Details

analyze512.0ms (5.2%)

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)

sample116.0ms (1.2%)

Algorithm

1×

intervals

Results

54.0ms	75×	body	1024	valid
23.0ms	37×	body	2048	valid
15.0ms	38×	body	512	valid
8.0ms	89×	body	128	valid
4.0ms	16×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify284.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune4.0ms (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: 50.6b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.8b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.4b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
15.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite38.0ms (0.4%)

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:

12.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
12.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
9.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series358.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

182.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
113.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
63.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify152.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	5385	862

prune126.0ms (1.3%)

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: 0.0b

Counts

52 → 4

Compiler

Compiled 830 to 550 computations (33.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
0.0b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
20.1b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite55.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2120`
15×	`associate-l_binary64_2042`
14×	`add-exp-log_binary64_2134`
11×	`add-cube-cbrt_binary64_2131` `add-log-exp_binary64_2135` `*-un-lft-identity_binary64_2099`
10×	`associate-r_binary64_2041`
8×	`unpow-prod-down_binary64_2175` `add-cbrt-cube_binary64_2132`
7×	`unswap-sqr_binary64_2067`
6×	`prod-exp_binary64_2145`
4×	`sqr-pow_binary64_2071` `pow1_binary64_2157` `cube-prod_binary64_2124`
2×	`pow-exp_binary64_2164` `*-commutative_binary64_2032` `pow-to-exp_binary64_2165` `sum-log_binary64_2187` `cbrt-unprod_binary64_2129` `diff-log_binary64_2188`
1×	`sub-neg_binary64_2092` `flip3-+_binary64_2102` `associate--l+_binary64_2038` `unpow3_binary64_2162` `+-commutative_binary64_2031` `flip3--_binary64_2103` `flip--_binary64_2074` `cube-mult_binary64_2126` `flip-+_binary64_2073`

Counts

4 → 80

Calls

4 calls:

17.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
11.0ms	(*.f64 (pow.f64 x 3) 1/6)
10.0ms	(*.f64 3/40 (pow.f64 x 5))
6.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))

series664.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

348.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
133.0ms	(*.f64 3/40 (pow.f64 x 5))
94.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
89.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify113.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4967	1201
1	4967	1201

prune196.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	91	5	96

Merged error: 0.0b

Counts

96 → 5

Compiler

Compiled 1724 to 1335 computations (22.6% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
1.7b	(log.f64 (exp.f64 (*.f64 (pow.f64 x 3) 1/6)))
24.8b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (log.f64 (exp.f64 (.f64 (pow.f64 x 3) 1/6))))

rewrite66.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_2120`
16×	`*-un-lft-identity_binary64_2099`
15×	`associate-l_binary64_2042`
14×	`add-exp-log_binary64_2134`
13×	`add-cube-cbrt_binary64_2131`
10×	`associate-r_binary64_2041`
8×	`unpow-prod-down_binary64_2175` `add-cbrt-cube_binary64_2132` `add-log-exp_binary64_2135`
7×	`unswap-sqr_binary64_2067`
6×	`log-prod_binary64_2182` `pow1_binary64_2157` `prod-exp_binary64_2145`
4×	`sqr-pow_binary64_2071` `log-pow_binary64_2185` `cube-prod_binary64_2124`
3×	`associate--r+_binary64_2037`
2×	`pow-exp_binary64_2164` `*-commutative_binary64_2032` `pow-to-exp_binary64_2165` `distribute-lft-out--_binary64_2053` `cbrt-unprod_binary64_2129` `diff-log_binary64_2188`
1×	`difference-of-squares_binary64_2068` `sub-neg_binary64_2092` `associate--l+_binary64_2038` `exp-to-pow_binary64_2158` `sum-log_binary64_2187` `unpow3_binary64_2162` `flip3--_binary64_2103` `flip--_binary64_2074` `rem-log-exp_binary64_2137` `exp-prod_binary64_2148` `cube-mult_binary64_2126`

Counts

4 → 89

Calls

4 calls:

17.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (log.f64 (exp.f64 (.f64 (pow.f64 x 3) 1/6))))
13.0ms	(*.f64 (pow.f64 x 3) 1/6)
12.0ms	(*.f64 3/40 (pow.f64 x 5))
4.0ms	(log.f64 (exp.f64 (*.f64 (pow.f64 x 3) 1/6)))

series754.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

368.0ms	(log.f64 (exp.f64 (*.f64 (pow.f64 x 3) 1/6)))
165.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (log.f64 (exp.f64 (.f64 (pow.f64 x 3) 1/6))))
122.0ms	(*.f64 3/40 (pow.f64 x 5))
99.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify124.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4866	1336
1	4866	1336

