Details

analyze102.0ms (0.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample28.0ms (0%)

Algorithm

1×

intervals

Results

10.0ms	71×	body	1024	valid
5.0ms	130×	body	128	valid
4.0ms	36×	body	512	valid
1.0ms	19×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

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

19.5b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
3.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite322.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

18.8b

Rules

124×	`add-sqr-sqrt_binary64_2828`
118×	`times-frac_binary64_2812`
113×	`*-un-lft-identity_binary64_2806`
72×	`sqrt-prod_binary64_2822`
54×	`add-cube-cbrt_binary64_2841`
27×	`cancel-sign-sub-inv_binary64_2772`
25×	`difference-of-squares_binary64_2775`
13×	`distribute-lft-out--_binary64_2758` `associate-/r*_binary64_2750`
11×	`add-exp-log_binary64_2844`
10×	`distribute-lft-out_binary64_2757`
7×	`pow1_binary64_2867` `add-cbrt-cube_binary64_2842` `div-inv_binary64_2803`
6×	`pow-flip_binary64_2880` `associate-/l*_binary64_2751`
5×	`add-log-exp_binary64_2845`
4×	`sqrt-div_binary64_2823` `associate-/r/_binary64_2752` `div-exp_binary64_2857`
2×	`flip3-+_binary64_2809` `flip-+_binary64_2780` `inv-pow_binary64_2891` `pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `1-exp_binary64_2850` `rec-exp_binary64_2856` `cbrt-undiv_binary64_2840` `frac-2neg_binary64_2817` `clear-num_binary64_2805`
1×	`diff-log_binary64_2898` `frac-sub_binary64_2815` `flip3--_binary64_2810` `sub-neg_binary64_2799` `flip--_binary64_2781`

Counts

3 → 173

Calls

3 calls:

41.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 3566 to 2737 computations (23.2% saved)

series68.0ms (0%)

Error

19.4b

Counts

3 → 12

Calls

3 calls:

27.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
21.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
12.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 369 to 304 computations (17.6% saved)

simplify106.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4846	3144
1	4846	3144

prune215.0ms (0.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	173	12	185
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	174	12	186

Error

18.8b

Counts

186 → 12

Compiler

Compiled 3304 to 2463 computations (25.5% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
3.2b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite163.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

18.5b

Rules

43×	`add-sqr-sqrt_binary64_2828`
38×	`sqrt-prod_binary64_2822`
34×	`*-un-lft-identity_binary64_2806`
12×	`difference-of-squares_binary64_2775`
11×	`add-cube-cbrt_binary64_2841`
10×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `times-frac_binary64_2812` `associate-/l*_binary64_2751`
9×	`distribute-lft-out--_binary64_2758`
7×	`pow1_binary64_2867` `associate-r_binary64_2746`
6×	`cancel-sign-sub-inv_binary64_2772` `associate-l_binary64_2747`
5×	`add-log-exp_binary64_2845`
4×	`distribute-lft-out_binary64_2757` `unswap-sqr_binary64_2774` `sqrt-div_binary64_2823` `associate-*r/_binary64_2748`
3×	`pow-prod-down_binary64_2877`
2×	`flip3--_binary64_2810` `flip--_binary64_2781` `pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `flip3-+_binary64_2809` `flip-+_binary64_2780` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `associate-/l/_binary64_2753` `associate-/r/_binary64_2752`
1×	`diff-log_binary64_2898` `sub-neg_binary64_2799` `sqrt-unprod_binary64_2826` `-commutative_binary64_2737` `frac-2neg_binary64_2817` `div-sub_binary64_2811` `clear-num_binary64_2805` `div-inv_binary64_2803` `associate-/r_binary64_2750`

Counts

3 → 97

Calls

3 calls:

20.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 2306 to 1441 computations (37.5% saved)

series129.0ms (0.1%)

Error

18.6b

Counts

3 → 12

Calls

3 calls:

59.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
31.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
26.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

Compiler

Compiled 534 to 416 computations (22.1% saved)

simplify68.0ms (0%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5675	1943

prune118.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	118	3	121

Error

0.2b

Counts

121 → 3

Compiler

Compiled 2191 to 1398 computations (36.2% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite338.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

