Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample14.0ms (0%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify395.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (305.0ms)

Iter	Nodes	Cost
0	7521	9

prune1.0ms (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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 6 to 5 computations (16.7% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`sqrt-prod_binary64_9642`
4×	`add-sqr-sqrt_binary64_9648`
3×	`*-un-lft-identity_binary64_9626`
2×	`add-cube-cbrt_binary64_9661` `difference-of-squares_binary64_9595` `pow1_binary64_9687` `sqrt-div_binary64_9643`
1×	`rem-sqrt-square_binary64_9639` `flip3--_binary64_9630` `add-log-exp_binary64_9665` `sqrt-pow1_binary64_9644` `pow1/2_binary64_9706` `flip--_binary64_9601` `add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`

Counts

1 → 17

Calls

2 calls:

3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series25.0ms (0%)

Counts

1 → 6

Calls

1 calls:

25.0ms

(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 77 to 73 computations (5.2% saved)

simplify153.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	4759	284
1	4759	284

prune80.0ms (0.1%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	4	19	23
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	4	20	24

Error

Counts

24 → 20

Compiler

Compiled 391 to 292 computations (25.3% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`sqrt-prod_binary64_9642`
4×	`add-sqr-sqrt_binary64_9648`
3×	`*-un-lft-identity_binary64_9626`
2×	`add-cube-cbrt_binary64_9661` `difference-of-squares_binary64_9595` `pow1_binary64_9687` `sqrt-div_binary64_9643`
1×	`rem-sqrt-square_binary64_9639` `flip3--_binary64_9630` `add-log-exp_binary64_9665` `sqrt-pow1_binary64_9644` `pow1/2_binary64_9706` `flip--_binary64_9601` `add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`

Counts

1 → 17

Calls

2 calls:

3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series24.0ms (0%)

Counts

1 → 6

Calls

1 calls:

24.0ms

(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 93 to 89 computations (4.3% saved)

simplify161.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (153.0ms)

Iter	Nodes	Cost
0	4759	284
1	4759	284

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 (.f64 x x) 1/2)
0.0b	(.f64 (.f64 x x) 1/2)

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`pow1_binary64_9687` `add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`
3×	`add-sqr-sqrt_binary64_9648` `prod-exp_binary64_9675` `pow-prod-down_binary64_9697` `associate-r_binary64_9566` `cbrt-unprod_binary64_9659`
2×	`add-cube-cbrt_binary64_9661` `*-un-lft-identity_binary64_9626`
1×	`associate-l_binary64_9567` `add-log-exp_binary64_9665` `*-commutative_binary64_9557` `unswap-sqr_binary64_9594`

Counts

1 → 19

Calls

2 calls:

6.0ms	(.f64 (.f64 x x) 1/2)
0.0ms	(.f64 (.f64 x x) 1/2)

series27.0ms (0%)

Counts

1 → 3

Calls

1 calls:

27.0ms

(*.f64 (*.f64 x x) 1/2)

Compiler

Compiled 42 to 42 computations (0% saved)

simplify56.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5001	181

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`sqrt-prod_binary64_9642`
4×	`add-sqr-sqrt_binary64_9648`
3×	`*-un-lft-identity_binary64_9626`
2×	`add-cube-cbrt_binary64_9661` `difference-of-squares_binary64_9595` `pow1_binary64_9687` `sqrt-div_binary64_9643`
1×	`rem-sqrt-square_binary64_9639` `flip3--_binary64_9630` `add-log-exp_binary64_9665` `sqrt-pow1_binary64_9644` `pow1/2_binary64_9706` `flip--_binary64_9601` `add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`

Counts

1 → 17

Calls

2 calls:

3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series25.0ms (0%)

Counts

1 → 6

Calls

1 calls:

24.0ms

(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 93 to 89 computations (4.3% saved)

simplify147.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	4759	284
1	4759	284

