Details

analyze875.0ms (9.7%)

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 (0.4%)

Algorithm

1×

intervals

Results

10.0ms	212×	body	128	valid
4.0ms	256×	pre	128	true
4.0ms	6×	body	512	valid
3.0ms	14×	body	2048	valid
3.0ms	15×	body	1024	valid
2.0ms	6×	body	4096	valid
0.0ms	3×	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%)

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

Error

9.4b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 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)))))))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.3b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
17.8b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite179.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

9.2b

Rules

22×	`*-un-lft-identity_binary64_2465`
21×	`add-sqr-sqrt_binary64_2487`
20×	`add-cube-cbrt_binary64_2500`
18×	`times-frac_binary64_2471`
16×	`sqrt-prod_binary64_2481`
8×	`pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482` `associate-/r*_binary64_2409`
4×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
3×	`sqrt-pow1_binary64_2483` `associate-/l*_binary64_2410`
2×	`pow1/2_binary64_2545` `associate-/r/_binary64_2411` `associate-*r/_binary64_2407`
1×	`rem-sqrt-square_binary64_2478` `sum-log_binary64_2556` `distribute-lft-out_binary64_2416` `+-commutative_binary64_2395` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `div-inv_binary64_2462` `pow-prod-down_binary64_2536`

Counts

4 → 81

Calls

4 calls:

14.0ms	(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)))))
8.0ms	(/.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)))

Compiler

Compiled 2495 to 1576 computations (36.8% saved)

series558.0ms (6.2%)

Error

2.0b

Counts

4 → 56

Calls

4 calls:

181.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
131.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
115.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
77.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 2199 to 1967 computations (10.6% saved)

simplify65.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5001	3047

prune154.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	5	137
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	132	6	138

Error

1.5b

Counts

138 → 6

Compiler

Compiled 3058 to 1999 computations (34.6% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))) (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
5.5b	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))
17.8b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))
17.8b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

rewrite289.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

Rules

42×	`add-sqr-sqrt_binary64_2487`
33×	`times-frac_binary64_2471`
28×	`*-un-lft-identity_binary64_2465`
24×	`cancel-sign-sub-inv_binary64_2431`
21×	`add-cube-cbrt_binary64_2500`
18×	`sqrt-prod_binary64_2481`
9×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
6×	`pow1_binary64_2526` `add-log-exp_binary64_2504` `sqrt-div_binary64_2482` `difference-of-squares_binary64_2434`
4×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-/r/_binary64_2411`
3×	`associate-/r*_binary64_2409` `distribute-rgt-out--_binary64_2419`
2×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `div-inv_binary64_2462`
1×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/l*_binary64_2410` `diff-log_binary64_2557` `frac-sub_binary64_2474` `flip3--_binary64_2469` `sub-neg_binary64_2458` `flip--_binary64_2440` `distribute-lft-out--_binary64_2417`

Counts

4 → 99

Calls

4 calls:

25.0ms	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))) (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
7.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

Compiler

Compiled 6326 to 3680 computations (41.8% saved)

series601.0ms (6.7%)

Error

1.5b

Counts

4 → 53

Calls

4 calls:

213.0ms	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))) (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
118.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))
92.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))
86.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

Compiler

Compiled 5760 to 4097 computations (28.9% saved)

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4953	3871
1	4953	3871

prune357.0ms (4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	152	6	158

Error

1.5b

Counts

158 → 6

Compiler

Compiled 8017 to 4776 computations (40.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
1.3b	(-.f64 1 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))))
5.5b	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))
17.8b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

rewrite257.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

Rules

42×	`add-sqr-sqrt_binary64_2487`
33×	`cancel-sign-sub-inv_binary64_2431`
31×	`*-un-lft-identity_binary64_2465`
30×	`times-frac_binary64_2471`
22×	`add-cube-cbrt_binary64_2500`
14×	`sqrt-prod_binary64_2481`
10×	`difference-of-squares_binary64_2434`
9×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
8×	`add-log-exp_binary64_2504`
6×	`associate-/r/_binary64_2411`
5×	`pow1_binary64_2526`
4×	`flip3-+_binary64_2468` `sqrt-div_binary64_2482` `flip-+_binary64_2439`
3×	`div-inv_binary64_2462` `associate-/r*_binary64_2409`
2×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `diff-log_binary64_2557` `flip3--_binary64_2469` `sub-neg_binary64_2458` `flip--_binary64_2440` `distribute-lft-out--_binary64_2417`
1×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/l*_binary64_2410`

