Details

analyze253.0ms (5.6%)

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)

sample60.0ms (1.3%)

Algorithm

1×

intervals

Results

27.0ms	70×	body	1024	valid
12.0ms	39×	body	2048	valid
8.0ms	41×	body	512	valid
4.0ms	90×	body	128	valid
2.0ms	16×	body	256	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify161.0ms (3.6%)

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: 49.1b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 x x) 1)
0.4b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.4b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.9b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

7.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
5.0ms	(+.f64 (*.f64 x x) 1)

series225.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
62.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
43.0ms	(+.f64 (*.f64 x x) 1)
37.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5125	1001

prune78.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	5	66

Merged error: 0.0b

Counts

66 → 5

Compiler

Compiled 1011 to 663 computations (34.4% saved)

localize12.0ms (0.3%)

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)
20.3b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite27.0ms (0.6%)

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)))

series340.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

167.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
66.0ms	(*.f64 3/40 (pow.f64 x 5))
59.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
48.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4967	1201
1	4967	1201

prune101.0ms (2.2%)

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)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.6b	(/.f64 1/8 (pow.f64 x 3))
10.5b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite93.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64_2436`
43×	`add-sqr-sqrt_binary64_2457`
40×	`times-frac_binary64_2442`
30×	`add-cube-cbrt_binary64_2468`
18×	`add-log-exp_binary64_2472`
13×	`unpow-prod-down_binary64_2512` `cube-prod_binary64_2461`
12×	`associate-/r*_binary64_2382`
10×	`add-exp-log_binary64_2471`
9×	`distribute-lft-out_binary64_2389`
6×	`distribute-lft-out--_binary64_2390` `add-cbrt-cube_binary64_2469` `log-prod_binary64_2519`
5×	`sum-log_binary64_2524` `sqr-pow_binary64_2408` `pow1_binary64_2494` `difference-of-squares_binary64_2405`
4×	`diff-log_binary64_2525` `cube-mult_binary64_2463` `unpow3_binary64_2499`
3×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/l*_binary64_2383` `div-exp_binary64_2484`
2×	`frac-sub_binary64_2445` `associate-+r+_binary64_2370` `log-div_binary64_2520` `associate--l+_binary64_2375` `sub-neg_binary64_2429`
1×	`cbrt-undiv_binary64_2467` `log-pow_binary64_2522` `div-inv_binary64_2433` `associate-+r-_binary64_2372` `flip3--_binary64_2440` `pow-to-exp_binary64_2502` `clear-num_binary64_2435` `pow-exp_binary64_2501` `+-commutative_binary64_2368` `frac-2neg_binary64_2447` `rem-log-exp_binary64_2474` `flip--_binary64_2411`

Counts

4 → 123

Calls

4 calls:

28.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
25.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
22.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

series204.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(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))))
44.0ms	(/.f64 1/8 (pow.f64 x 3))
37.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))

simplify53.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5535	2608

prune153.0ms (3.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	135	5	140

Merged error: 0.0b

Counts

140 → 5

Compiler

Compiled 2826 to 2026 computations (28.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.2b	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
2.2b	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
14.9b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.9b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_2436` `sqrt-prod_binary64_2451` `log-prod_binary64_2519`
12×	`add-sqr-sqrt_binary64_2457`
10×	`add-cube-cbrt_binary64_2468` `pow1_binary64_2494`
8×	`sqrt-div_binary64_2452`
6×	`log-pow_binary64_2522` `add-exp-log_binary64_2471`
4×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `add-log-exp_binary64_2472` `pow1/2_binary64_2513` `add-cbrt-cube_binary64_2469` `log-div_binary64_2520` `sqrt-pow1_binary64_2453`
2×	`distribute-lft-out_binary64_2389` `rem-sqrt-square_binary64_2449` `rem-log-exp_binary64_2474`

Counts

4 → 70

Calls

4 calls:

7.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
7.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series203.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
68.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
33.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
31.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify62.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5126	1612

prune103.0ms (2.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	82	5	87

Merged error: 0.0b

Counts

87 → 5

Compiler

Compiled 2270 to 1484 computations (34.6% saved)

regimes43.0ms (0.9%)

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

bsearch34.0ms (0.8%)

Steps

Iters	Range		Point
8	0.0007531855139248682	23.575992414981645	0.9475279190554214
9	-1680000.618228654	-0.016292050559205556	-1.0860109172826882

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%)

sample2.1s (46.9%)

Algorithm

1×

intervals

Results

939.0ms	2516×	body	1024	valid
387.0ms	1157×	body	2048	valid
267.0ms	1262×	body	512	valid
107.0ms	2374×	body	128	valid
73.0ms	648×	body	256	valid
20.0ms	43×	body	4096	valid

Compiler

Compiled 160 to 126 computations (21.3% saved)

Details

analyze253.0ms (5.6%)

sample60.0ms (1.3%)

simplify161.0ms (3.6%)

prune2.0ms (0%)

localize9.0ms (0.2%)

rewrite26.0ms (0.6%)

series225.0ms (4.9%)

simplify57.0ms (1.3%)

prune78.0ms (1.7%)

localize12.0ms (0.3%)

rewrite27.0ms (0.6%)

series340.0ms (7.5%)

simplify56.0ms (1.2%)

prune101.0ms (2.2%)

localize10.0ms (0.2%)

rewrite93.0ms (2%)

series204.0ms (4.5%)

simplify53.0ms (1.2%)

prune153.0ms (3.4%)

localize9.0ms (0.2%)

rewrite33.0ms (0.7%)

series203.0ms (4.5%)

simplify62.0ms (1.4%)

prune103.0ms (2.3%)

regimes43.0ms (0.9%)

bsearch34.0ms (0.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.1s (46.9%)

Profiling