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (.f64 x x) 1/2)
0.0b	(+.f64 (.f64 (pow.f64 x 4) 1/8) (+.f64 (.f64 (.f64 x x) 1/2) (.f64 (pow.f64 x 6) 1/16)))
0.0b	(+.f64 (.f64 (.f64 x x) 1/2) (*.f64 (pow.f64 x 6) 1/16))
0.0b	(*.f64 (pow.f64 x 4) 1/8)
0.0b	(*.f64 (pow.f64 x 4) 1/8)
0.0b	(+.f64 (.f64 (.f64 x x) 1/2) (*.f64 (pow.f64 x 6) 1/16))
0.0b	(.f64 (.f64 x x) 1/2)
0.0b	(+.f64 (.f64 (pow.f64 x 4) 1/8) (+.f64 (.f64 (.f64 x x) 1/2) (.f64 (pow.f64 x 6) 1/16)))

rewrite36.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_9648` `add-exp-log_binary64_9664`
11×	`add-log-exp_binary64_9665` `add-cbrt-cube_binary64_9662`
9×	`pow1_binary64_9687`
8×	`associate-l_binary64_9567` `add-cube-cbrt_binary64_9661` `*-un-lft-identity_binary64_9626`
6×	`prod-exp_binary64_9675` `associate-r_binary64_9566`
4×	`unpow-prod-down_binary64_9705` `unswap-sqr_binary64_9594` `sum-log_binary64_9717` `cbrt-unprod_binary64_9659`
3×	`pow-prod-down_binary64_9697`
2×	`sqr-pow_binary64_9598` `+-commutative_binary64_9556` `*-commutative_binary64_9557` `flip-+_binary64_9600` `flip3-+_binary64_9629`
1×	`pow-to-exp_binary64_9695` `pow-exp_binary64_9694` `associate-+r+_binary64_9558`

Counts

4 → 68

Calls

8 calls:

10.0ms	(+.f64 (.f64 (pow.f64 x 4) 1/8) (+.f64 (.f64 (.f64 x x) 1/2) (.f64 (pow.f64 x 6) 1/16)))
6.0ms	(+.f64 (.f64 (.f64 x x) 1/2) (*.f64 (pow.f64 x 6) 1/16))
6.0ms	(.f64 (.f64 x x) 1/2)
5.0ms	(*.f64 (pow.f64 x 4) 1/8)
0.0ms	(*.f64 (pow.f64 x 4) 1/8)

series242.0ms (0.4%)

Counts

4 → 17

Calls

4 calls:

119.0ms	(+.f64 (.f64 (.f64 x x) 1/2) (*.f64 (pow.f64 x 6) 1/16))
59.0ms	(+.f64 (.f64 (pow.f64 x 4) 1/8) (+.f64 (.f64 (.f64 x x) 1/2) (.f64 (pow.f64 x 6) 1/16)))
36.0ms	(*.f64 (pow.f64 x 4) 1/8)
28.0ms	(.f64 (.f64 x x) 1/2)

Compiler

Compiled 479 to 427 computations (10.9% saved)

simplify83.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4941	1260
1	4941	1260

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))
0.0b	(sqrt.f64 (+.f64 1 (*.f64 x x)))
0.0b	(sqrt.f64 (+.f64 1 (*.f64 x x)))
0.0b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))

rewrite30.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`sqrt-prod_binary64_9642`
95×	`add-sqr-sqrt_binary64_9648`
80×	`*-un-lft-identity_binary64_9626`
78×	`times-frac_binary64_9632`
45×	`add-cube-cbrt_binary64_9661`
42×	`difference-of-squares_binary64_9595`
14×	`unpow-prod-down_binary64_9705` `sqr-pow_binary64_9598`
13×	`associate-/l*_binary64_9571`
7×	`distribute-lft-out--_binary64_9578`
6×	`sqrt-div_binary64_9643` `associate-/r*_binary64_9570`
4×	`add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`
3×	`pow1_binary64_9687`
2×	`add-log-exp_binary64_9665` `associate-/l/_binary64_9573` `flip-+_binary64_9600` `associate-/r/_binary64_9572` `flip3-+_binary64_9629`
1×	`rem-sqrt-square_binary64_9639` `flip3--_binary64_9630` `div-exp_binary64_9677` `sqrt-pow1_binary64_9644` `pow1/2_binary64_9706` `flip--_binary64_9601` `cbrt-undiv_binary64_9660` `sqrt-undiv_binary64_9647` `frac-2neg_binary64_9637` `div-inv_binary64_9623` `clear-num_binary64_9625`