prune228.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	101	5	106

Merged error: 0.0b

Counts

106 → 5

Compiler

Compiled 2035 to 1623 computations (20.2% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 1/6)
1.7b	(log.f64 (sqrt.f64 (exp.f64 (*.f64 (pow.f64 x 3) 1/6))))
1.7b	(log.f64 (sqrt.f64 (exp.f64 (*.f64 (pow.f64 x 3) 1/6))))
24.8b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (log.f64 (sqrt.f64 (exp.f64 (.f64 (pow.f64 x 3) 1/6)))))

rewrite65.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2120`
18×	`log-prod_binary64_2182`
17×	`*-un-lft-identity_binary64_2099`
14×	`add-cube-cbrt_binary64_2131`
12×	`associate-l_binary64_2042`
11×	`log-pow_binary64_2185` `add-exp-log_binary64_2134`
9×	`pow1_binary64_2157` `add-log-exp_binary64_2135` `sqrt-prod_binary64_2114`
6×	`add-cbrt-cube_binary64_2132` `associate--r+_binary64_2037` `sqrt-pow1_binary64_2116`
4×	`unpow-prod-down_binary64_2175` `cube-prod_binary64_2124` `unswap-sqr_binary64_2067`
3×	`prod-exp_binary64_2145` `associate-r_binary64_2041`
2×	`sqr-pow_binary64_2071` `exp-to-pow_binary64_2158` `pow1/2_binary64_2176` `rem-log-exp_binary64_2137` `exp-prod_binary64_2148` `distribute-lft-out--_binary64_2053` `diff-log_binary64_2188`
1×	`difference-of-squares_binary64_2068` `sub-neg_binary64_2092` `associate--l+_binary64_2038` `pow-exp_binary64_2164` `*-commutative_binary64_2032` `pow-to-exp_binary64_2165` `sum-log_binary64_2187` `unpow3_binary64_2162` `flip3--_binary64_2103` `flip--_binary64_2074` `cube-mult_binary64_2126` `cbrt-unprod_binary64_2129`

Counts

4 → 91

Calls

4 calls:

20.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (log.f64 (sqrt.f64 (exp.f64 (.f64 (pow.f64 x 3) 1/6)))))
13.0ms	(*.f64 (pow.f64 x 3) 1/6)
5.0ms	(log.f64 (sqrt.f64 (exp.f64 (*.f64 (pow.f64 x 3) 1/6))))
5.0ms	(log.f64 (sqrt.f64 (exp.f64 (*.f64 (pow.f64 x 3) 1/6))))

series1.1s (11.3%)

Counts

4 → 12

Calls

4 calls:

446.0ms	(log.f64 (sqrt.f64 (exp.f64 (*.f64 (pow.f64 x 3) 1/6))))
379.0ms	(log.f64 (sqrt.f64 (exp.f64 (*.f64 (pow.f64 x 3) 1/6))))
180.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (log.f64 (sqrt.f64 (exp.f64 (.f64 (pow.f64 x 3) 1/6)))))
102.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify149.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4904	1656
1	4904	1656

prune353.0ms (3.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	103	5	108

Merged error: 0.0b

Counts

108 → 5

Compiler

Compiled 3079 to 2581 computations (16.2% saved)

regimes54.0ms (0.6%)

Compiler: Compiled 99 to 81 computations (18.2% saved)

bsearch67.0ms (0.7%)

Steps

Iters	Range		Point
8	0.4083067443185698	831.0480905311955	0.9498214140747597
8	-3.2608973828814465	-0.0004011308616725907	-1.083119750808268

Compiler

Compiled 1 to 1 computations (0% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample4.1s (42.1%)

Algorithm

1×

intervals

Results

1.8s	2592×	body	1024	valid
748.0ms	1188×	body	2048	valid
478.0ms	1210×	body	512	valid
200.0ms	2325×	body	128	valid
137.0ms	636×	body	256	valid
44.0ms	49×	body	4096	valid

Compiler

Compiled 182 to 145 computations (20.3% saved)

Details

analyze512.0ms (5.2%)

sample116.0ms (1.2%)

simplify284.0ms (2.9%)

prune4.0ms (0%)

localize13.0ms (0.1%)

rewrite38.0ms (0.4%)

series358.0ms (3.7%)

simplify152.0ms (1.5%)

prune126.0ms (1.3%)

localize19.0ms (0.2%)

rewrite55.0ms (0.6%)

series664.0ms (6.8%)

simplify113.0ms (1.1%)

prune196.0ms (2%)

localize25.0ms (0.3%)

rewrite66.0ms (0.7%)

series754.0ms (7.7%)

simplify124.0ms (1.3%)

prune228.0ms (2.3%)

localize32.0ms (0.3%)

rewrite65.0ms (0.7%)

series1.1s (11.3%)

simplify149.0ms (1.5%)

prune353.0ms (3.6%)

regimes54.0ms (0.6%)

bsearch67.0ms (0.7%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample4.1s (42.1%)

Profiling