binary64_1085` `frac-times_binary64_1121` `flip3-+_binary64_1114`
3×	`times-frac_binary64_1117` `-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133` `associate-/r_binary64_1055` `flip3--_binary64_1115` `add-cube-cbrt_binary64_1146` `flip--_binary64_1086`
2×	`associate-l/_binary64_1054` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `associate-r/_binary64_1053` `associate-/r/_binary64_1057`
1×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `div-inv_binary64_1108` `frac-2neg_binary64_1122` `associate-/l*_binary64_1056` `add-log-exp_binary64_1150` `pow1_binary64_1172` `clear-num_binary64_1110`

Counts

1 → 31

Calls

1 calls:

14.0ms

(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))

series91.0ms (4.2%)

Counts

1 → 3

Calls

1 calls:

91.0ms

(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))

simplify55.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5543	785

prune61.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	30	4	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	4	35

Merged error: 0.8b

Counts

35 → 4

Compiler

Compiled 1201 to 387 computations (67.8% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune3.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Merged error: 0.8b

Counts

4 → 4

Compiler

Compiled 34 to 22 computations (35.3% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b

(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y))) 3))

0.0b

(pow.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y))) 3)

22.6b

(/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y)))

rewrite51.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`times-frac_binary64_1117`
46×	`*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146`
42×	`cbrt-prod_binary64_1142`
36×	`unpow-prod-down_binary64_1190` `cube-prod_binary64_1139`
16×	`difference-of-squares_binary64_1080`
10×	`associate-/r/_binary64_1057`
8×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
5×	`div-inv_binary64_1108` `flip-+_binary64_1085` `flip3-+_binary64_1114`
4×	`associate-/l*_binary64_1056` `pow1_binary64_1172`
3×	`associate-/r*_binary64_1055` `pow-unpow_binary64_1188` `add-log-exp_binary64_1150`
2×	`cube-div_binary64_1140` `cube-mult_binary64_1141` `associate-/l/_binary64_1058` `div-exp_binary64_1162` `pow-exp_binary64_1179` `cbrt-undiv_binary64_1145` `rem-cube-cbrt_binary64_1134` `unpow3_binary64_1177` `sqr-pow_binary64_1083`
1×	`pow1/3_binary64_1193` `frac-2neg_binary64_1122` `flip3--_binary64_1115` `rem-cbrt-cube_binary64_1135` `pow-pow_binary64_1183` `pow-to-exp_binary64_1180` `cbrt-div_binary64_1143` `clear-num_binary64_1110` `div-sub_binary64_1116` `flip--_binary64_1086`

Counts

3 → 144

Calls

3 calls:

12.0ms

(pow.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y))) 3)

12.0ms

(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y))) 3))

10.0ms

(/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y)))

series226.0ms (10.3%)

Counts

3 → 9

Calls

3 calls:

91.0ms

(pow.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y))) 3)

69.0ms

(/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y)))

67.0ms

(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y))) 3))

simplify96.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5053	5017

prune136.0ms (6.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	153	4	157

Merged error: 0.8b

Counts

157 → 4

Compiler

Compiled 4096 to 840 computations (79.5% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.2b	(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (+.f64 (.f64 x x) (*.f64 y y))))
22.1b	(/.f64 (+.f64 x y) (+.f64 (.f64 x x) (.f64 y y)))

rewrite35.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_1111`
27×	`add-sqr-sqrt_binary64_1133`
25×	`times-frac_binary64_1117`
20×	`add-cube-cbrt_binary64_1146`
18×	`associate-r_binary64_1051`
9×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
7×	`distribute-lft-out_binary64_1062`
5×	`associate-l_binary64_1052`
4×	`associate-/l*_binary64_1056` `pow1_binary64_1172` `associate-/r/_binary64_1057`
3×	`flip-+_binary64_1085` `associate-/r*_binary64_1055` `flip3-+_binary64_1114`
2×	`prod-exp_binary64_1160` `associate-*l/_binary64_1054` `cbrt-unprod_binary64_1144` `div-inv_binary64_1108` `frac-times_binary64_1121` `flip3--_binary64_1115` `associate-/l/_binary64_1058` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `unswap-sqr_binary64_1079` `add-log-exp_binary64_1150` `flip--_binary64_1086`
1×	`-commutative_binary64_1042` `frac-2neg_binary64_1122` `pow-prod-down_binary64_1182` `difference-of-squares_binary64_1080` `clear-num_binary64_1110` `distribute-lft-out--_binary64_1063` `associate-r/_binary64_1053`

Counts

2 → 78

Calls

2 calls:

18.0ms	(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (+.f64 (.f64 x x) (*.f64 y y))))
9.0ms	(/.f64 (+.f64 x y) (+.f64 (.f64 x x) (.f64 y y)))

series149.0ms (6.8%)

Counts

2 → 6

Calls

2 calls:

84.0ms	(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (+.f64 (.f64 x x) (*.f64 y y))))
65.0ms	(/.f64 (+.f64 x y) (+.f64 (.f64 x x) (.f64 y y)))

simplify57.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5023	1980

prune58.0ms (2.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	84	4	88

Merged error: 0.8b

Counts

88 → 4

Compiler

Compiled 1969 to 272 computations (86.2% saved)

regimes43.0ms (2%)

Compiler: Compiled 74 to 58 computations (21.6% saved)

bsearch30.0ms (1.4%)

Steps

Iters	Range	Point
7	4.554246020067214e-164	2.748640955280589e-162	3.60390796991782e-163
3	9.219262616979464e-198	1.219506282477916e-197	1.1265125259841753e-197
6	-2.7888866739901093e-160	-2.153734372005664e-161	-2.5805430812011672e-160

Iters

Range

Point

4.554246020067214e-164

2.748640955280589e-162

3.60390796991782e-163

9.219262616979464e-198

1.219506282477916e-197

1.1265125259841753e-197

-2.7888866739901093e-160

-2.153734372005664e-161

-2.5805430812011672e-160

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	48
1	41	48

end0.0ms (0%)

sample776.0ms (35.3%)

Algorithm

1×

intervals

Results

311.0ms	8000×	body	128	valid
162.0ms	8000×	pre	128	true

Compiler

Compiled 127 to 86 computations (32.3% saved)

Details

analyze12.0ms (0.6%)

sample22.0ms (1%)

simplify240.0ms (10.9%)

prune2.0ms (0.1%)

localize9.0ms (0.4%)

rewrite18.0ms (0.8%)

series91.0ms (4.2%)

simplify55.0ms (2.5%)

prune61.0ms (2.8%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.3%)

prune3.0ms (0.1%)

localize10.0ms (0.4%)

rewrite51.0ms (2.3%)

series226.0ms (10.3%)

simplify96.0ms (4.4%)

prune136.0ms (6.2%)

localize10.0ms (0.4%)

rewrite35.0ms (1.6%)

series149.0ms (6.8%)

simplify57.0ms (2.6%)

prune58.0ms (2.6%)

regimes43.0ms (2%)

bsearch30.0ms (1.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample776.0ms (35.3%)

Profiling