Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample97.0ms (1.8%)

Algorithm

1×

intervals

Results

68.0ms	128×	body	2048	valid
17.0ms	67×	body	1024	valid
4.0ms	31×	body	512	valid
2.0ms	24×	body	256	valid
0.0ms	6×	body	128	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify178.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4809	13
1	4809	13

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

Error

31.7b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
0.1b	(-.f64 (exp.f64 x) 2)
0.1b	(-.f64 (exp.f64 x) 2)
4.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_1101`
9×	`add-log-exp_binary64_1140`
6×	`add-sqr-sqrt_binary64_1123` `cancel-sign-sub-inv_binary64_1067`
4×	`add-cube-cbrt_binary64_1136` `frac-add_binary64_1109` `associate-+l+_binary64_1034`
3×	`flip--_binary64_1076` `flip3--_binary64_1105`
2×	`diff-log_binary64_1193` `distribute-lft-out_binary64_1052` `sum-log_binary64_1192` `add-exp-log_binary64_1139` `pow1_binary64_1162` `sub-neg_binary64_1094` `exp-diff_binary64_1149` `distribute-lft-out--_binary64_1053` `neg-sub0_binary64_1096` `add-cbrt-cube_binary64_1137` `exp-neg_binary64_1148`
1×	`difference-of-squares_binary64_1070` `flip3-+_binary64_1104` `associate-+l-_binary64_1036` `+-commutative_binary64_1031` `flip-+_binary64_1075`

Counts

2 → 39

Calls

4 calls:

9.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
5.0ms	(-.f64 (exp.f64 x) 2)
0.0ms	(-.f64 (exp.f64 x) 2)
0.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series48.0ms (0.9%)

Counts

2 → 12

Calls

2 calls:

31.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
16.0ms	(-.f64 (exp.f64 x) 2)

Compiler

Compiled 158 to 138 computations (12.7% saved)

simplify75.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4844	726
1	4844	726

prune80.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	3	52

Error

0.0b

Counts

52 → 3

Compiler

Compiled 712 to 378 computations (46.9% saved)

localize12.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 1/12 (pow.f64 x 4))
0.1b	(*.f64 1/360 (pow.f64 x 6))
0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))
0.0b	(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6)))
0.0b	(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6)))
0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))
0.1b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1123`
14×	`add-exp-log_binary64_1139` `associate-r_binary64_1041`
11×	`add-log-exp_binary64_1140`
10×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
8×	`unpow-prod-down_binary64_1180` `add-cbrt-cube_binary64_1137`
6×	`prod-exp_binary64_1150` `associate-l_binary64_1042` `unswap-sqr_binary64_1069`
4×	`sum-log_binary64_1192` `pow1_binary64_1162` `sqr-pow_binary64_1073`
2×	`*-commutative_binary64_1032` `pow-exp_binary64_1169` `cbrt-unprod_binary64_1134` `flip3-+_binary64_1104` `+-commutative_binary64_1031` `flip-+_binary64_1075` `pow-to-exp_binary64_1170`
1×	`associate-+r+_binary64_1033`

Counts

4 → 74

Calls

8 calls:

8.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))
6.0ms	(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6)))
6.0ms	(*.f64 1/12 (pow.f64 x 4))
6.0ms	(*.f64 1/360 (pow.f64 x 6))
0.0ms	(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6)))

series351.0ms (6.4%)

Counts

4 → 21

Calls

4 calls:

175.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))
102.0ms	(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6)))
39.0ms	(*.f64 1/360 (pow.f64 x 6))
34.0ms	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 431 to 356 computations (17.4% saved)

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5040	1349

prune114.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	94	4	98

Error

0.0b

Counts

98 → 4

Compiler

Compiled 1871 to 1316 computations (29.7% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 1/12 (pow.f64 x 4))
0.1b	(*.f64 1/360 (pow.f64 x 6))
0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))
0.0b	(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6)))
0.1b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))
0.1b	(pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))) 3)
21.3b	(cbrt.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))) 3))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_1123`
16×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
15×	`add-exp-log_binary64_1139`
14×	`unpow-prod-down_binary64_1180` `associate-r_binary64_1041`
12×	`cbrt-prod_binary64_1132`
9×	`add-cbrt-cube_binary64_1137`
6×	`cube-prod_binary64_1129` `prod-exp_binary64_1150` `associate-l_binary64_1042` `unswap-sqr_binary64_1069` `sqr-pow_binary64_1073`
5×	`pow1_binary64_1162`
4×	`add-log-exp_binary64_1140` `cube-div_binary64_1130`
3×	`pow-exp_binary64_1169` `pow-unpow_binary64_1178` `pow-to-exp_binary64_1170`
2×	`*-commutative_binary64_1032` `cube-mult_binary64_1131` `cbrt-unprod_binary64_1134` `flip3-+_binary64_1104` `unpow3_binary64_1167` `flip-+_binary64_1075` `cbrt-div_binary64_1133`
1×	`rem-cube-cbrt_binary64_1124` `pow1/3_binary64_1183` `pow-pow_binary64_1173` `rem-cbrt-cube_binary64_1125`

