Details

analyze136.0ms (2.3%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	43.7%	12.6%	6
53.1%	31.2%	15.7%	7
59.3%	18.7%	22%	8
62.4%	14%	23.5%	9
64.8%	8.6%	26.6%	10
66%	6.6%	27.4%	11
66.9%	4.1%	29%	12
67.4%	3.2%	29.4%	13
67.9%	2%	30.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample47.0ms (0.8%)

Algorithm

1×

intervals

Results

22.0ms	234×	body	128	valid
8.0ms	10×	body	1024	valid
3.0ms	8×	body	512	valid
1.0ms	4×	body	256	valid

Compiler

Compiled 19 to 19 computations (0% saved)

simplify292.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	96	14
1	96	14

prune9.0ms (0.2%)

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: 0.5b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
0.5b	(log.f64 (+.f64 1 (exp.f64 x)))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64_2436` `log-prod_binary64_2519`
4×	`add-sqr-sqrt_binary64_2457` `add-cube-cbrt_binary64_2468` `log-div_binary64_2520` `associate--l+_binary64_2375`
3×	`add-log-exp_binary64_2472` `add-exp-log_binary64_2471` `pow1_binary64_2494`
2×	`flip3-+_binary64_2439` `distribute-lft-out_binary64_2389` `flip-+_binary64_2410` `add-cbrt-cube_binary64_2469` `associate--l-_binary64_2376`
1×	`log-pow_binary64_2522` `diff-log_binary64_2525` `flip3--_binary64_2440` `rem-log-exp_binary64_2474` `flip--_binary64_2411` `sub-neg_binary64_2429`

Counts

2 → 32

Calls

2 calls:

14.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
7.0ms	(log.f64 (+.f64 1 (exp.f64 x)))

series280.0ms (4.6%)

Counts

2 → 6

Calls

2 calls:

142.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
138.0ms	(log.f64 (+.f64 1 (exp.f64 x)))

simplify221.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (197.0ms)

Iter	Nodes	Cost
0	4858	617
1	4858	617

prune74.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	34	4	38
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	35	4	39

Merged error: 0.2b

Counts

39 → 4

Compiler

Compiled 648 to 378 computations (41.7% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0b	(-.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (*.f64 x y))
1.2b	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
1.2b	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))

rewrite75.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_2436`
14×	`log-prod_binary64_2519`
12×	`sqrt-prod_binary64_2451`
10×	`add-sqr-sqrt_binary64_2457` `sqrt-div_binary64_2452`
9×	`add-cube-cbrt_binary64_2468` `pow1_binary64_2494`
8×	`log-div_binary64_2520`
7×	`add-log-exp_binary64_2472`
6×	`log-pow_binary64_2522` `add-exp-log_binary64_2471`
5×	`flip3-+_binary64_2439` `flip-+_binary64_2410`
4×	`add-cbrt-cube_binary64_2469` `associate--l-_binary64_2376`
3×	`distribute-lft-out_binary64_2389` `pow1/2_binary64_2513` `sqrt-pow1_binary64_2453`
2×	`diff-log_binary64_2525` `associate-+l-_binary64_2373` `associate-+r-_binary64_2372` `rem-log-exp_binary64_2474`
1×	`flip3--_binary64_2440` `sum-log_binary64_2524` `rem-sqrt-square_binary64_2449` `flip--_binary64_2411` `associate--l+_binary64_2375` `sub-neg_binary64_2429`

Counts

4 → 73

Calls

4 calls:

31.0ms	(-.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (*.f64 x y))
13.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
10.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
8.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

series742.0ms (12.3%)

Counts

4 → 12

Calls

4 calls:

254.0ms	(-.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (*.f64 x y))
217.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
199.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
71.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

simplify168.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (134.0ms)

Iter	Nodes	Cost
0	4870	1372
1	4870	1372

prune181.0ms (3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	85	4	89

Merged error: 0.2b

Counts

89 → 4

Compiler

Compiled 1889 to 1192 computations (36.9% saved)

localize28.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(log.f64 (+.f64 1 (exp.f64 x)))
0.5b	(log.f64 (+.f64 1 (exp.f64 x)))
0.7b	(*.f64 (log.f64 (+.f64 1 (exp.f64 x))) (log.f64 (+.f64 1 (exp.f64 x))))
10.3b	(/.f64 (-.f64 (.f64 (log.f64 (+.f64 1 (exp.f64 x))) (log.f64 (+.f64 1 (exp.f64 x)))) (.f64 (.f64 x y) (.f64 x y))) (+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y)))

rewrite85.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64_2436`
23×	`add-sqr-sqrt_binary64_2457`
21×	`add-cube-cbrt_binary64_2468`
19×	`pow1_binary64_2494`
16×	`log-prod_binary64_2519`
12×	`times-frac_binary64_2442`
10×	`add-exp-log_binary64_2471`
8×	`log-pow_binary64_2522` `add-cbrt-cube_binary64_2469`
6×	`swap-sqr_binary64_2403`
4×	`distribute-lft-out_binary64_2389` `distribute-rgt-in_binary64_2388` `associate-/l_binary64_2383` `add-log-exp_binary64_2472` `associate-r_binary64_2378` `log-div_binary64_2520` `associate-l*_binary64_2379` `distribute-lft-in_binary64_2387` `difference-of-squares_binary64_2405`
3×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/r*_binary64_2382`
2×	`associate-/r/_binary64_2384` `associate-/l/_binary64_2385` `rem-log-exp_binary64_2474`
1×	`prod-exp_binary64_2482` `cbrt-undiv_binary64_2467` `*-commutative_binary64_2369` `div-inv_binary64_2433` `pow2_binary64_2514` `pow-prod-down_binary64_2504` `div-exp_binary64_2484` `flip3--_binary64_2440` `cbrt-unprod_binary64_2466` `unswap-sqr_binary64_2404` `clear-num_binary64_2435` `pow-prod-up_binary64_2503` `div-sub_binary64_2441` `frac-2neg_binary64_2447` `pow-plus_binary64_2496` `flip--_binary64_2411` `pow-sqr_binary64_2409`

