Details

analyze9.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 106 to 71 computations (33% saved)

sample103.0ms (0.3%)

Algorithm

1×

intervals

Results

80.0ms	256×	body	128	valid
5.0ms	261×	pre	128	true
1.0ms	5×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify210.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	5512	47

prune13.0ms (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

2.4b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.4b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
1.0b	(sqrt.f64 PI.f64)
2.4b	(exp.f64 (*.f64 x x))

rewrite133.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

129×	`times-frac_binary64_1448`
84×	`add-sqr-sqrt_binary64_1464`
79×	`*-un-lft-identity_binary64_1442`
70×	`associate-l_binary64_1383` `add-cube-cbrt_binary64_1477`
31×	`sqrt-prod_binary64_1458`
18×	`add-cbrt-cube_binary64_1478`
17×	`add-exp-log_binary64_1480`
7×	`pow1_binary64_1503`
6×	`add-log-exp_binary64_1481`
5×	`associate-r_binary64_1382` `cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `distribute-lft-out_binary64_1393` `div-exp_binary64_1493`
4×	`cbrt-unprod_binary64_1475` `associate-/l*_binary64_1387` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`associate-*r/_binary64_1384` `associate-/l/_binary64_1389` `frac-times_binary64_1452`
1×	`sqrt-pow1_binary64_1460` `associate-/r_binary64_1386` `rem-sqrt-square_binary64_1455` `clear-num_binary64_1441` `rem-exp-log_binary64_1482` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `exp-prod_binary64_1494` `frac-2neg_binary64_1453` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `exp-to-pow_binary64_1504` `pow1/2_binary64_1522` `associate-*l/_binary64_1385`

Counts

4 → 149

Calls

4 calls:

81.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

series185.0ms (0.6%)

Counts

4 → 10

Calls

4 calls:

116.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
55.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
14.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify185.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4944	6254
1	4944	6254

prune496.0ms (1.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	139	20	159
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	140	21	161

Error

0.2b

Counts

161 → 21

Compiler

Compiled 7838 to 3653 computations (53.4% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
1.0b	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
1.0b	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
1.0b	(pow.f64 (exp.f64 x) x)

rewrite74.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_1464`
29×	`pow1_binary64_1503`
24×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
18×	`sqrt-pow1_binary64_1460` `pow1/3_binary64_1524`
16×	`cbrt-prod_binary64_1473`
12×	`times-frac_binary64_1448`
11×	`pow-flip_binary64_1516`
10×	`add-exp-log_binary64_1480`
6×	`associate-r_binary64_1382` `add-cbrt-cube_binary64_1478` `swap-sqr_binary64_1409` `associate-l_binary64_1383` `pow-prod-down_binary64_1513` `pow-sqr_binary64_1415` `pow-prod-up_binary64_1512`
5×	`sqrt-prod_binary64_1458`
4×	`associate-/r*_binary64_1386` `add-log-exp_binary64_1481` `unswap-sqr_binary64_1410` `pow-pow_binary64_1514`
3×	`pow2_binary64_1523` `associate-/l*_binary64_1387` `pow-plus_binary64_1505` `pow-unpow_binary64_1519` `exp-prod_binary64_1494` `unpow-prod-down_binary64_1521`
2×	`pow1/2_binary64_1522` `div-exp_binary64_1493`
1×	`inv-pow_binary64_1527` `cbrt-undiv_binary64_1476` `rem-sqrt-square_binary64_1455` `cbrt-unprod_binary64_1475` `pow-exp_binary64_1510` `div-inv_binary64_1439` `clear-num_binary64_1441` `1-exp_binary64_1486` `*-commutative_binary64_1373` `rec-exp_binary64_1492` `frac-2neg_binary64_1453` `sqr-pow_binary64_1414` `prod-exp_binary64_1491` `pow-to-exp_binary64_1511`

Counts

4 → 124

Calls

4 calls:

14.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
13.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
8.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
7.0ms	(pow.f64 (exp.f64 x) x)

series36.0ms (0.1%)

Counts

4 → 6

Calls

4 calls:

36.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
0.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
0.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))

simplify98.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5052	1416

prune443.0ms (1.5%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	123	7	130
Fresh	5	15	20
Picked	0	1	1
Done	0	0	0
Total	128	23	151

Error

0.1b

Counts

151 → 23

Compiler

Compiled 7249 to 3304 computations (54.4% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.0b	(pow.f64 (exp.f64 x) x)

