Details

analyze4.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50%	0.4%	49.6%	10
50.2%	0.2%	49.6%	11
50.2%	0.1%	49.7%	12
50.2%	0%	49.8%	13
50.2%	0%	49.8%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample13.0ms (0%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify165.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5037	9

prune8.0ms (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 → 2

Compiler

Compiled 6 to 5 computations (16.7% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`exp-prod_binary64_130`
4×	`add-sqr-sqrt_binary64_100` `add-log-exp_binary64_117` `exp-sum_binary64_124` `*-un-lft-identity_binary64_78`
3×	`add-cube-cbrt_binary64_113` `cancel-sign-sub-inv_binary64_44`
2×	`rem-exp-log_binary64_118` `difference-of-squares_binary64_47`
1×	`add-cbrt-cube_binary64_114` `diff-log_binary64_170` `exp-diff_binary64_126` `add-exp-log_binary64_116` `difference-of-sqr-1_binary64_48` `sub-neg_binary64_71` `pow1_binary64_139`

Counts

1 → 20

Calls

2 calls:

6.0ms	(exp.f64 (-.f64 (*.f64 x x) 1))
0.0ms	(exp.f64 (-.f64 (*.f64 x x) 1))

series23.0ms (0.1%)

Counts

1 → 6

Calls

1 calls:

23.0ms

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

Compiler

Compiled 80 to 78 computations (2.5% saved)

simplify72.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4906	266
1	4906	266

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
0.0b	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`exp-prod_binary64_130`
6×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
5×	`distribute-lft-neg-in_binary64_35` `add-log-exp_binary64_117` `distribute-rgt-neg-in_binary64_36`
4×	`add-cube-cbrt_binary64_113` `difference-of-squares_binary64_47`
3×	`rem-exp-log_binary64_118`
2×	`exp-sum_binary64_124` `distribute-neg-in_binary64_39` `neg-log_binary64_171`
1×	`add-cbrt-cube_binary64_114` `neg-mul-1_binary64_74` `diff-log_binary64_170` `exp-neg_binary64_125` `exp-diff_binary64_126` `add-exp-log_binary64_116` `neg-sub0_binary64_73` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71` `pow1_binary64_139`

Counts

1 → 28

Calls

2 calls:

6.0ms	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
0.0ms	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

series23.0ms (0.1%)

Counts

1 → 6

Calls

1 calls:

23.0ms

(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

Compiler

Compiled 80 to 78 computations (2.5% saved)

simplify96.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4829	343
1	4829	343

prune185.0ms (0.7%)

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	34	26	60
Fresh	0	0	0
Picked	0	0	0
Done	0	2	2
Total	34	28	62

Error

Counts

62 → 28

Compiler

Compiled 765 to 529 computations (30.8% saved)

localize6.0ms (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

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 1 (*.f64 x x)) E.f64)
0.0b	(/.f64 (+.f64 1 (*.f64 x x)) E.f64)

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `times-frac_binary64_84` `*-un-lft-identity_binary64_78`
4×	`add-exp-log_binary64_116`
3×	`add-cbrt-cube_binary64_114` `associate-/l_binary64_23` `associate-/r_binary64_22`
2×	`div-exp_binary64_129` `associate-/l/_binary64_25`
1×	`add-log-exp_binary64_117` `cbrt-undiv_binary64_112` `flip-+_binary64_52` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `pow1_binary64_139` `e-exp-1_binary64_123` `flip3-+_binary64_81`

Counts

1 → 30

Calls

2 calls:

5.0ms	(/.f64 (+.f64 1 (*.f64 x x)) E.f64)
0.0ms	(/.f64 (+.f64 1 (*.f64 x x)) E.f64)

series54.0ms (0.2%)

Counts

1 → 6

Calls

1 calls:

54.0ms

(/.f64 (+.f64 1 (*.f64 x x)) E.f64)

Compiler

Compiled 67 to 62 computations (7.5% saved)

simplify83.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4879	592
1	4879	592

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 (+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4)))) E.f64)
0.0b	(+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4)))
0.0b	(+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4)))
0.0b	(/.f64 (+.f64 1 (+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4)))) E.f64)

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_78`
12×	`times-frac_binary64_84`
11×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
5×	`add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `associate-/l*_binary64_23` `distribute-lft-out_binary64_29`
3×	`associate-/r*_binary64_22`
2×	`div-exp_binary64_129` `flip-+_binary64_52` `associate-/l/_binary64_25` `pow1_binary64_139` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `sum-log_binary64_169` `e-exp-1_binary64_123`

Counts

2 → 45

Calls

4 calls:

