Details

analyze449.0ms (9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample70.0ms (1.4%)

Algorithm

1×

intervals

Results

35.0ms	87×	body	1024	valid
15.0ms	46×	body	2048	valid
8.0ms	36×	body	512	valid
3.0ms	70×	body	128	valid
2.0ms	16×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify162.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

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: 53.0b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.4b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.2b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
15.7b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_2436`
6×	`add-sqr-sqrt_binary64_2457`
5×	`add-log-exp_binary64_2472` `add-cube-cbrt_binary64_2468` `pow1_binary64_2494`
4×	`add-exp-log_binary64_2471` `log-prod_binary64_2519`
3×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `add-cbrt-cube_binary64_2469` `sqrt-prod_binary64_2451`
2×	`distribute-lft-out_binary64_2389` `log-div_binary64_2520` `sqrt-div_binary64_2452`
1×	`log-pow_binary64_2522` `pow1/2_binary64_2513` `sum-log_binary64_2524` `rem-sqrt-square_binary64_2449` `+-commutative_binary64_2368` `rem-log-exp_binary64_2474` `sqrt-pow1_binary64_2453`

Counts

3 → 42

Calls

3 calls:

7.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
7.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series177.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

93.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
49.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
35.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify85.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5385	862

prune68.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	5	52

Merged error: 0.0b

Counts

52 → 5

Compiler

Compiled 833 to 553 computations (33.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
20.9b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2457`
15×	`associate-l_binary64_2379`
14×	`add-exp-log_binary64_2471`
11×	`add-log-exp_binary64_2472` `add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
10×	`associate-r_binary64_2378`
8×	`unpow-prod-down_binary64_2512` `add-cbrt-cube_binary64_2469`
7×	`unswap-sqr_binary64_2404`
6×	`prod-exp_binary64_2482`
4×	`cube-prod_binary64_2461` `sqr-pow_binary64_2408` `pow1_binary64_2494`
2×	`*-commutative_binary64_2369` `diff-log_binary64_2525` `sum-log_binary64_2524` `cbrt-unprod_binary64_2466` `pow-to-exp_binary64_2502` `pow-exp_binary64_2501`
1×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `flip3--_binary64_2440` `cube-mult_binary64_2463` `unpow3_binary64_2499` `+-commutative_binary64_2368` `flip--_binary64_2411` `associate--l+_binary64_2375` `sub-neg_binary64_2429`

Counts

4 → 80

Calls

4 calls:

7.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
6.0ms	(*.f64 3/40 (pow.f64 x 5))
3.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))

series334.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

167.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
65.0ms	(*.f64 3/40 (pow.f64 x 5))
57.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
45.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify61.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4967	1201
1	4967	1201

prune96.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	92	5	97

Merged error: 0.0b

Counts

97 → 5

Compiler

Compiled 1712 to 1325 computations (22.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/16 (pow.f64 x 5))
0.4b	(/.f64 1/8 (pow.f64 x 3))
12.2b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
21.5b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite117.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_2457`
71×	`times-frac_binary64_2442`
68×	`*-un-lft-identity_binary64_2436`
46×	`add-cube-cbrt_binary64_2468`
26×	`unpow-prod-down_binary64_2512`
19×	`associate-/r*_binary64_2382`
15×	`add-exp-log_binary64_2471`
14×	`cube-prod_binary64_2461`
11×	`log-prod_binary64_2519`
10×	`sqr-pow_binary64_2408` `difference-of-squares_binary64_2405`
9×	`add-log-exp_binary64_2472`
8×	`add-cbrt-cube_binary64_2469`
6×	`distribute-lft-out--_binary64_2390` `frac-sub_binary64_2445` `associate-/l*_binary64_2383` `div-exp_binary64_2484`
5×	`log-div_binary64_2520` `pow1_binary64_2494`
4×	`distribute-lft-out_binary64_2389` `cube-mult_binary64_2463` `unpow3_binary64_2499`
2×	`flip3-+_binary64_2439` `cbrt-undiv_binary64_2467` `flip-+_binary64_2410` `div-inv_binary64_2433` `diff-log_binary64_2525` `frac-add_binary64_2444` `flip3--_binary64_2440` `pow-to-exp_binary64_2502` `clear-num_binary64_2435` `pow-exp_binary64_2501` `frac-2neg_binary64_2447` `flip--_binary64_2411`
1×	`associate--r+_binary64_2374` `log-pow_binary64_2522` `sum-log_binary64_2524` `rem-log-exp_binary64_2474` `sub-neg_binary64_2429`