Counts

2 → 129

Calls

4 calls:

13.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 x x)))
0.0ms	(sqrt.f64 (+.f64 1 (*.f64 x x)))
0.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))

series86.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

51.0ms	(sqrt.f64 (+.f64 1 (*.f64 x x)))
34.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))

Compiler

Compiled 296 to 266 computations (10.1% saved)

simplify103.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4942	4409
1	4942	4409

prune2.7s (3.9%)

Pruning

131 alts after pruning (125 fresh and 6 done)

	Pruned	Kept	Total
New	185	113	298
Fresh	2	12	14
Picked	0	0	0
Done	0	6	6
Total	187	131	318

Error

Counts

318 → 131

Compiler

Compiled 6354 to 4869 computations (23.4% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 1 (pow.f64 x 4)) (+.f64 1 (*.f64 x x)))
0.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 x 4)) (+.f64 1 (*.f64 x x))))
0.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 x 4)) (+.f64 1 (*.f64 x x))))
0.0b	(/.f64 (-.f64 1 (pow.f64 x 4)) (+.f64 1 (*.f64 x x)))

rewrite34.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`add-sqr-sqrt_binary64_9648`
66×	`*-un-lft-identity_binary64_9626`
61×	`times-frac_binary64_9632`
42×	`difference-of-squares_binary64_9595`
36×	`sqrt-prod_binary64_9642`
31×	`add-cube-cbrt_binary64_9661`
14×	`unpow-prod-down_binary64_9705` `sqr-pow_binary64_9598`
10×	`associate-/l*_binary64_9571`
7×	`distribute-lft-out--_binary64_9578`
4×	`add-exp-log_binary64_9664` `associate-/r/_binary64_9572` `add-cbrt-cube_binary64_9662`
3×	`pow1_binary64_9687` `associate-/r*_binary64_9570`
2×	`rem-sqrt-square_binary64_9639` `add-log-exp_binary64_9665` `associate-/l/_binary64_9573` `flip-+_binary64_9600` `div-inv_binary64_9623` `flip3-+_binary64_9629`
1×	`flip3--_binary64_9630` `div-exp_binary64_9677` `sqrt-pow1_binary64_9644` `pow1/2_binary64_9706` `flip--_binary64_9601` `cbrt-undiv_binary64_9660` `frac-2neg_binary64_9637` `clear-num_binary64_9625` `sqrt-div_binary64_9643` `div-sub_binary64_9631`

Counts

2 → 108

Calls

4 calls:

12.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 x 4)) (+.f64 1 (*.f64 x x))))
11.0ms	(/.f64 (-.f64 1 (pow.f64 x 4)) (+.f64 1 (*.f64 x x)))
0.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 x 4)) (+.f64 1 (*.f64 x x))))
0.0ms	(/.f64 (-.f64 1 (pow.f64 x 4)) (+.f64 1 (*.f64 x x)))

series114.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

76.0ms	(/.f64 (-.f64 1 (pow.f64 x 4)) (+.f64 1 (*.f64 x x)))
38.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 x 4)) (+.f64 1 (*.f64 x x))))

Compiler

Compiled 127 to 124 computations (2.4% saved)

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	6099	3268

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

0.0b	(log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0b	(exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))

rewrite16.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`exp-prod_binary64_9678`
15×	`sqrt-prod_binary64_9642`
13×	`add-sqr-sqrt_binary64_9648`
12×	`*-un-lft-identity_binary64_9626`
9×	`add-cube-cbrt_binary64_9661` `log-pow_binary64_9715`
6×	`difference-of-squares_binary64_9595`
5×	`pow1_binary64_9687`
4×	`add-log-exp_binary64_9665`
3×	`log-prod_binary64_9712` `add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`
2×	`sqrt-div_binary64_9643`
1×	`rem-sqrt-square_binary64_9639` `flip3--_binary64_9630` `rem-exp-log_binary64_9666` `rem-log-exp_binary64_9667` `sqrt-pow1_binary64_9644` `pow1/2_binary64_9706` `flip--_binary64_9601`

Counts

3 → 53

Calls

6 calls:

