Details

analyze888.0ms (16.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	52
1	67	52
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample40.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	186×	body	128	valid
6.0ms	23×	body	2048	valid
5.0ms	256×	pre	128	true
4.0ms	18×	body	1024	valid
4.0ms	11×	body	4096	valid
2.0ms	13×	body	512	valid
1.0ms	5×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.5b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize18.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b

(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))))

1.0b

(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))

15.9b

(sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64_1844`
6×	`*-un-lft-identity_binary64_1783`
5×	`add-sqr-sqrt_binary64_1805` `add-log-exp_binary64_1822`
4×	`add-cube-cbrt_binary64_1818` `sqrt-prod_binary64_1799` `sqrt-div_binary64_1800`
3×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `flip-+_binary64_1757` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801`
2×	`associate-*r/_binary64_1725` `pow1/2_binary64_1863`
1×	`+-commutative_binary64_1713` `distribute-lft-out_binary64_1734` `sum-log_binary64_1874` `pow-prod-down_binary64_1854` `rem-sqrt-square_binary64_1796`

Counts

3 → 40

Calls

3 calls:

13.0ms

(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))))

13.0ms

(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))

5.0ms

(sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))

series178.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

106.0ms

(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))))

44.0ms

(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))

28.0ms

(sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))

simplify114.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4827	1041
1	4827	1041

prune82.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	40	9	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	9	50

Merged error: 14.2b

Counts

50 → 9

Compiler

Compiled 1319 to 901 computations (31.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))
1.0b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
1.1b	(log.f64 (exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
15.9b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite51.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_1783`
9×	`add-sqr-sqrt_binary64_1805` `add-log-exp_binary64_1822`
8×	`add-cube-cbrt_binary64_1818` `exp-prod_binary64_1835`
6×	`pow1_binary64_1844`
5×	`log-pow_binary64_1872`
4×	`add-cbrt-cube_binary64_1819` `log-prod_binary64_1869` `add-exp-log_binary64_1821`
3×	`distribute-lft-out_binary64_1734` `sqrt-prod_binary64_1799`
2×	`rem-exp-log_binary64_1823` `exp-sum_binary64_1829` `flip-+_binary64_1757` `sqrt-div_binary64_1800` `sum-log_binary64_1874` `flip3-+_binary64_1786`
1×	`+-commutative_binary64_1713` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `rem-log-exp_binary64_1824`

Counts

4 → 58

Calls

4 calls:

14.0ms	(log.f64 (exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
13.0ms	(exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))
13.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series192.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(log.f64 (exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
58.0ms	(exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))
40.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
29.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5256	1392

prune105.0ms (1.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	68	11	79

Merged error: 14.2b

Counts

79 → 11

Compiler

Compiled 1948 to 1366 computations (29.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 1/2 (log.f64 (.f64 E.f64 (exp.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))))))))
0.2b	(.f64 E.f64 (exp.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))))
1.1b	(log.f64 (.f64 E.f64 (exp.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))))
15.9b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

rewrite56.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`pow1_binary64_1844`
10×	`add-sqr-sqrt_binary64_1805`
7×	`add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`add-cbrt-cube_binary64_1819`
4×	`prod-exp_binary64_1832` `sqrt-prod_binary64_1799` `add-log-exp_binary64_1822`
3×	`associate-l_binary64_1724` `sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854` `rem-log-exp_binary64_1824` `associate-r_binary64_1723`
2×	`log-pow_binary64_1872` `pow1/2_binary64_1863` `e-exp-1_binary64_1828` `sqrt-div_binary64_1800`
1×	`log-prod_binary64_1869` `cbrt-unprod_binary64_1816` `flip-+_binary64_1757` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `unswap-sqr_binary64_1751` `rem-sqrt-square_binary64_1796`

Counts

4 → 58

Calls

4 calls:

