Details

analyze269.0ms (5.9%)

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 (1.5%)

Algorithm

1×

intervals

Results

36.0ms	86×	body	1024	valid
15.0ms	45×	body	2048	valid
6.0ms	33×	body	512	valid
3.0ms	70×	body	128	valid
2.0ms	21×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify160.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune2.0ms (0.1%)

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: 53.9b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.8b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.2b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
15.9b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_2099`
6×	`add-sqr-sqrt_binary64_2120`
5×	`add-cube-cbrt_binary64_2131` `pow1_binary64_2157` `add-log-exp_binary64_2135`
4×	`log-prod_binary64_2182` `add-exp-log_binary64_2134`
3×	`flip3-+_binary64_2102` `add-cbrt-cube_binary64_2132` `flip-+_binary64_2073` `sqrt-prod_binary64_2114`
2×	`distribute-lft-out_binary64_2052` `log-div_binary64_2183` `sqrt-div_binary64_2115`
1×	`log-pow_binary64_2185` `sum-log_binary64_2187` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `+-commutative_binary64_2031` `rem-log-exp_binary64_2137` `sqrt-pow1_binary64_2116`

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)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series190.0ms (4.1%)

Counts

3 → 9

Calls

3 calls:

98.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
57.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
34.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify83.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5385	862

prune68.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0b

Counts

52 → 4

Compiler

Compiled 812 to 538 computations (33.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 3/40 (pow.f64 x 5))
0.3b	(*.f64 (pow.f64 x 3) 1/6)
20.6b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_2120`
15×	`associate-l_binary64_2042`
13×	`add-exp-log_binary64_2134`
10×	`add-cube-cbrt_binary64_2131` `-un-lft-identity_binary64_2099` `associate-r*_binary64_2041`
8×	`unpow-prod-down_binary64_2175` `add-log-exp_binary64_2135`
7×	`add-cbrt-cube_binary64_2132` `unswap-sqr_binary64_2067`
6×	`prod-exp_binary64_2145`
4×	`sqr-pow_binary64_2071` `cube-prod_binary64_2124`
3×	`pow1_binary64_2157`
2×	`pow-exp_binary64_2164` `*-commutative_binary64_2032` `pow-to-exp_binary64_2165` `cbrt-unprod_binary64_2129` `diff-log_binary64_2188`
1×	`sub-neg_binary64_2092` `associate--l+_binary64_2038` `sum-log_binary64_2187` `unpow3_binary64_2162` `flip3--_binary64_2103` `flip--_binary64_2074` `cube-mult_binary64_2126`

Counts

3 → 69

Calls

3 calls:

6.0ms	(-.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))

series163.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

58.0ms	(*.f64 3/40 (pow.f64 x 5))
54.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
51.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify73.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4845	999
1	4845	999

prune83.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	78	4	82

Merged error: 0b

Counts

82 → 4

Compiler

Compiled 1437 to 1113 computations (22.5% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/16 (pow.f64 x 5))
0.3b	(/.f64 1/8 (pow.f64 x 3))
9.2b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
21.4b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite112.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_2120`
71×	`times-frac_binary64_2105`
68×	`*-un-lft-identity_binary64_2099`
46×	`add-cube-cbrt_binary64_2131`
26×	`unpow-prod-down_binary64_2175`
19×	`associate-/r*_binary64_2045`
15×	`add-exp-log_binary64_2134`
14×	`cube-prod_binary64_2124`
11×	`log-prod_binary64_2182`
10×	`sqr-pow_binary64_2071` `difference-of-squares_binary64_2068`
9×	`add-log-exp_binary64_2135`
8×	`add-cbrt-cube_binary64_2132`
6×	`frac-sub_binary64_2108` `div-exp_binary64_2147` `associate-/l*_binary64_2046` `distribute-lft-out--_binary64_2053`
5×	`log-div_binary64_2183` `pow1_binary64_2157`
4×	`distribute-lft-out_binary64_2052` `unpow3_binary64_2162` `cube-mult_binary64_2126`
2×	`cbrt-undiv_binary64_2130` `flip3-+_binary64_2102` `pow-exp_binary64_2164` `pow-to-exp_binary64_2165` `frac-2neg_binary64_2110` `flip3--_binary64_2103` `flip--_binary64_2074` `clear-num_binary64_2098` `div-inv_binary64_2096` `flip-+_binary64_2073` `diff-log_binary64_2188` `frac-add_binary64_2107`
1×	`sub-neg_binary64_2092` `log-pow_binary64_2185` `sum-log_binary64_2187` `associate--r+_binary64_2037` `rem-log-exp_binary64_2137`