4.0ms	(log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
4.0ms	(exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms	(exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series142.0ms (0.2%)

Counts

3 → 18

Calls

3 calls:

89.0ms	(log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
28.0ms	(exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
25.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 301 to 287 computations (4.7% saved)

simplify92.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4871	887
1	4871	887

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (+.f64 1 (.f64 x x))) (sqrt.f64 (-.f64 1 (.f64 x x))))
0.0b	(sqrt.f64 (+.f64 1 (*.f64 x x)))
0.0b	(sqrt.f64 (+.f64 1 (pow.f64 x (/.f64 4 2))))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(sqrt.f64 (+.f64 1 (*.f64 x x)))
0.0b	(sqrt.f64 (+.f64 1 (pow.f64 x (/.f64 4 2))))
0.0b	(/.f64 (sqrt.f64 (+.f64 1 (.f64 x x))) (sqrt.f64 (-.f64 1 (.f64 x x))))
0.0b	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x (/.f64 4 2)))) (/.f64 (sqrt.f64 (+.f64 1 (.f64 x x))) (sqrt.f64 (-.f64 1 (.f64 x x)))))

rewrite152.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

810×	`times-frac_binary64_9632`
721×	`sqrt-prod_binary64_9642`
547×	`*-un-lft-identity_binary64_9626`
437×	`add-sqr-sqrt_binary64_9648`
380×	`add-cube-cbrt_binary64_9661`
110×	`difference-of-squares_binary64_9595`
62×	`associate-/r*_binary64_9570`
56×	`distribute-lft-out_binary64_9577`
26×	`sqrt-div_binary64_9643`
19×	`associate-/r/_binary64_9572`
13×	`associate-/l*_binary64_9571`
11×	`add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`
10×	`div-inv_binary64_9623`
9×	`flip3--_binary64_9630` `flip--_binary64_9601`
6×	`pow1_binary64_9687`
4×	`add-log-exp_binary64_9665` `div-exp_binary64_9677` `associate-/l/_binary64_9573` `cbrt-undiv_binary64_9660` `flip-+_binary64_9600` `flip3-+_binary64_9629`
3×	`sqrt-undiv_binary64_9647`
2×	`rem-sqrt-square_binary64_9639` `sqrt-pow1_binary64_9644` `pow1/2_binary64_9706` `frac-2neg_binary64_9637` `clear-num_binary64_9625`

Counts

4 → 567

Calls

8 calls:

26.0ms	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x (/.f64 4 2)))) (/.f64 (sqrt.f64 (+.f64 1 (.f64 x x))) (sqrt.f64 (-.f64 1 (.f64 x x)))))
9.0ms	(/.f64 (sqrt.f64 (+.f64 1 (.f64 x x))) (sqrt.f64 (-.f64 1 (.f64 x x))))
5.0ms	(sqrt.f64 (+.f64 1 (pow.f64 x (/.f64 4 2))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 x x)))
0.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series136.0ms (0.2%)

Counts

4 → 28

Calls

4 calls:

51.0ms	(sqrt.f64 (+.f64 1 (*.f64 x x)))
35.0ms	(/.f64 (sqrt.f64 (+.f64 1 (.f64 x x))) (sqrt.f64 (-.f64 1 (.f64 x x))))
27.0ms	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x (/.f64 4 2)))) (/.f64 (sqrt.f64 (+.f64 1 (.f64 x x))) (sqrt.f64 (-.f64 1 (.f64 x x)))))
23.0ms	(sqrt.f64 (+.f64 1 (pow.f64 x (/.f64 4 2))))

Compiler

Compiled 707 to 601 computations (15% saved)