118×	`*-un-lft-identity_binary64_2806`
78×	`times-frac_binary64_2812`
55×	`sqrt-prod_binary64_2822`
47×	`add-sqr-sqrt_binary64_2828`
45×	`distribute-lft-out_binary64_2757`
39×	`add-cube-cbrt_binary64_2841`
32×	`add-exp-log_binary64_2844`
27×	`associate-/l*_binary64_2751`
20×	`add-cbrt-cube_binary64_2842`
14×	`div-exp_binary64_2857`
9×	`pow1_binary64_2867`
8×	`associate-/r/_binary64_2752`
7×	`associate-r_binary64_2746` `cbrt-undiv_binary64_2840` `associate-/r*_binary64_2750`
6×	`add-log-exp_binary64_2845` `flip3-+_binary64_2809` `flip-+_binary64_2780` `associate-l_binary64_2747`
5×	`prod-exp_binary64_2855`
4×	`unswap-sqr_binary64_2774` `sqrt-div_binary64_2823` `associate-*r/_binary64_2748` `div-inv_binary64_2803`
3×	`pow-prod-down_binary64_2877` `cbrt-unprod_binary64_2839` `1-exp_binary64_2850` `rec-exp_binary64_2856`
2×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `frac-2neg_binary64_2817` `clear-num_binary64_2805`
1×	`sqrt-unprod_binary64_2826` `*-commutative_binary64_2737` `inv-pow_binary64_2891` `pow-flip_binary64_2880` `associate-/l/_binary64_2753` `sum-log_binary64_2897` `+-commutative_binary64_2736`

Counts

4 → 166

Calls

4 calls:

20.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 4418 to 3053 computations (30.9% saved)

series122.0ms (0.1%)

Error

0.1b

Counts

4 → 15

Calls

4 calls:

46.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
28.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
19.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
18.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 561 to 452 computations (19.4% saved)

simplify96.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4965	3678
1	4965	3678

prune240.0ms (0.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	174	7	181
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	175	9	184

Error

Counts

184 → 9

Compiler

Compiled 4183 to 2880 computations (31.1% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.2b	(/.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 (sqrt.f64 x) (/.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 x 1)))))

rewrite2.5min (98.6%)

Algorithm

1×	rewrite-expression-head

Rules

179892×	`times-frac_binary64_2812`
112393×	`*-un-lft-identity_binary64_2806`
110242×	`sqrt-prod_binary64_2822`
54194×	`add-cube-cbrt_binary64_2841` `add-sqr-sqrt_binary64_2828`
32425×	`distribute-lft-out_binary64_2757`
18390×	`cbrt-prod_binary64_2837`
6699×	`associate-/r/_binary64_2752`
6682×	`sqrt-div_binary64_2823`
3358×	`div-inv_binary64_2803`
3341×	`flip3-+_binary64_2809` `flip-+_binary64_2780`
2586×	`associate-/r*_binary64_2750`
82×	`associate-/l*_binary64_2751`
70×	`add-exp-log_binary64_2844`
55×	`add-cbrt-cube_binary64_2842`
44×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840`
5×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
4×	`pow1_binary64_2867` `add-log-exp_binary64_2845` `frac-2neg_binary64_2817` `clear-num_binary64_2805`
2×	`associate-/l/_binary64_2753`

Counts

4 → 41649

Calls

4 calls:

1.4s	(/.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 (sqrt.f64 x) (/.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 x 1)))))
33.0ms	(/.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 x 1)))
16.0ms	(/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
13.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))

Details

analyze102.0ms (0.1%)

sample28.0ms (0%)

simplify10.0ms (0%)

prune3.0ms (0%)

localize7.0ms (0%)

rewrite322.0ms (0.2%)

series68.0ms (0%)

simplify106.0ms (0.1%)

prune215.0ms (0.1%)

localize7.0ms (0%)

rewrite163.0ms (0.1%)

series129.0ms (0.1%)

simplify68.0ms (0%)

prune118.0ms (0.1%)

localize9.0ms (0%)

rewrite338.0ms (0.2%)

series122.0ms (0.1%)

simplify96.0ms (0.1%)

prune240.0ms (0.2%)

localize18.0ms (0%)

rewrite2.5min (98.6%)

Profiling