Counts

4 → 98

Calls

8 calls:

9.0ms	(pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))) 3)
8.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))) 3))
6.0ms	(*.f64 1/360 (pow.f64 x 6))
6.0ms	(*.f64 1/12 (pow.f64 x 4))
0.0ms	(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6)))

series328.0ms (6%)

Counts

4 → 27

Calls

4 calls:

158.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))) 3))
99.0ms	(pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))) 3)
39.0ms	(*.f64 1/360 (pow.f64 x 6))
32.0ms	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 522 to 453 computations (13.2% saved)

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5106	2525

prune176.0ms (3.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	125	4	129

Error

0.0b

Counts

129 → 4

Compiler

Compiled 2924 to 2158 computations (26.2% saved)

localize12.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) -2)
0.0b	(*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2))
0.0b	(-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
0.0b	(/.f64 (-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2)) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
0.1b	(-.f64 (exp.f64 x) 2)
0.1b	(-.f64 (exp.f64 x) 2)
0.1b	(-.f64 (exp.f64 x) 2)
3.7b	(-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`cancel-sign-sub-inv_binary64_1067`
19×	`add-sqr-sqrt_binary64_1123`
17×	`*-un-lft-identity_binary64_1101`
12×	`add-log-exp_binary64_1140`
11×	`add-cube-cbrt_binary64_1136`
8×	`associate--l+_binary64_1038`
6×	`difference-of-squares_binary64_1070` `sub-neg_binary64_1094`
4×	`diff-log_binary64_1193` `unpow-prod-down_binary64_1180` `add-exp-log_binary64_1139` `pow1_binary64_1162` `distribute-lft-in_binary64_1050` `flip--_binary64_1076` `flip3--_binary64_1105` `add-cbrt-cube_binary64_1137` `distribute-rgt-in_binary64_1051`
3×	`distribute-lft-out--_binary64_1053`
2×	`sqr-pow_binary64_1073`

Counts

4 → 77

Calls

8 calls:

19.0ms	(-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2))
5.0ms	(-.f64 (exp.f64 x) 2)
5.0ms	(-.f64 (exp.f64 x) 2)
5.0ms	(-.f64 (exp.f64 x) 2)
0.0ms	(/.f64 (-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2)) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))

series151.0ms (2.7%)

Counts

4 → 24

Calls

4 calls:

88.0ms	(-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2))
24.0ms	(-.f64 (exp.f64 x) 2)
20.0ms	(-.f64 (exp.f64 x) 2)
20.0ms	(-.f64 (exp.f64 x) 2)

Compiler

Compiled 788 to 584 computations (25.9% saved)

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4979	1257
1	4979	1257

prune124.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	101	4	105

Error

Counts

105 → 4

Compiler

Compiled 2673 to 1471 computations (45% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	182	448
1	182	448

regimes37.0ms (0.7%)

Compiler: Compiled 287 to 217 computations (24.4% saved)

bsearch0.0ms (0%)

regimes13.0ms (0.2%)

Compiler: Compiled 33 to 31 computations (6.1% saved)

bsearch0.0ms (0%)

regimes8.0ms (0.1%)

Compiler: Compiled 8 to 10 computations (-25% saved)

bsearch0.0ms (0%)

regimes7.0ms (0.1%)

Accuracy

Total 0.6b remaining (97.6%)

Threshold costs 0.6b (97.6%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 29 to 25 computations (13.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	41
1	21	41

end0.0ms (0%)

sample3.3s (59.6%)

Algorithm

1×

intervals

Results

2.1s	4122×	body	2048	valid
445.0ms	1995×	body	1024	valid
117.0ms	992×	body	512	valid
38.0ms	533×	body	256	valid
14.0ms	358×	body	128	valid

Compiler

Compiled 331 to 257 computations (22.4% saved)

Pareto

0.9840047261277791

Details

analyze4.0ms (0.1%)

sample97.0ms (1.8%)

simplify178.0ms (3.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite20.0ms (0.4%)

series48.0ms (0.9%)

simplify75.0ms (1.4%)

prune80.0ms (1.5%)

localize12.0ms (0.2%)

rewrite32.0ms (0.6%)

series351.0ms (6.4%)

simplify83.0ms (1.5%)

prune114.0ms (2.1%)

localize13.0ms (0.2%)

rewrite38.0ms (0.7%)

series328.0ms (6%)

simplify79.0ms (1.4%)

prune176.0ms (3.2%)

localize12.0ms (0.2%)

rewrite41.0ms (0.7%)

series151.0ms (2.7%)

simplify83.0ms (1.5%)

prune124.0ms (2.3%)

simplify9.0ms (0.2%)

regimes37.0ms (0.7%)

bsearch0.0ms (0%)

regimes13.0ms (0.2%)

bsearch0.0ms (0%)

regimes8.0ms (0.1%)

bsearch0.0ms (0%)

regimes7.0ms (0.1%)

bsearch3.0ms (0.1%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.3s (59.6%)

Profiling