simplify526.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

595 → 595

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	5000	24808

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 4) (*.f64 1/8 (pow.f64 (cbrt.f64 x) 4)))
0.0b	(+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 4) (.f64 1/8 (pow.f64 (cbrt.f64 x) 4))) (+.f64 (.f64 (.f64 x x) 1/2) (.f64 (pow.f64 x 6) 1/16)))
0.0b	(.f64 (.f64 x x) 1/2)
0.0b	(+.f64 (.f64 (.f64 x x) 1/2) (*.f64 (pow.f64 x 6) 1/16))
0.7b	(pow.f64 (cbrt.f64 x) 4)
0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64_9657`
10×	`add-sqr-sqrt_binary64_9648` `add-cube-cbrt_binary64_9661` `*-un-lft-identity_binary64_9626`
6×	`unpow-prod-down_binary64_9705`
5×	`pow1_binary64_9687` `add-exp-log_binary64_9664`
4×	`add-log-exp_binary64_9665` `pow1/3_binary64_9708` `add-cbrt-cube_binary64_9662`
3×	`pow-unpow_binary64_9703`
2×	`pow-pow_binary64_9698`
1×	`sqr-pow_binary64_9598` `pow-to-exp_binary64_9695` `pow-exp_binary64_9694`

Counts

4 → 54

Calls

8 calls:

3.0ms	(pow.f64 (cbrt.f64 x) 4)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
0.0ms	(+.f64 (.f64 (.f64 x x) 1/2) (*.f64 (pow.f64 x 6) 1/16))

series332.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(pow.f64 (cbrt.f64 x) 4)
78.0ms	(cbrt.f64 x)
74.0ms	(cbrt.f64 x)
68.0ms	(cbrt.f64 x)

Compiler

Compiled 736 to 592 computations (19.6% saved)

simplify57.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4766	402
1	4766	402

prune17.0s (25%)

Pruning

297 alts after pruning (287 fresh and 10 done)

	Pruned	Kept	Total
New	663	189	852
Fresh	22	98	120
Picked	0	0	0
Done	1	10	11
Total	686	297	983

Error

Counts

983 → 297

Compiler

Compiled 19351 to 13462 computations (30.4% saved)

localize12.0ms (0%)

Local error

Found 6 expressions with local error:

0.0b	(/.f64 1 (+.f64 1 (*.f64 x x)))
0.0b	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 x x))))
0.0b	(.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 x x)))))
0.0b	(.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 x x)))))
0.0b	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 x x))))
0.0b	(/.f64 1 (+.f64 1 (*.f64 x x)))

rewrite42.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64_9648`
50×	`sqrt-prod_binary64_9642`
36×	`*-un-lft-identity_binary64_9626`
33×	`times-frac_binary64_9632`
28×	`add-cube-cbrt_binary64_9661`
18×	`associate-r_binary64_9566`
13×	`associate-l_binary64_9567`
10×	`pow1_binary64_9687`
9×	`add-exp-log_binary64_9664`
8×	`unswap-sqr_binary64_9594` `sqrt-div_binary64_9643`
7×	`add-cbrt-cube_binary64_9662`
6×	`difference-of-squares_binary64_9595` `associate-/r/_binary64_9572`
5×	`sqrt-pow1_binary64_9644`
3×	`rem-sqrt-square_binary64_9639` `add-log-exp_binary64_9665` `pow-prod-down_binary64_9697` `pow1/2_binary64_9706` `flip-+_binary64_9600` `associate-/l_binary64_9571` `div-inv_binary64_9623` `flip3-+_binary64_9629` `associate-/r_binary64_9570`
2×	`associate-*l/_binary64_9569` `flip3--_binary64_9630` `div-exp_binary64_9677` `frac-times_binary64_9636` `inv-pow_binary64_9711` `unpow-prod-down_binary64_9705` `sqr-pow_binary64_9598` `pow-flip_binary64_9700` `flip--_binary64_9601`
1×	`1-exp_binary64_9670` `rec-exp_binary64_9676` `sqrt-unprod_binary64_9646` `prod-exp_binary64_9675` `distribute-lft-out--_binary64_9578` `-commutative_binary64_9557` `cbrt-undiv_binary64_9660` `frac-2neg_binary64_9637` `clear-num_binary64_9625` `associate-r/_binary64_9568` `cbrt-unprod_binary64_9659`

Counts

3 → 121

Calls

6 calls:

21.0ms	(.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 x x)))))
5.0ms	(/.f64 1 (+.f64 1 (*.f64 x x)))
5.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 x x))))
0.0ms	(.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 x x)))))
0.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 x x))))

series99.0ms (0.1%)

Counts

3 → 20

Calls

3 calls:

43.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 x x))))
33.0ms	(.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 x x)))))
23.0ms	(/.f64 1 (+.f64 1 (*.f64 x x)))