9.0ms	(/.f64 (+.f64 1 (+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4)))) E.f64)
4.0ms	(+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4)))
0.0ms	(+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4)))
0.0ms	(/.f64 (+.f64 1 (+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4)))) E.f64)

series213.0ms (0.8%)

Counts

2 → 15

Calls

2 calls:

142.0ms	(/.f64 (+.f64 1 (+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4)))) E.f64)
70.0ms	(+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4)))

Compiler

Compiled 257 to 229 computations (10.9% saved)

simplify98.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4915	1416
1	4915	1416

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 (+.f64 x 1)) (-.f64 x (sqrt.f64 1)))
0.0b	(exp.f64 (+.f64 x 1))
0.0b	(exp.f64 (+.f64 x 1))
0.0b	(pow.f64 (exp.f64 (+.f64 x 1)) (-.f64 x (sqrt.f64 1)))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_78`
13×	`add-sqr-sqrt_binary64_100`
8×	`add-cube-cbrt_binary64_113` `exp-prod_binary64_130`
7×	`unpow-prod-up_binary64_156` `pow-unpow_binary64_155`
6×	`cancel-sign-sub-inv_binary64_44`
5×	`sqrt-prod_binary64_94` `add-log-exp_binary64_117` `pow-pow_binary64_150`
4×	`unpow-prod-down_binary64_157`
3×	`difference-of-squares_binary64_47` `pow1_binary64_139`
2×	`add-cbrt-cube_binary64_114` `exp-sum_binary64_124` `rem-exp-log_binary64_118` `add-exp-log_binary64_116` `distribute-lft-out_binary64_29`
1×	`pow-sub_binary64_154` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `distribute-lft-out--_binary64_30` `sqr-pow_binary64_50` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

2 → 48

Calls

4 calls:

10.0ms	(pow.f64 (exp.f64 (+.f64 x 1)) (-.f64 x (sqrt.f64 1)))
4.0ms	(exp.f64 (+.f64 x 1))
0.0ms	(exp.f64 (+.f64 x 1))
0.0ms	(pow.f64 (exp.f64 (+.f64 x 1)) (-.f64 x (sqrt.f64 1)))

series62.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

47.0ms	(pow.f64 (exp.f64 (+.f64 x 1)) (-.f64 x (sqrt.f64 1)))
15.0ms	(exp.f64 (+.f64 x 1))

Compiler

Compiled 192 to 170 computations (11.5% saved)

simplify83.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4870	775
1	4870	775

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`sqrt-prod_binary64_94` `pow-unpow_binary64_155`
16×	`add-sqr-sqrt_binary64_100` `exp-prod_binary64_130` `*-un-lft-identity_binary64_78`
12×	`add-cube-cbrt_binary64_113`
9×	`pow-pow_binary64_150`
8×	`distribute-lft-neg-in_binary64_35` `difference-of-squares_binary64_47` `distribute-rgt-neg-in_binary64_36`
3×	`add-log-exp_binary64_117` `unpow-prod-down_binary64_157` `pow1_binary64_139`
2×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
1×	`pow-sub_binary64_154` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `neg-mul-1_binary64_74` `rem-exp-log_binary64_118` `sqr-pow_binary64_50` `neg-sub0_binary64_73` `pow-neg_binary64_151`

Counts

2 → 60

Calls

4 calls:

9.0ms	(pow.f64 (exp.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))
4.0ms	(exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0ms	(exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0ms	(pow.f64 (exp.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))

series98.0ms (0.4%)

Counts

2 → 12

Calls

2 calls:

61.0ms	(pow.f64 (exp.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))
36.0ms	(exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

Compiler

Compiled 272 to 242 computations (11% saved)

simplify132.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4883	1222
1	4883	1222

prune2.5s (9.3%)

Pruning

131 alts after pruning (125 fresh and 6 done)

	Pruned	Kept	Total
New	122	106	228
Fresh	2	19	21
Picked	0	0	0
Done	1	6	7
Total	125	131	256

Error

Counts

256 → 131

Compiler

Compiled 5276 to 3726 computations (29.4% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
0.0b	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`exp-prod_binary64_130`
6×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
5×	`distribute-lft-neg-in_binary64_35` `add-log-exp_binary64_117` `distribute-rgt-neg-in_binary64_36`
4×	`add-cube-cbrt_binary64_113` `difference-of-squares_binary64_47`
3×	`rem-exp-log_binary64_118`
2×	`exp-sum_binary64_124` `distribute-neg-in_binary64_39` `neg-log_binary64_171`
1×	`add-cbrt-cube_binary64_114` `neg-mul-1_binary64_74` `diff-log_binary64_170` `exp-neg_binary64_125` `exp-diff_binary64_126` `add-exp-log_binary64_116` `neg-sub0_binary64_73` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71` `pow1_binary64_139`