Counts

4 → 159

Calls

4 calls:

45.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
44.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
6.0ms	(/.f64 1/8 (pow.f64 x 3))
5.0ms	(/.f64 1/16 (pow.f64 x 5))

series238.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
60.0ms	(/.f64 1/16 (pow.f64 x 5))
50.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
50.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4929	3605
1	4929	3605

prune248.0ms (4.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	171	5	176

Merged error: 0.0b

Counts

176 → 5

Compiler

Compiled 4114 to 3270 computations (20.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 1/2 x))
0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.4b	(/.f64 1/8 (pow.f64 x 3))
11.4b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite78.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64_2436`
36×	`times-frac_binary64_2442`
30×	`add-sqr-sqrt_binary64_2457` `add-cube-cbrt_binary64_2468`
15×	`add-log-exp_binary64_2472`
12×	`unpow-prod-down_binary64_2512` `cube-prod_binary64_2461` `associate-/r*_binary64_2382`
10×	`add-exp-log_binary64_2471`
9×	`distribute-lft-out_binary64_2389`
6×	`add-cbrt-cube_binary64_2469` `log-prod_binary64_2519`
5×	`sum-log_binary64_2524` `pow1_binary64_2494`
4×	`distribute-lft-out--_binary64_2390` `cube-mult_binary64_2463` `unpow3_binary64_2499` `sqr-pow_binary64_2408`
3×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/l*_binary64_2383` `div-exp_binary64_2484`
2×	`diff-log_binary64_2525` `associate-+r+_binary64_2370` `log-div_binary64_2520` `+-commutative_binary64_2368`
1×	`cbrt-undiv_binary64_2467` `log-pow_binary64_2522` `div-inv_binary64_2433` `associate-+r-_binary64_2372` `pow-to-exp_binary64_2502` `clear-num_binary64_2435` `pow-exp_binary64_2501` `frac-2neg_binary64_2447` `rem-log-exp_binary64_2474` `associate--l+_binary64_2375` `sub-neg_binary64_2429`

Counts

4 → 113

Calls

4 calls:

29.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
26.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
6.0ms	(+.f64 x (/.f64 1/2 x))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

series225.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
55.0ms	(+.f64 x (/.f64 1/2 x))
51.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
45.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify45.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4955	2077
1	4955	2077

prune131.0ms (2.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	125	5	130

Merged error: 0.0b

Counts

130 → 5

Compiler

Compiled 2462 to 1759 computations (28.6% saved)

regimes47.0ms (0.9%)

Compiler: Compiled 168 to 134 computations (20.2% saved)

bsearch35.0ms (0.7%)

Steps

Iters	Range		Point
8	0.01563332148347837	11.235691960663045	0.948177599351215
9	-3.997572220062307	-2.5253607039033134e-09	-1.0536742239209531

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample2.2s (43.5%)

Algorithm

1×

intervals

Results

947.0ms	2483×	body	1024	valid
415.0ms	1215×	body	2048	valid
271.0ms	1272×	body	512	valid
111.0ms	2363×	body	128	valid
71.0ms	620×	body	256	valid
22.0ms	47×	body	4096	valid

Compiler

Compiled 160 to 126 computations (21.3% saved)

Details

analyze449.0ms (9%)

sample70.0ms (1.4%)

simplify162.0ms (3.2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite23.0ms (0.5%)

series177.0ms (3.5%)

simplify85.0ms (1.7%)

prune68.0ms (1.4%)

localize9.0ms (0.2%)

rewrite36.0ms (0.7%)

series334.0ms (6.7%)

simplify61.0ms (1.2%)

prune96.0ms (1.9%)

localize12.0ms (0.2%)

rewrite117.0ms (2.3%)

series238.0ms (4.7%)

simplify62.0ms (1.2%)

prune248.0ms (4.9%)

localize10.0ms (0.2%)

rewrite78.0ms (1.6%)

series225.0ms (4.5%)

simplify45.0ms (0.9%)

prune131.0ms (2.6%)

regimes47.0ms (0.9%)

bsearch35.0ms (0.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.2s (43.5%)

Profiling