Compiler

Compiled 377 to 343 computations (9% saved)

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4925	2801
1	4925	2801

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 (.f64 x x) 1/2)
0.0b	(.f64 (.f64 x x) 1/2)

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`pow1_binary64_9687` `add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`
3×	`add-sqr-sqrt_binary64_9648` `prod-exp_binary64_9675` `pow-prod-down_binary64_9697` `associate-r_binary64_9566` `cbrt-unprod_binary64_9659`
2×	`add-cube-cbrt_binary64_9661` `*-un-lft-identity_binary64_9626`
1×	`associate-l_binary64_9567` `add-log-exp_binary64_9665` `*-commutative_binary64_9557` `unswap-sqr_binary64_9594`

Counts

1 → 19

Calls

2 calls:

6.0ms	(.f64 (.f64 x x) 1/2)
0.0ms	(.f64 (.f64 x x) 1/2)

series27.0ms (0%)

Counts

1 → 3

Calls

1 calls:

26.0ms

(*.f64 (*.f64 x x) 1/2)

Compiler

Compiled 54 to 54 computations (0% saved)

simplify56.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5001	181

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

3.5b	(log.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
3.5b	(log.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`sqrt-prod_binary64_9642`
8×	`add-sqr-sqrt_binary64_9648` `log-prod_binary64_9712`
7×	`*-un-lft-identity_binary64_9626`
5×	`add-cube-cbrt_binary64_9661` `pow1_binary64_9687`
4×	`difference-of-squares_binary64_9595` `sqrt-div_binary64_9643`
3×	`log-pow_binary64_9715` `add-exp-log_binary64_9664`
2×	`flip3--_binary64_9630` `add-log-exp_binary64_9665` `sqrt-pow1_binary64_9644` `pow1/2_binary64_9706` `flip--_binary64_9601` `log-div_binary64_9713` `add-cbrt-cube_binary64_9662`
1×	`rem-sqrt-square_binary64_9639` `rem-log-exp_binary64_9667`

Counts

2 → 38

Calls

4 calls:

4.0ms	(log.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms	(log.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

series92.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

62.0ms	(log.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
30.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 250 to 238 computations (4.8% saved)

simplify109.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4876	738
1	4876	738

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 x x)))))
0.0b	(cbrt.f64 (+.f64 1 (*.f64 x x)))
0.0b	(cbrt.f64 (+.f64 1 (*.f64 x x)))
0.0b	(sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 x x))))
0.0b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 x x)))))
0.0b	(cbrt.f64 (+.f64 1 (*.f64 x x)))
0.0b	(cbrt.f64 (+.f64 1 (*.f64 x x)))
0.0b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 x x))))))

rewrite39.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_9648`
28×	`sqrt-prod_binary64_9642`
24×	`*-un-lft-identity_binary64_9626`
14×	`add-cube-cbrt_binary64_9661`
13×	`times-frac_binary64_9632` `associate-/l*_binary64_9571`
12×	`difference-of-squares_binary64_9595`
11×	`add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`
10×	`cbrt-prod_binary64_9657`
9×	`associate-r_binary64_9566`
8×	`cbrt-div_binary64_9658`
6×	`pow1_binary64_9687` `sqrt-div_binary64_9643`
4×	`add-log-exp_binary64_9665` `unpow-prod-down_binary64_9705` `sqr-pow_binary64_9598` `flip-+_binary64_9600` `flip3-+_binary64_9629` `associate-*r/_binary64_9568`
3×	`associate-l_binary64_9567` `unswap-sqr_binary64_9594`
2×	`div-exp_binary64_9677` `pow1/3_binary64_9708` `prod-exp_binary64_9675` `distribute-lft-out--_binary64_9578` `associate-/l/_binary64_9573` `cbrt-undiv_binary64_9660` `associate-/r/_binary64_9572` `cbrt-unprod_binary64_9659`
1×	`flip3--_binary64_9630` `pow-prod-down_binary64_9697` `-commutative_binary64_9557` `flip--_binary64_9601` `frac-2neg_binary64_9637` `div-inv_binary64_9623` `clear-num_binary64_9625` `associate-/r_binary64_9570`