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_1442`
13×	`add-sqr-sqrt_binary64_1464`
11×	`add-cube-cbrt_binary64_1477`
9×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
7×	`pow1_binary64_1503`
6×	`sqrt-prod_binary64_1458`
4×	`times-frac_binary64_1448` `associate-/l*_binary64_1387` `add-log-exp_binary64_1481` `pow-pow_binary64_1514`
3×	`pow-unpow_binary64_1519` `exp-prod_binary64_1494` `unpow-prod-down_binary64_1521`
2×	`sqrt-pow1_binary64_1460` `cbrt-undiv_binary64_1476` `rem-sqrt-square_binary64_1455` `associate-/l/_binary64_1389` `distribute-lft-out_binary64_1393` `pow1/2_binary64_1522` `div-exp_binary64_1493`
1×	`associate-/r*_binary64_1386` `cbrt-unprod_binary64_1475` `pow-exp_binary64_1510` `div-inv_binary64_1439` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `sqr-pow_binary64_1414` `flip3-+_binary64_1445` `flip-+_binary64_1416` `prod-exp_binary64_1491` `pow-to-exp_binary64_1511`

Counts

4 → 71

Calls

4 calls:

10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
4.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series131.0ms (0.4%)

Counts

4 → 8

Calls

4 calls:

94.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
37.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify151.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	4963	1016
1	4963	1016

prune262.0ms (0.9%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	5	16	21
Picked	0	1	1
Done	0	1	1
Total	80	22	102

Error

0.1b

Counts

102 → 22

Compiler

Compiled 4409 to 2373 computations (46.2% saved)

localize36.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (fabs.f64 x)) (sqrt.f64 (sqrt.f64 PI.f64))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.0b	(pow.f64 (exp.f64 x) x)

rewrite1.6s (5.3%)

Algorithm

1×	rewrite-expression-head

Rules

5445×	`times-frac_binary64_1448`
3612×	`sqrt-prod_binary64_1458`
2469×	`add-sqr-sqrt_binary64_1464`
2323×	`*-un-lft-identity_binary64_1442`
2318×	`add-cube-cbrt_binary64_1477`
1849×	`associate-r_binary64_1382`
741×	`unpow-prod-down_binary64_1521`
253×	`sqr-pow_binary64_1414`
37×	`div-inv_binary64_1439`
34×	`unswap-sqr_binary64_1410`
26×	`add-exp-log_binary64_1480`
18×	`add-cbrt-cube_binary64_1478`
12×	`div-exp_binary64_1493`
9×	`pow1_binary64_1503`
6×	`cbrt-undiv_binary64_1476` `prod-exp_binary64_1491`
5×	`associate-l_binary64_1383`
4×	`cbrt-unprod_binary64_1475` `add-log-exp_binary64_1481` `pow-pow_binary64_1514`
3×	`pow-unpow_binary64_1519` `distribute-lft-out_binary64_1393` `exp-prod_binary64_1494`
2×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `pow-exp_binary64_1510` `frac-times_binary64_1452` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522` `associate-*l/_binary64_1385` `pow-to-exp_binary64_1511`
1×	`associate-r/_binary64_1384` `pow-prod-down_binary64_1513` `-commutative_binary64_1373`

Counts

4 → 1958

Calls

4 calls:

791.0ms	(.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (fabs.f64 x)) (sqrt.f64 (sqrt.f64 PI.f64))))
4.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series204.0ms (0.7%)

Counts

4 → 8

Calls

4 calls:

172.0ms	(.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (fabs.f64 x)) (sqrt.f64 (sqrt.f64 PI.f64))))
32.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify1.4s (4.8%)

Algorithm

1×	egg-herbie

Counts

1966 → 1966

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4973	119163
1	4973	119163

prune7.3s (24.5%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	1950	16	1966
Fresh	9	10	19
Picked	1	0	1
Done	2	0	2
Total	1962	26	1988

Error

0.0b

Counts

1988 → 26

Compiler

Compiled 109018 to 33381 computations (69.4% saved)

regimes2.9s (9.6%)

Accuracy

Total 1.1b remaining (91.3%)

Threshold costs 0b (0%)

Compiler

Compiled 29279 to 17826 computations (39.1% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	60
1	32	60

end0.0ms (0%)

sample13.7s (46%)

Algorithm

1×

intervals

Results

2.6s	8000×	body	128	valid
154.0ms	8126×	pre	128	true
42.0ms	126×	body	128	invalid

Compiler

Compiled 9832 to 5992 computations (39.1% saved)

Details

analyze9.0ms (0%)

sample103.0ms (0.3%)

simplify210.0ms (0.7%)

prune13.0ms (0%)

localize19.0ms (0.1%)

rewrite133.0ms (0.4%)

series185.0ms (0.6%)

simplify185.0ms (0.6%)

prune496.0ms (1.7%)

localize35.0ms (0.1%)

rewrite74.0ms (0.2%)

series36.0ms (0.1%)

simplify98.0ms (0.3%)

prune443.0ms (1.5%)

localize27.0ms (0.1%)

rewrite26.0ms (0.1%)

series131.0ms (0.4%)

simplify151.0ms (0.5%)

prune262.0ms (0.9%)

localize36.0ms (0.1%)

rewrite1.6s (5.3%)

series204.0ms (0.7%)

simplify1.4s (4.8%)

prune7.3s (24.5%)

regimes2.9s (9.6%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample13.7s (46%)

Profiling