Details

analyze9.0ms (0.1%)

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)

sample65.0ms (0.6%)

Algorithm

1×

intervals

Results

49.0ms	256×	body	80	valid
3.0ms	260×	pre	80	true
1.0ms	4×	body	80	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify238.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (219.0ms)

Iter	Nodes	Cost
0	4938	55
1	4938	55

prune10.0ms (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: 2.7b

Counts

2 → 2

Compiler

Compiled 171 to 121 computations (29.2% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
0.6b	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
1.0b	(sqrt.f64 PI.f64)
2.5b	(exp.f64 (pow.f64 (fabs.f64 x) 2))

rewrite98.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64_1577`
45×	`add-sqr-sqrt_binary64_1562`
42×	`times-frac_binary64_1572`
36×	`add-cube-cbrt_binary64_1548`
25×	`sqrt-prod_binary64_1556`
22×	`associate-l_binary64_1637`
18×	`frac-add_binary64_1567`
12×	`distribute-lft-out_binary64_1621`
11×	`add-cbrt-cube_binary64_1549`
9×	`add-exp-log_binary64_1541`
8×	`exp-prod_binary64_1527` `associate-r_binary64_1636`
7×	`pow1_binary64_1519` `frac-times_binary64_1569` `associate-*r/_binary64_1638`
6×	`flip3-+_binary64_1575` `associate-/r*_binary64_1640` `flip-+_binary64_1602`
5×	`add-log-exp_binary64_1542`
3×	`unpow-prod-down_binary64_1508` `unswap-sqr_binary64_1605` `associate-/l*_binary64_1641` `div-inv_binary64_1578`
2×	`prod-exp_binary64_1524` `div-exp_binary64_1526` `cbrt-undiv_binary64_1547` `cbrt-unprod_binary64_1546`
1×	`sqrt-pow1_binary64_1558` `sqr-pow_binary64_1609` `pow1/2_binary64_1509` `-commutative_binary64_1645` `unpow2_binary64_1516` `clear-num_binary64_1580` `rem-sqrt-square_binary64_1565` `pow-prod-down_binary64_1500` `distribute-lft-in_binary64_1619` `distribute-rgt-in_binary64_1620` `frac-2neg_binary64_1570` `associate-l/_binary64_1639` `rem-exp-log_binary64_1539`

Counts

4 → 131

Calls

4 calls:

78.0ms	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
8.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
4.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))
1.0ms	(sqrt.f64 PI.f64)

series1.1s (9.4%)

Counts

4 → 10

Calls

4 calls:

895.0ms	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
134.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
80.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)

simplify158.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5039	6082

prune452.0ms (3.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	125	16	141
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	127	16	143

Merged error: 0.7b

Counts

143 → 16

Compiler

Compiled 7721 to 5078 computations (34.2% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
0.6b	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite110.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`times-frac_binary64_1572`
86×	`*-un-lft-identity_binary64_1577`
85×	`add-sqr-sqrt_binary64_1562`
66×	`add-cube-cbrt_binary64_1548`
51×	`sqrt-prod_binary64_1556`
46×	`associate-l_binary64_1637`
44×	`unpow-prod-down_binary64_1508`
18×	`frac-add_binary64_1567`
17×	`add-exp-log_binary64_1541`
16×	`sqr-pow_binary64_1609`
12×	`distribute-lft-out_binary64_1621`
11×	`add-cbrt-cube_binary64_1549`
8×	`pow1_binary64_1519` `associate-r_binary64_1636`
7×	`frac-times_binary64_1569` `unswap-sqr_binary64_1605` `associate-/l_binary64_1641` `associate-r/_binary64_1638`
6×	`div-exp_binary64_1526` `flip3-+_binary64_1575` `associate-/r*_binary64_1640` `flip-+_binary64_1602`
4×	`prod-exp_binary64_1524` `pow-pow_binary64_1501` `add-log-exp_binary64_1542`
3×	`exp-prod_binary64_1527` `pow-exp_binary64_1497` `pow-to-exp_binary64_1498` `div-inv_binary64_1578` `pow-unpow_binary64_1506`
2×	`cbrt-undiv_binary64_1547` `cbrt-unprod_binary64_1546`
1×	`sqrt-pow1_binary64_1558` `pow1/2_binary64_1509` `-commutative_binary64_1645` `clear-num_binary64_1580` `rem-sqrt-square_binary64_1565` `pow-prod-down_binary64_1500` `distribute-lft-in_binary64_1619` `distribute-rgt-in_binary64_1620` `frac-2neg_binary64_1570` `associate-l/_binary64_1639`

Counts

4 → 195

Calls

4 calls:

85.0ms	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
8.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 PI.f64)

series1.5s (12.9%)

Counts

4 → 10

Calls

4 calls:

1.0s	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
268.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
205.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify156.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5477	9229

prune631.0ms (5.4%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	188	17	205
Fresh	8	7	15
Picked	0	1	1
Done	0	0	0
Total	196	25	221