Counts

4 → 99

Calls

8 calls:

14.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 x x))))))
9.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 x x)))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 x x)))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 x x)))
0.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 x x))))

series359.0ms (0.5%)

Counts

4 → 28

Calls

4 calls:

123.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 x x))))))
81.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 x x)))))
78.0ms	(cbrt.f64 (+.f64 1 (*.f64 x x)))
77.0ms	(cbrt.f64 (+.f64 1 (*.f64 x x)))

Compiler

Compiled 1090 to 966 computations (11.4% saved)

simplify97.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5265	3552

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x)) 4) (.f64 1/8 (pow.f64 (cbrt.f64 x) 4)))
0.0b	(.f64 (.f64 x x) 1/2)
0.0b	(+.f64 (.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x)) 4) (.f64 1/8 (pow.f64 (cbrt.f64 x) 4))) (+.f64 (.f64 (.f64 x x) 1/2) (*.f64 (pow.f64 x 6) 1/16)))
0.0b	(+.f64 (.f64 (.f64 x x) 1/2) (*.f64 (pow.f64 x 6) 1/16))
0.3b	(cbrt.f64 (sqrt.f64 x))
0.7b	(pow.f64 (cbrt.f64 x) 4)
0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cbrt-prod_binary64_9657`
11×	`add-sqr-sqrt_binary64_9648` `add-cube-cbrt_binary64_9661` `*-un-lft-identity_binary64_9626`
6×	`unpow-prod-down_binary64_9705`
5×	`pow1_binary64_9687` `add-exp-log_binary64_9664`
4×	`add-log-exp_binary64_9665` `pow1/3_binary64_9708` `add-cbrt-cube_binary64_9662`
3×	`sqrt-prod_binary64_9642` `pow-unpow_binary64_9703`
2×	`pow-pow_binary64_9698`
1×	`sqr-pow_binary64_9598` `pow-to-exp_binary64_9695` `pow-exp_binary64_9694`

Counts

4 → 57

Calls

8 calls:

3.0ms	(pow.f64 (cbrt.f64 x) 4)
2.0ms	(cbrt.f64 (sqrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
0.0ms	(+.f64 (.f64 (.f64 x x) 1/2) (*.f64 (pow.f64 x 6) 1/16))

series349.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(pow.f64 (cbrt.f64 x) 4)
88.0ms	(cbrt.f64 x)
85.0ms	(cbrt.f64 x)
52.0ms	(cbrt.f64 (sqrt.f64 x))

Compiler

Compiled 852 to 666 computations (21.8% saved)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5414	468

prune19.1s (28.2%)

Pruning

394 alts after pruning (379 fresh and 15 done)

	Pruned	Kept	Total
New	281	128	409
Fresh	31	251	282
Picked	0	0	0
Done	0	15	15
Total	312	394	706

Error

Counts

706 → 394

Compiler

Compiled 7725 to 5290 computations (31.5% saved)

simplify484.0ms (0.7%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4987	32896
1	4987	32896

regimes5.6s (8.2%)

Compiler: Compiled 77210 to 57718 computations (25.2% saved)

bsearch0.0ms (0%)

regimes376.0ms (0.6%)

Compiler: Compiled 3249 to 2751 computations (15.3% saved)

bsearch0.0ms (0%)

regimes160.0ms (0.2%)

Compiler: Compiled 1030 to 927 computations (10% saved)

bsearch0.0ms (0%)

regimes120.0ms (0.2%)

Compiler: Compiled 806 to 724 computations (10.2% saved)

bsearch0.0ms (0%)

regimes36.0ms (0.1%)

Compiler: Compiled 110 to 108 computations (1.8% saved)

bsearch0.0ms (0%)

regimes7.0ms (0%)

Accuracy

Total 0.0b remaining (100%)

Threshold costs 0.0b (100%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch4.0ms (0%)

Compiler: Compiled 49 to 43 computations (12.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	76	73
1	76	73

end0.0ms (0%)

sample17.2s (25.4%)

Algorithm

1×

intervals

Results

194.0ms

8000×

body

128

valid

Compiler

Compiled 17991 to 13527 computations (24.8% saved)

Pareto

0.833422614655509