Details

analyze559.0ms (12.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
12.5%	87.3%	0.2%	10
25%	74.9%	0.2%	11
31.2%	63.9%	4.9%	12
39%	50.9%	10.1%	13
44.8%	44.4%	10.7%	14

Compiler

Compiled 8 to 8 computations (0% saved)

sample17.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	128	valid
1.0ms	38×	body	128	invalid

Compiler

Compiled 15 to 19 computations (-26.7% saved)

simplify172.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	160	14
1	160	14

prune2.0ms (0%)

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: 0.0b

Counts

2 → 1

Compiler

Compiled 14 to 14 computations (0% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_1150`
1×	`add-cbrt-cube_binary64_1147` `*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133` `cancel-sign-sub-inv_binary64_1077` `flip3--_binary64_1115` `add-cube-cbrt_binary64_1146` `diff-log_binary64_1203` `pow1_binary64_1172` `sub-neg_binary64_1104` `flip--_binary64_1086` `add-exp-log_binary64_1149`

Counts

1 → 12

Calls

1 calls:

4.0ms

(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

series84.0ms (1.9%)

Counts

1 → 3

Calls

1 calls:

83.0ms

(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

simplify68.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4948	294
1	4948	294

prune30.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	4	16

Merged error: 0.0b

Counts

16 → 4

Compiler

Compiled 505 to 258 computations (48.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.3b	(.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
1.0b	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
1.0b	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

rewrite37.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1133`
24×	`sqrt-prod_binary64_1127`
21×	`pow1_binary64_1172`
16×	`sqrt-div_binary64_1128`
14×	`*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146`
10×	`pow1/2_binary64_1191` `sqrt-pow1_binary64_1129`
9×	`flip3--_binary64_1115` `flip--_binary64_1086`
8×	`swap-sqr_binary64_1078`
6×	`add-cbrt-cube_binary64_1147` `associate-r_binary64_1051` `associate-l_binary64_1052` `add-log-exp_binary64_1150` `add-exp-log_binary64_1149`
5×	`pow-prod-up_binary64_1181`
4×	`rem-sqrt-square_binary64_1124` `frac-times_binary64_1121` `unswap-sqr_binary64_1079`
3×	`pow-sqr_binary64_1084` `pow-prod-down_binary64_1182`
2×	`associate-l/_binary64_1054` `associate-r/_binary64_1053`
1×	`*-commutative_binary64_1042` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `cancel-sign-sub-inv_binary64_1077` `rem-square-sqrt_binary64_1123` `diff-log_binary64_1203` `pow-plus_binary64_1174` `pow2_binary64_1192` `sqrt-unprod_binary64_1131` `sqr-abs_binary64_1126` `sub-neg_binary64_1104`

Counts

4 → 100

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
4.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
4.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
4.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series517.0ms (11.8%)

Counts

4 → 12

Calls

4 calls:

187.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
165.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
83.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
82.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

simplify61.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4953	2577
1	4953	2577

prune90.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	112	4	116

Merged error: 0.0b

Counts

116 → 4

Compiler

Compiled 2530 to 551 computations (78.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
1.0b	(log.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
2.7b	(exp.f64 (log.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64_1197` `*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146`
5×	`add-log-exp_binary64_1150` `pow1_binary64_1172`
4×	`log-div_binary64_1198` `exp-prod_binary64_1163` `add-exp-log_binary64_1149`
3×	`add-cbrt-cube_binary64_1147` `exp-sum_binary64_1157` `flip3--_binary64_1115` `flip--_binary64_1086`
2×	`exp-diff_binary64_1159` `log-pow_binary64_1200`
1×	`cancel-sign-sub-inv_binary64_1077` `diff-log_binary64_1203` `rem-exp-log_binary64_1151` `rem-log-exp_binary64_1152` `sub-neg_binary64_1104`

Counts

3 → 43

Calls

3 calls:

6.0ms	(log.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
5.0ms	(exp.f64 (log.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
4.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series415.0ms (9.5%)

Counts

3 → 9

Calls

3 calls:

