Details

analyze48.0ms (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)

sample39.0ms (1%)

Algorithm

1×

intervals

Results

15.0ms	48×	body	2048	valid
9.0ms	59×	body	1024	valid
4.0ms	46×	body	512	valid
2.0ms	91×	body	128	valid
1.0ms	12×	body	256	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify63.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5029	9

prune2.0ms (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: 30.0b

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))
1.8b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
3×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
2×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-sqr-1_binary64` `rem-exp-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

2 → 28

Calls

2 calls:

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

series72.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

49.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
23.0ms	(exp.f64 (*.f64 a x))

simplify48.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5006	377

prune72.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	28	6	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	7	35

Merged error: 3.8b

Counts

35 → 7

Compiler

Compiled 840 to 580 computations (31% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
5.3b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
7.2b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
7.5b	(+.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`
13×	`add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `prod-exp_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64`
4×	`associate-*r/_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64`
1×	`pow-to-exp_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 74

Calls

4 calls:

10.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
7.0ms	(+.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)))))))

series506.0ms (12.9%)

Counts

4 → 12

Calls

4 calls:

183.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
165.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
80.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
77.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify59.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4991	1832
1	4991	1832

prune161.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	84	9	93

Merged error: 1.7b

Counts

93 → 9

Compiler

Compiled 3100 to 1989 computations (35.8% 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)))
4.1b	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
5.3b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite48.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
17×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
12×	`associate-*r/_binary64` `add-sqr-sqrt_binary64`
10×	`associate-l_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-r_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`unswap-sqr_binary64`

Counts

4 → 102

Calls

4 calls:

13.0ms	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
11.0ms	(.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)))
4.0ms	(*.f64 x 1/6)

series380.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
140.0ms	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
70.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
20.0ms	(*.f64 x 1/6)

simplify45.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5104	2104

prune120.0ms (3.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	114	9	123

Merged error: 1.7b

Counts

123 → 9

Compiler

Compiled 2839 to 1541 computations (45.7% saved)

localize13.0ms (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)))
1.2b	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
5.3b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
11×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
10×	`-un-lft-identity_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
8×	`associate-*r/_binary64`
6×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
3×	`flip3-+_binary64` `unswap-sqr_binary64` `flip-+_binary64`

Counts

4 → 90

Calls

4 calls:

11.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
8.0ms	(.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)

series412.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

173.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
148.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
69.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
22.0ms	(*.f64 x 1/6)

simplify44.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5685	1933

prune113.0ms (2.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	102	9	111

Merged error: 1.7b

Counts

111 → 9

Compiler

Compiled 2569 to 1505 computations (41.4% saved)

regimes187.0ms (4.8%)

Compiler: Compiled 964 to 750 computations (22.2% 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	43
1	39	43

end0.0ms (0%)

sample1.4s (35.2%)

Algorithm

1×

intervals

Results

470.0ms	1442×	body	2048	valid
275.0ms	1725×	body	1024	valid
113.0ms	1143×	body	512	valid
88.0ms	3049×	body	128	valid
40.0ms	641×	body	256	valid
5.0ms	158×	body	128	invalid

Compiler

Compiled 225 to 163 computations (27.6% saved)

Details

analyze48.0ms (1.2%)

sample39.0ms (1%)

simplify63.0ms (1.6%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite8.0ms (0.2%)

series72.0ms (1.8%)

simplify48.0ms (1.2%)

prune72.0ms (1.8%)

localize12.0ms (0.3%)

rewrite40.0ms (1%)

series506.0ms (12.9%)

simplify59.0ms (1.5%)

prune161.0ms (4.1%)

localize11.0ms (0.3%)

rewrite48.0ms (1.2%)

series380.0ms (9.7%)

simplify45.0ms (1.1%)

prune120.0ms (3.1%)

localize13.0ms (0.3%)

rewrite39.0ms (1%)

series412.0ms (10.5%)

simplify44.0ms (1.1%)

prune113.0ms (2.9%)

regimes187.0ms (4.8%)

bsearch1.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.4s (35.2%)

Profiling