Counts

4 → 105

Calls

4 calls:

17.0ms	(-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
9.0ms	(-.f64 1 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))))
7.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

Compiler

Compiled 5162 to 3045 computations (41% saved)

series510.0ms (5.7%)

Error

1.5b

Counts

4 → 49

Calls

4 calls:

134.0ms	(-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
123.0ms	(-.f64 1 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))))
108.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))
82.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

Compiler

Compiled 3974 to 2992 computations (24.7% saved)

simplify97.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4955	3611
1	4955	3611

prune265.0ms (2.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	154	6	160

Error

1.5b

Counts

160 → 6

Compiler

Compiled 6018 to 3644 computations (39.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.4b	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
5.5b	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))
15.1b	(-.f64 1 (/.f64 x (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))))
17.8b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

rewrite310.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

Rules

48×	`add-sqr-sqrt_binary64_2487`
36×	`times-frac_binary64_2471`
35×	`*-un-lft-identity_binary64_2465`
33×	`cancel-sign-sub-inv_binary64_2431`
29×	`add-cube-cbrt_binary64_2500`
28×	`log-prod_binary64_2551` `exp-sum_binary64_2511`
17×	`sqrt-prod_binary64_2481`
9×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
8×	`difference-of-squares_binary64_2434`
7×	`pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `sqrt-div_binary64_2482` `exp-prod_binary64_2517`
4×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `log-div_binary64_2552` `exp-diff_binary64_2513` `associate-/r/_binary64_2411`
3×	`associate-/r*_binary64_2409` `log-pow_binary64_2554`
2×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `div-inv_binary64_2462` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499`
1×	`rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `flip3--_binary64_2469` `sub-neg_binary64_2458` `flip--_binary64_2440` `distribute-lft-out--_binary64_2417` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/l*_binary64_2410` `rem-exp-log_binary64_2505`

Counts

4 → 113

Calls

4 calls:

21.0ms	(-.f64 1 (/.f64 x (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))))
7.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))
6.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

Compiler

Compiled 5843 to 3597 computations (38.4% saved)

series814.0ms (9%)

Error

1.5b

Counts

4 → 59

Calls

4 calls:

251.0ms	(-.f64 1 (/.f64 x (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))))
199.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
152.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))
117.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))

Compiler

Compiled 5773 to 4327 computations (25% saved)

simplify89.0ms (1%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4973	3824
1	4973	3824

prune333.0ms (3.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	172	6	178

Error

1.5b

Counts

178 → 6

Compiler

Compiled 6839 to 4184 computations (38.8% saved)

regimes697.0ms (7.7%)

Accuracy

Total 2.9b remaining (51.8%)

Threshold costs 0b (0%)

Compiler

Compiled 9817 to 7417 computations (24.4% saved)

bsearch3.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	70
1	36	70

end0.0ms (0%)

sample2.4s (26.2%)

Algorithm

1×

intervals

Results

322.0ms	6052×	body	128	valid
194.0ms	763×	body	2048	valid
147.0ms	8000×	pre	128	true
107.0ms	528×	body	1024	valid
87.0ms	279×	body	4096	valid
35.0ms	241×	body	512	valid
14.0ms	137×	body	256	valid

Compiler

Compiled 1427 to 1071 computations (24.9% saved)

Details

analyze875.0ms (9.7%)

sample40.0ms (0.4%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize11.0ms (0.1%)

rewrite179.0ms (2%)

series558.0ms (6.2%)

simplify65.0ms (0.7%)

prune154.0ms (1.7%)

localize19.0ms (0.2%)

rewrite289.0ms (3.2%)

series601.0ms (6.7%)

simplify82.0ms (0.9%)

prune357.0ms (4%)

localize15.0ms (0.2%)

rewrite257.0ms (2.8%)

series510.0ms (5.7%)

simplify97.0ms (1.1%)

prune265.0ms (2.9%)

localize19.0ms (0.2%)

rewrite310.0ms (3.4%)

series814.0ms (9%)

simplify89.0ms (1%)

prune333.0ms (3.7%)

regimes697.0ms (7.7%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.4s (26.2%)

Profiling