Details

analyze47.0ms (1.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 7 to 7 computations (0% saved)

sample40.0ms (1%)

Algorithm

1×

intervals

Results

17.0ms	48×	body	2048	valid
9.0ms	53×	body	1024	valid
4.0ms	39×	body	512	valid
3.0ms	97×	body	128	valid
1.0ms	19×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify236.0ms (5.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5029	9

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: 29.4b

Counts

2 → 1

Compiler

Compiled 12 to 12 computations (0% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
3.9b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64_1477`
6×	`add-log-exp_binary64_1494` `*-un-lft-identity_binary64_1455`
3×	`add-cube-cbrt_binary64_1490` `cancel-sign-sub-inv_binary64_1421`
2×	`pow1_binary64_1516` `difference-of-squares_binary64_1424` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
1×	`distribute-lft-out--_binary64_1407` `flip--_binary64_1430` `diff-log_binary64_1547` `exp-prod_binary64_1507` `sub-neg_binary64_1448` `rem-exp-log_binary64_1495` `exp-to-pow_binary64_1517` `flip3--_binary64_1459` `difference-of-sqr-1_binary64_1425`

Counts

2 → 28

Calls

2 calls:

5.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
2.0ms	(exp.f64 (*.f64 a x))

series70.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

46.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
23.0ms	(exp.f64 (*.f64 a x))

simplify49.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5005	377

prune90.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	28	6	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	6	35

Merged error: 3.7b

Counts

35 → 6

Compiler

Compiled 1210 to 803 computations (33.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.7b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
5.7b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
6.6b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
10.1b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite40.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_1493`
13×	`add-sqr-sqrt_binary64_1477` `add-cbrt-cube_binary64_1491`
10×	`pow1_binary64_1516`
9×	`prod-exp_binary64_1504` `add-cube-cbrt_binary64_1490` `associate-l_binary64_1396` `*-un-lft-identity_binary64_1455`
7×	`associate-r_binary64_1395`
6×	`add-log-exp_binary64_1494`
5×	`cbrt-unprod_binary64_1488`
4×	`associate-*r/_binary64_1397`
3×	`flip-+_binary64_1429` `*-commutative_binary64_1386` `flip3-+_binary64_1458` `pow-prod-down_binary64_1526`
2×	`distribute-rgt-in_binary64_1405` `distribute-lft-in_binary64_1404` `unswap-sqr_binary64_1423`
1×	`pow-to-exp_binary64_1524` `pow-exp_binary64_1523` `sum-log_binary64_1546` `+-commutative_binary64_1385`

Counts

4 → 74

Calls

4 calls:

11.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
8.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
7.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
6.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))

series532.0ms (13.3%)

Counts

4 → 12

Calls

4 calls:

190.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
174.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
85.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
84.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify60.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4991	1832
1	4991	1832

prune276.0ms (6.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	84	8	92

Merged error: 2.3b

Counts

92 → 8

Compiler

Compiled 3007 to 1864 computations (38% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 x 1/6)
0.6b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
1.7b	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
6.6b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
15×	`add-sqr-sqrt_binary64_1477`
11×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488` `pow-prod-down_binary64_1526`
10×	`associate-r_binary64_1395` `add-cube-cbrt_binary64_1490` `associate-l_binary64_1396` `*-un-lft-identity_binary64_1455`
8×	`associate-*r/_binary64_1397`
6×	`distribute-rgt-in_binary64_1405` `distribute-lft-in_binary64_1404`
4×	`add-log-exp_binary64_1494` `*-commutative_binary64_1386`
3×	`flip-+_binary64_1429` `flip3-+_binary64_1458` `unswap-sqr_binary64_1423`

Counts

4 → 90

Calls

4 calls:

12.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
9.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
7.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
4.0ms	(*.f64 x 1/6)

series407.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
149.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
67.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
21.0ms	(*.f64 x 1/6)

simplify45.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5686	1933

prune106.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	102	8	110

Merged error: 2.3b

Counts

110 → 8

Compiler

Compiled 2466 to 1432 computations (41.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 (*.f64 a x)) 2)
0.0b	(exp.f64 (*.f64 a x))
0.0b	(exp.f64 (*.f64 a x))
3.9b	(+.f64 (pow.f64 (exp.f64 (*.f64 a x)) 2) -1)

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-log-exp_binary64_1494`
8×	`add-sqr-sqrt_binary64_1477` `*-un-lft-identity_binary64_1455`
6×	`add-cube-cbrt_binary64_1490`
5×	`pow1_binary64_1516`
4×	`difference-of-sqr--1_binary64_1426` `unpow-prod-down_binary64_1534` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
3×	`pow-pow_binary64_1527` `exp-prod_binary64_1507` `exp-to-pow_binary64_1517` `pow-unpow_binary64_1532`
2×	`unpow2_binary64_1520` `sqr-pow_binary64_1427` `rem-exp-log_binary64_1495`
1×	`distribute-lft-out_binary64_1406` `flip-+_binary64_1429` `pow-to-exp_binary64_1524` `flip3-+_binary64_1458` `pow-exp_binary64_1523` `sum-log_binary64_1546` `+-commutative_binary64_1385`

Counts

4 → 56

Calls

4 calls:

7.0ms	(+.f64 (pow.f64 (exp.f64 (*.f64 a x)) 2) -1)
4.0ms	(pow.f64 (exp.f64 (*.f64 a x)) 2)
2.0ms	(exp.f64 (*.f64 a x))
2.0ms	(exp.f64 (*.f64 a x))

series158.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(+.f64 (pow.f64 (exp.f64 (*.f64 a x)) 2) -1)
40.0ms	(pow.f64 (exp.f64 (*.f64 a x)) 2)
22.0ms	(exp.f64 (*.f64 a x))
22.0ms	(exp.f64 (*.f64 a x))

simplify86.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4974	738
1	4974	738

prune96.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	68	8	76

Merged error: 2.3b

Counts

76 → 8

Compiler

Compiled 1929 to 1070 computations (44.5% saved)

regimes159.0ms (4%)

Compiler: Compiled 1093 to 769 computations (29.6% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	61
1	39	61

end0.0ms (0%)

sample1.4s (35%)

Algorithm

1×

intervals

Results

491.0ms	1483×	body	2048	valid
281.0ms	1701×	body	1024	valid
110.0ms	1093×	body	512	valid
87.0ms	3111×	body	128	valid
36.0ms	612×	body	256	valid
4.0ms	145×	body	128	invalid

Compiler

Compiled 254 to 176 computations (30.7% saved)

Details

analyze47.0ms (1.2%)

sample40.0ms (1%)

simplify236.0ms (5.9%)

prune2.0ms (0%)

localize4.0ms (0.1%)

rewrite9.0ms (0.2%)

series70.0ms (1.7%)

simplify49.0ms (1.2%)

prune90.0ms (2.2%)

localize13.0ms (0.3%)

rewrite40.0ms (1%)

series532.0ms (13.3%)

simplify60.0ms (1.5%)

prune276.0ms (6.9%)

localize11.0ms (0.3%)

rewrite41.0ms (1%)

series407.0ms (10.1%)

simplify45.0ms (1.1%)

prune106.0ms (2.6%)

localize9.0ms (0.2%)

rewrite18.0ms (0.5%)

series158.0ms (3.9%)

simplify86.0ms (2.2%)

prune96.0ms (2.4%)

regimes159.0ms (4%)

bsearch1.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.4s (35%)

Profiling