16.0ms	(.f64 E.f64 (exp.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))))
15.0ms	(sqrt.f64 (.f64 1/2 (log.f64 (.f64 E.f64 (exp.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))))))))
15.0ms	(log.f64 (.f64 E.f64 (exp.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

series301.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(sqrt.f64 (.f64 1/2 (log.f64 (.f64 E.f64 (exp.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))))))))
78.0ms	(log.f64 (.f64 E.f64 (exp.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))))
60.0ms	(.f64 E.f64 (exp.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))))
28.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

simplify109.0ms (2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4721	1335
1	4721	1335

prune94.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	72	9	81

Merged error: 14.2b

Counts

81 → 9

Compiler

Compiled 1819 to 1241 computations (31.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
9.8b	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
15.9b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
15.9b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite63.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`sqrt-prod_binary64_1799`
58×	`add-sqr-sqrt_binary64_1805`
34×	`sqrt-pow1_binary64_1801`
29×	`pow1_binary64_1844`
28×	`sqrt-div_binary64_1800`
20×	`*-un-lft-identity_binary64_1783`
18×	`add-cube-cbrt_binary64_1818` `pow1/2_binary64_1863`
15×	`swap-sqr_binary64_1750`
10×	`rem-sqrt-square_binary64_1796`
9×	`flip-+_binary64_1757` `pow-prod-up_binary64_1853` `associate-l_binary64_1724` `flip3-+_binary64_1786` `unswap-sqr_binary64_1751` `associate-r_binary64_1723`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-log-exp_binary64_1822`
5×	`pow-sqr_binary64_1756` `pow-prod-down_binary64_1854`
4×	`frac-times_binary64_1793` `sqr-abs_binary64_1798`
2×	`associate-r/_binary64_1725` `associate-l/_binary64_1726`
1×	`+-commutative_binary64_1713` `distribute-lft-out_binary64_1734` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `sqrt-unprod_binary64_1803` `pow-plus_binary64_1846` `*-commutative_binary64_1714` `sum-log_binary64_1874` `rem-square-sqrt_binary64_1795` `pow2_binary64_1864`

Counts

4 → 129

Calls

4 calls:

21.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
10.0ms	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series122.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
28.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
26.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
24.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify105.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4925	2792
1	4925	2792

prune207.0ms (3.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	141	9	150

Merged error: 14.2b

Counts

150 → 9

Compiler

Compiled 4182 to 2723 computations (34.9% saved)

regimes536.0ms (9.9%)

Compiler: Compiled 7260 to 5662 computations (22% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	30
1	23	30

end0.0ms (0%)

sample2.0s (36.8%)

Algorithm

1×

intervals

Results

319.0ms	6038×	body	128	valid
212.0ms	779×	body	2048	valid
151.0ms	8000×	pre	128	true
109.0ms	516×	body	1024	valid
91.0ms	281×	body	4096	valid
39.0ms	254×	body	512	valid
13.0ms	132×	body	256	valid

Compiler

Compiled 1031 to 798 computations (22.6% saved)

Details

analyze888.0ms (16.3%)

sample40.0ms (0.7%)

simplify8.0ms (0.1%)

prune3.0ms (0.1%)

localize18.0ms (0.3%)

rewrite35.0ms (0.6%)

series178.0ms (3.3%)

simplify114.0ms (2.1%)

prune82.0ms (1.5%)

localize14.0ms (0.3%)

rewrite51.0ms (0.9%)

series192.0ms (3.5%)

simplify78.0ms (1.4%)

prune105.0ms (1.9%)

localize14.0ms (0.3%)

rewrite56.0ms (1%)

series301.0ms (5.5%)

simplify109.0ms (2%)

prune94.0ms (1.7%)

localize15.0ms (0.3%)

rewrite63.0ms (1.2%)

series122.0ms (2.3%)

simplify105.0ms (1.9%)

prune207.0ms (3.8%)

regimes536.0ms (9.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (36.8%)

Profiling