Counts

1 → 28

Calls

2 calls:

7.0ms	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
0.0ms	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

series22.0ms (0.1%)

Counts

1 → 6

Calls

1 calls:

22.0ms

(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

Compiler

Compiled 96 to 94 computations (2.1% saved)

simplify93.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4829	343
1	4829	343

localize3.0ms (0%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (*.f64 x x) E.f64)
0.2b	(/.f64 (*.f64 x x) E.f64)

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log_binary64_116`
6×	`add-cbrt-cube_binary64_114`
4×	`div-exp_binary64_129`
3×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `times-frac_binary64_84` `associate-/r_binary64_22` `-un-lft-identity_binary64_78`
2×	`cbrt-undiv_binary64_112` `prod-exp_binary64_127` `e-exp-1_binary64_123`
1×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77` `pow1_binary64_139`

Counts

1 → 23

Calls

2 calls:

5.0ms	(/.f64 (*.f64 x x) E.f64)
0.0ms	(/.f64 (*.f64 x x) E.f64)

series30.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

30.0ms

(/.f64 (*.f64 x x) E.f64)

Compiler

Compiled 30 to 30 computations (0% saved)

simplify72.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5023	254

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow-pow_binary64_150`
6×	`exp-prod_binary64_130`
5×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`pow-unpow_binary64_155`
3×	`sqrt-prod_binary64_94` `unpow-prod-down_binary64_157`
2×	`pow1_binary64_139`
1×	`add-cbrt-cube_binary64_114` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `add-log-exp_binary64_117` `sqr-pow_binary64_50` `unpow-prod-up_binary64_156` `add-exp-log_binary64_116` `difference-of-sqr--1_binary64_49`

Counts

1 → 25

Calls

2 calls:

7.0ms	(pow.f64 (exp.f64 (sqrt.f64 1)) (+.f64 (*.f64 x x) -1))
0.0ms	(pow.f64 (exp.f64 (sqrt.f64 1)) (+.f64 (*.f64 x x) -1))

series42.0ms (0.2%)

Counts

1 → 6

Calls

1 calls:

42.0ms

(pow.f64 (exp.f64 (sqrt.f64 1)) (+.f64 (*.f64 x x) -1))

Compiler

Compiled 84 to 82 computations (2.4% saved)

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5101	418

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 E.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0b	(pow.f64 (pow.f64 E.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))
0.0b	(pow.f64 (pow.f64 E.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))
0.0b	(pow.f64 E.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`pow-unpow_binary64_155`
15×	`sqrt-prod_binary64_94` `add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
13×	`unpow-prod-down_binary64_157`
12×	`add-cube-cbrt_binary64_113`
8×	`distribute-lft-neg-in_binary64_35` `pow-exp_binary64_146` `distribute-rgt-neg-in_binary64_36`
6×	`difference-of-squares_binary64_47`
5×	`add-exp-log_binary64_116`
3×	`pow-to-exp_binary64_147` `sqr-pow_binary64_50` `pow1_binary64_139`
2×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `pow-pow_binary64_150` `e-exp-1_binary64_123`
1×	`pow-sub_binary64_154` `neg-mul-1_binary64_74` `neg-sub0_binary64_73` `pow-neg_binary64_151`

Counts

2 → 66

Calls

4 calls:

6.0ms	(pow.f64 (pow.f64 E.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))
4.0ms	(pow.f64 E.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0ms	(pow.f64 (pow.f64 E.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))
0.0ms	(pow.f64 E.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

series136.0ms (0.5%)

Counts

2 → 12

Calls

2 calls:

73.0ms	(pow.f64 (pow.f64 E.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))
62.0ms	(pow.f64 E.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

Compiler

Compiled 276 to 246 computations (10.9% saved)

simplify71.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5874	1465

localize17.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (.f64 (cbrt.f64 (+.f64 1 (.f64 x x))) (cbrt.f64 (+.f64 1 (.f64 x x)))) (.f64 (cbrt.f64 E.f64) (cbrt.f64 E.f64)))
0.0b	(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)))
1.0b	(*.f64 (cbrt.f64 E.f64) (cbrt.f64 E.f64))
1.6b	(cbrt.f64 E.f64)
1.6b	(cbrt.f64 E.f64)
1.6b	(cbrt.f64 E.f64)

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_109`
23×	`add-sqr-sqrt_binary64_100`
15×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
11×	`pow1_binary64_139`
9×	`pow1/3_binary64_160`
6×	`associate-l_binary64_19` `swap-sqr_binary64_45` `associate-r_binary64_18` `add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `unswap-sqr_binary64_46`
2×	`pow-sqr_binary64_51` `pow-prod-up_binary64_148` `pow-prod-down_binary64_149`
1×	`pow2_binary64_159` `*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-plus_binary64_141`