Counts

4 → 159

Calls

4 calls:

43.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
42.0ms	(-.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))

series237.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
56.0ms	(/.f64 1/8 (pow.f64 x 3))
56.0ms	(/.f64 1/16 (pow.f64 x 5))
47.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4929	3605
1	4929	3605

prune262.0ms (5.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	171	4	175

Merged error: 0b

Counts

175 → 4

Compiler

Compiled 4093 to 3255 computations (20.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.3b	(/.f64 1/8 (pow.f64 x 3))
8.0b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite67.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_2099`
36×	`times-frac_binary64_2105`
29×	`add-sqr-sqrt_binary64_2120` `add-cube-cbrt_binary64_2131`
12×	`unpow-prod-down_binary64_2175` `cube-prod_binary64_2124` `add-log-exp_binary64_2135` `associate-/r*_binary64_2045`
9×	`add-exp-log_binary64_2134`
8×	`distribute-lft-out_binary64_2052`
6×	`log-prod_binary64_2182`
5×	`add-cbrt-cube_binary64_2132`
4×	`sqr-pow_binary64_2071` `pow1_binary64_2157` `sum-log_binary64_2187` `unpow3_binary64_2162` `distribute-lft-out--_binary64_2053` `cube-mult_binary64_2126`
3×	`div-exp_binary64_2147` `associate-/l*_binary64_2046`
2×	`flip3-+_binary64_2102` `log-div_binary64_2183` `flip-+_binary64_2073` `associate-+r+_binary64_2033` `diff-log_binary64_2188`
1×	`sub-neg_binary64_2092` `cbrt-undiv_binary64_2130` `associate--l+_binary64_2038` `log-pow_binary64_2185` `pow-exp_binary64_2164` `pow-to-exp_binary64_2165` `frac-2neg_binary64_2110` `+-commutative_binary64_2031` `rem-log-exp_binary64_2137` `clear-num_binary64_2098` `associate-+r-_binary64_2035` `div-inv_binary64_2096`

Counts

3 → 101

Calls

3 calls:

25.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
24.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
8.0ms	(/.f64 1/8 (pow.f64 x 3))

series161.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

67.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
48.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
46.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify74.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4927	1914
1	4927	1914

prune117.0ms (2.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	110	4	114

Merged error: 0b

Counts

114 → 4

Compiler

Compiled 2189 to 1606 computations (26.6% saved)

regimes23.0ms (0.5%)

Compiler: Compiled 56 to 47 computations (16.1% saved)

bsearch44.0ms (1%)

Steps

Iters	Range		Point
11	1.169618262283517e-20	235.0181740853703	0.964660585450246
10	-7.846889230034133	-1.073109143245617e-11	-1.0503381756509498

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample2.2s (47.3%)

Algorithm

1×

intervals

Results

969.0ms	2523×	body	1024	valid
413.0ms	1224×	body	2048	valid
268.0ms	1259×	body	512	valid
111.0ms	2382×	body	128	valid
67.0ms	577×	body	256	valid
16.0ms	35×	body	4096	valid

Compiler

Compiled 139 to 111 computations (20.1% saved)

Details

analyze269.0ms (5.9%)

sample70.0ms (1.5%)

simplify160.0ms (3.5%)

prune2.0ms (0.1%)

localize6.0ms (0.1%)

rewrite25.0ms (0.6%)

series190.0ms (4.1%)

simplify83.0ms (1.8%)

prune68.0ms (1.5%)

localize9.0ms (0.2%)

rewrite24.0ms (0.5%)

series163.0ms (3.6%)

simplify73.0ms (1.6%)

prune83.0ms (1.8%)

localize14.0ms (0.3%)

rewrite112.0ms (2.4%)

series237.0ms (5.2%)

simplify63.0ms (1.4%)

prune262.0ms (5.7%)

localize9.0ms (0.2%)

rewrite67.0ms (1.5%)

series161.0ms (3.5%)

simplify74.0ms (1.6%)

prune117.0ms (2.6%)

regimes23.0ms (0.5%)

bsearch44.0ms (1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.2s (47.3%)

Profiling