Counts

4 → 104

Calls

4 calls:

25.0ms	(/.f64 (-.f64 (.f64 (log.f64 (+.f64 1 (exp.f64 x))) (log.f64 (+.f64 1 (exp.f64 x)))) (.f64 (.f64 x y) (.f64 x y))) (+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y)))
15.0ms	(*.f64 (log.f64 (+.f64 1 (exp.f64 x))) (log.f64 (+.f64 1 (exp.f64 x))))
8.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
8.0ms	(log.f64 (+.f64 1 (exp.f64 x)))

series852.0ms (14.1%)

Counts

4 → 12

Calls

4 calls:

371.0ms	(/.f64 (-.f64 (.f64 (log.f64 (+.f64 1 (exp.f64 x))) (log.f64 (+.f64 1 (exp.f64 x)))) (.f64 (.f64 x y) (.f64 x y))) (+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y)))
196.0ms	(*.f64 (log.f64 (+.f64 1 (exp.f64 x))) (log.f64 (+.f64 1 (exp.f64 x))))
150.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
135.0ms	(log.f64 (+.f64 1 (exp.f64 x)))

simplify180.0ms (3%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	4951	2664
1	4951	2664

prune324.0ms (5.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	116	4	120

Merged error: 0.2b

Counts

120 → 4

Compiler

Compiled 3818 to 1995 computations (47.7% saved)

localize21.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (log.f64 2) (.f64 x (+.f64 1/2 (.f64 x 1/8))))
0.0b	(.f64 x (+.f64 1/2 (.f64 x 1/8)))
0.0b	(-.f64 (+.f64 (log.f64 2) (.f64 x (+.f64 1/2 (.f64 x 1/8)))) (*.f64 x y))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_2457` `add-log-exp_binary64_2472`
6×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
5×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `pow1_binary64_2494`
3×	`associate-r_binary64_2378` `associate-+l+_binary64_2371` `associate-l_binary64_2379` `log-prod_binary64_2519`
2×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `distribute-rgt-in_binary64_2388` `diff-log_binary64_2525` `associate-*r/_binary64_2380` `sum-log_binary64_2524` `associate-+r+_binary64_2370` `distribute-lft-in_binary64_2387`
1×	`prod-exp_binary64_2482` `*-commutative_binary64_2369` `pow-prod-down_binary64_2504` `flip3--_binary64_2440` `cbrt-unprod_binary64_2466` `unswap-sqr_binary64_2404` `+-commutative_binary64_2368` `flip--_binary64_2411` `associate--l+_binary64_2375` `sub-neg_binary64_2429`

Counts

3 → 51

Calls

3 calls:

13.0ms	(-.f64 (+.f64 (log.f64 2) (.f64 x (+.f64 1/2 (.f64 x 1/8)))) (*.f64 x y))
12.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/8)))
9.0ms	(+.f64 (log.f64 2) (.f64 x (+.f64 1/2 (.f64 x 1/8))))

series291.0ms (4.8%)

Counts

3 → 9

Calls

3 calls:

162.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/8)))
88.0ms	(-.f64 (+.f64 (log.f64 2) (.f64 x (+.f64 1/2 (.f64 x 1/8)))) (*.f64 x y))
41.0ms	(+.f64 (log.f64 2) (.f64 x (+.f64 1/2 (.f64 x 1/8))))

simplify121.0ms (2%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	5255	1066

prune113.0ms (1.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	59	5	64

Merged error: 0.2b

Counts

64 → 5

Compiler

Compiled 1174 to 833 computations (29% saved)

regimes82.0ms (1.4%)

Compiler: Compiled 280 to 228 computations (18.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	28
1	39	28

end0.0ms (0%)

sample1.6s (26.7%)

Algorithm

1×

intervals

Results

676.0ms	7337×	body	128	valid
161.0ms	213×	body	1024	valid
118.0ms	275×	body	512	valid
40.0ms	172×	body	256	valid
6.0ms	3×	body	2048	valid
5.0ms	48×	body	128	invalid
1.0ms	9×	body	128	overflowed

Compiler

Compiled 139 to 113 computations (18.7% saved)

Details

analyze136.0ms (2.3%)

sample47.0ms (0.8%)

simplify292.0ms (4.8%)

prune9.0ms (0.2%)

localize16.0ms (0.3%)

rewrite26.0ms (0.4%)

series280.0ms (4.6%)

simplify221.0ms (3.7%)

prune74.0ms (1.2%)

localize19.0ms (0.3%)

rewrite75.0ms (1.2%)

series742.0ms (12.3%)

simplify168.0ms (2.8%)

prune181.0ms (3%)

localize28.0ms (0.5%)

rewrite85.0ms (1.4%)

series852.0ms (14.1%)

simplify180.0ms (3%)

prune324.0ms (5.4%)

localize21.0ms (0.3%)

rewrite42.0ms (0.7%)

series291.0ms (4.8%)

simplify121.0ms (2%)

prune113.0ms (1.9%)

regimes82.0ms (1.4%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.6s (26.7%)

Profiling