220.0ms	(exp.f64 (log.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
120.0ms	(log.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
74.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

simplify54.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4956	1063
1	4956	1063

prune43.0ms (1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	52	4	56

Merged error: 0.0b

Counts

56 → 4

Compiler

Compiled 912 to 303 computations (66.8% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(+.f64 (.f64 (.f64 x.re y.re) (.f64 x.re y.re)) (.f64 x.im (.f64 y.im (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))))
1.8b	(-.f64 (pow.f64 (.f64 x.re y.re) 3) (pow.f64 (.f64 x.im y.im) 3))
4.3b	(.f64 x.im (.f64 y.im (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
37.9b	(/.f64 (-.f64 (pow.f64 (.f64 x.re y.re) 3) (pow.f64 (.f64 x.im y.im) 3)) (+.f64 (.f64 (.f64 x.re y.re) (.f64 x.re y.re)) (.f64 x.im (.f64 y.im (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))))

rewrite67.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_1133`
30×	`*-un-lft-identity_binary64_1111`
27×	`times-frac_binary64_1117`
21×	`sqr-pow_binary64_1083`
20×	`add-cube-cbrt_binary64_1146` `difference-of-squares_binary64_1080`
11×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
9×	`associate-/l*_binary64_1056` `pow1_binary64_1172`
8×	`cancel-sign-sub-inv_binary64_1077` `distribute-lft-in_binary64_1060` `add-log-exp_binary64_1150` `distribute-rgt-in_binary64_1061`
5×	`distribute-lft-out--_binary64_1063` `difference-cubes_binary64_1113`
4×	`associate-*r/_binary64_1053` `associate-+r+_binary64_1043`
3×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `flip-+_binary64_1085` `associate-/r_binary64_1055` `flip3-+_binary64_1114` `pow-prod-down_binary64_1182` `associate-l*_binary64_1052`
2×	`flip3--_binary64_1115` `associate-/l/_binary64_1058` `flip--_binary64_1086` `associate-/r/_binary64_1057`
1×	`-commutative_binary64_1042` `unpow-prod-down_binary64_1190` `cube-mult_binary64_1141` `div-inv_binary64_1108` `frac-2neg_binary64_1122` `diff-log_binary64_1203` `associate-r*_binary64_1051` `+-commutative_binary64_1041` `cube-prod_binary64_1139` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `unpow3_binary64_1177` `sum-log_binary64_1202` `sub-neg_binary64_1104` `clear-num_binary64_1110` `div-sub_binary64_1116`

Counts

4 → 120

Calls

4 calls:

21.0ms	(/.f64 (-.f64 (pow.f64 (.f64 x.re y.re) 3) (pow.f64 (.f64 x.im y.im) 3)) (+.f64 (.f64 (.f64 x.re y.re) (.f64 x.re y.re)) (.f64 x.im (.f64 y.im (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))))
9.0ms	(+.f64 (.f64 (.f64 x.re y.re) (.f64 x.re y.re)) (.f64 x.im (.f64 y.im (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))))
9.0ms	(-.f64 (pow.f64 (.f64 x.re y.re) 3) (pow.f64 (.f64 x.im y.im) 3))
9.0ms	(.f64 x.im (.f64 y.im (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))))

series1.1s (25.5%)

Counts

4 → 12

Calls

4 calls:

352.0ms	(-.f64 (pow.f64 (.f64 x.re y.re) 3) (pow.f64 (.f64 x.im y.im) 3))
316.0ms	(/.f64 (-.f64 (pow.f64 (.f64 x.re y.re) 3) (pow.f64 (.f64 x.im y.im) 3)) (+.f64 (.f64 (.f64 x.re y.re) (.f64 x.re y.re)) (.f64 x.im (.f64 y.im (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))))
267.0ms	(.f64 x.im (.f64 y.im (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
183.0ms	(+.f64 (.f64 (.f64 x.re y.re) (.f64 x.re y.re)) (.f64 x.im (.f64 y.im (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))))

simplify118.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4985	7167
1	4985	7167

prune207.0ms (4.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	132	4	136

Merged error: 0.0b

Counts

136 → 4

Compiler

Compiled 5851 to 2053 computations (64.9% saved)

regimes81.0ms (1.8%)

Compiler: Compiled 482 to 360 computations (25.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	14
1	38	14

end0.0ms (0%)

sample579.0ms (13.2%)

Algorithm

1×

intervals

Results

216.0ms	8000×	body	128	valid
35.0ms	1398×	body	128	invalid

Compiler

Compiled 79 to 61 computations (22.8% saved)

Details

analyze559.0ms (12.8%)

sample17.0ms (0.4%)

simplify172.0ms (3.9%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite5.0ms (0.1%)

series84.0ms (1.9%)

simplify68.0ms (1.6%)

prune30.0ms (0.7%)

localize8.0ms (0.2%)

rewrite37.0ms (0.8%)

series517.0ms (11.8%)

simplify61.0ms (1.4%)

prune90.0ms (2.1%)

localize8.0ms (0.2%)

rewrite18.0ms (0.4%)

series415.0ms (9.5%)

simplify54.0ms (1.2%)

prune43.0ms (1%)

localize16.0ms (0.4%)

rewrite67.0ms (1.5%)

series1.1s (25.5%)

simplify118.0ms (2.7%)

prune207.0ms (4.7%)

regimes81.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample579.0ms (13.2%)

Profiling