Merged error: 0.2b

Counts

221 → 25

Compiler

Compiled 11344 to 6666 computations (41.2% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))) (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)))
0.7b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.7b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
1.0b	(sqrt.f64 PI.f64)

rewrite107.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64_1577`
70×	`times-frac_binary64_1572` `add-sqr-sqrt_binary64_1562`
51×	`add-cube-cbrt_binary64_1548`
46×	`associate-r_binary64_1636`
27×	`sqrt-prod_binary64_1556`
26×	`unpow-prod-down_binary64_1508` `pow-unpow_binary64_1506`
18×	`frac-add_binary64_1567`
13×	`add-exp-log_binary64_1541`
12×	`distribute-lft-out_binary64_1621`
10×	`sqr-pow_binary64_1609`
9×	`pow1_binary64_1519` `add-cbrt-cube_binary64_1549`
8×	`associate-l_binary64_1637` `pow-pow_binary64_1501`
7×	`frac-times_binary64_1569` `unswap-sqr_binary64_1605` `associate-*l/_binary64_1639`
6×	`exp-prod_binary64_1527` `flip3-+_binary64_1575` `flip-+_binary64_1602`
4×	`prod-exp_binary64_1524` `add-log-exp_binary64_1542` `div-inv_binary64_1578`
3×	`div-exp_binary64_1526` `pow-exp_binary64_1497` `pow-to-exp_binary64_1498`
2×	`cbrt-unprod_binary64_1546`
1×	`sqrt-pow1_binary64_1558` `pow1/2_binary64_1509` `-commutative_binary64_1645` `rem-sqrt-square_binary64_1565` `pow-prod-down_binary64_1500` `cbrt-undiv_binary64_1547` `associate-r/_binary64_1638`

Counts

4 → 164

Calls

4 calls:

85.0ms	(*.f64 (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))) (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)))
6.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
6.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
2.0ms	(sqrt.f64 PI.f64)

series1.5s (13%)

Counts

4 → 10

Calls

4 calls:

1.1s	(*.f64 (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))) (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)))
232.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
221.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)

simplify212.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	4916	8434
1	4916	8434

prune740.0ms (6.3%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	163	11	174
Fresh	5	18	23
Picked	1	0	1
Done	0	1	1
Total	169	30	199

Merged error: 0.1b

Counts

199 → 30

Compiler

Compiled 12621 to 7535 computations (40.3% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.7b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_1562` `pow-unpow_binary64_1506`
24×	`add-cube-cbrt_binary64_1548` `*-un-lft-identity_binary64_1577`
18×	`times-frac_binary64_1572`
8×	`pow1_binary64_1519` `pow-pow_binary64_1501`
6×	`exp-prod_binary64_1527` `unpow-prod-down_binary64_1508` `sqrt-prod_binary64_1556`
4×	`add-exp-log_binary64_1541` `add-log-exp_binary64_1542` `add-cbrt-cube_binary64_1549`
2×	`sqrt-pow1_binary64_1558` `sqr-pow_binary64_1609` `pow1/2_binary64_1509` `rem-sqrt-square_binary64_1565` `pow-exp_binary64_1497` `pow-to-exp_binary64_1498` `div-inv_binary64_1578`

Counts

4 → 86

Calls

4 calls:

6.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
6.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series451.0ms (3.8%)

Counts

4 → 8

Calls

4 calls:

226.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
225.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify124.0ms (1%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4887	1238
1	4887	1238

prune320.0ms (2.7%)

Pruning

33 alts after pruning (31 fresh and 2 done)

	Pruned	Kept	Total
New	89	5	94
Fresh	2	26	28
Picked	0	1	1
Done	0	1	1
Total	91	33	124

Merged error: 0.1b

Counts

124 → 33

Compiler

Compiled 6220 to 3611 computations (41.9% saved)

regimes285.0ms (2.4%)

Compiler: Compiled 3990 to 2592 computations (35% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	100
1	40	100

end0.0ms (0%)

sample3.3s (28.2%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	80	valid
105.0ms	8119×	pre	80	true
24.0ms	119×	body	80	invalid

Compiler

Compiled 2158 to 1403 computations (35% saved)

Details

analyze9.0ms (0.1%)

sample65.0ms (0.6%)

simplify238.0ms (2%)

prune10.0ms (0.1%)

localize23.0ms (0.2%)

rewrite98.0ms (0.8%)

series1.1s (9.4%)

simplify158.0ms (1.3%)

prune452.0ms (3.8%)

localize28.0ms (0.2%)

rewrite110.0ms (0.9%)

series1.5s (12.9%)

simplify156.0ms (1.3%)

prune631.0ms (5.4%)

localize30.0ms (0.3%)

rewrite107.0ms (0.9%)

series1.5s (13%)

simplify212.0ms (1.8%)

prune740.0ms (6.3%)

localize34.0ms (0.3%)

rewrite18.0ms (0.2%)

series451.0ms (3.8%)

simplify124.0ms (1%)

prune320.0ms (2.7%)

regimes285.0ms (2.4%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample3.3s (28.2%)

Profiling