Counts

4 → 73

Calls

8 calls:

6.0ms	(*.f64 (cbrt.f64 E.f64) (cbrt.f64 E.f64))
1.0ms	(cbrt.f64 E.f64)
1.0ms	(cbrt.f64 E.f64)
1.0ms	(cbrt.f64 E.f64)
0.0ms	(cbrt.f64 (+.f64 1 (*.f64 x x)))

series0.0ms (0%)

Counts

4 → 0

Calls

4 calls:

0.0ms	(cbrt.f64 E.f64)
0.0ms	(*.f64 (cbrt.f64 E.f64) (cbrt.f64 E.f64))
0.0ms	(cbrt.f64 E.f64)
0.0ms	(cbrt.f64 E.f64)

simplify72.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5077	595

prune3.6s (13.6%)

Pruning

177 alts after pruning (166 fresh and 11 done)

	Pruned	Kept	Total
New	184	58	242
Fresh	12	108	120
Picked	0	0	0
Done	0	11	11
Total	196	177	373

Error

Counts

373 → 177

Compiler

Compiled 7006 to 4554 computations (35% saved)

localize7.0ms (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

localize4.0ms (0%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 E.f64 x)
0.1b	(/.f64 x (/.f64 E.f64 x))
0.1b	(/.f64 x (/.f64 E.f64 x))
0.4b	(/.f64 E.f64 x)

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64_84`
52×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
16×	`associate-/r*_binary64_22`
12×	`add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114`
7×	`div-exp_binary64_129`
6×	`div-inv_binary64_75` `associate-/l*_binary64_23`
4×	`cbrt-undiv_binary64_112`
2×	`add-log-exp_binary64_117` `frac-2neg_binary64_89` `clear-num_binary64_77` `pow1_binary64_139` `e-exp-1_binary64_123`
1×	`associate-/r/_binary64_24`

Counts

2 → 99

Calls

4 calls:

6.0ms	(/.f64 x (/.f64 E.f64 x))
3.0ms	(/.f64 E.f64 x)
0.0ms	(/.f64 x (/.f64 E.f64 x))
0.0ms	(/.f64 E.f64 x)

series52.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

33.0ms	(/.f64 x (/.f64 E.f64 x))
19.0ms	(/.f64 E.f64 x)

Compiler

Compiled 60 to 54 computations (10% saved)

simplify114.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4910	1455
1	4910	1455

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 -1 x))
0.0b	(pow.f64 (exp.f64 (-.f64 -1 x)) (-.f64 (sqrt.f64 1) x))
0.0b	(pow.f64 (exp.f64 (-.f64 -1 x)) (-.f64 (sqrt.f64 1) x))
0.0b	(exp.f64 (-.f64 -1 x))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_100`
16×	`*-un-lft-identity_binary64_78`
10×	`exp-prod_binary64_130`
9×	`add-cube-cbrt_binary64_113` `cancel-sign-sub-inv_binary64_44`
8×	`exp-sum_binary64_124`
7×	`unpow-prod-down_binary64_157` `pow-unpow_binary64_155`
6×	`pow-pow_binary64_150`
5×	`add-log-exp_binary64_117` `difference-of-squares_binary64_47`
4×	`unpow-prod-up_binary64_156`
3×	`distribute-lft-out--_binary64_30` `sub-neg_binary64_71` `pow1_binary64_139`
2×	`add-cbrt-cube_binary64_114` `sqrt-prod_binary64_94` `rem-exp-log_binary64_118` `add-exp-log_binary64_116`
1×	`pow-sub_binary64_154` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `diff-log_binary64_170` `sqr-pow_binary64_50` `exp-diff_binary64_126`

Counts

2 → 54

Calls

4 calls:

11.0ms	(pow.f64 (exp.f64 (-.f64 -1 x)) (-.f64 (sqrt.f64 1) x))
6.0ms	(exp.f64 (-.f64 -1 x))
0.0ms	(pow.f64 (exp.f64 (-.f64 -1 x)) (-.f64 (sqrt.f64 1) x))
0.0ms	(exp.f64 (-.f64 -1 x))

series47.0ms (0.2%)

Counts

2 → 9

Calls

2 calls:

27.0ms	(pow.f64 (exp.f64 (-.f64 -1 x)) (-.f64 (sqrt.f64 1) x))
20.0ms	(exp.f64 (-.f64 -1 x))

Compiler

Compiled 200 to 186 computations (7% saved)

simplify68.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4877	789
1	4877	789

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow-unpow_binary64_155`
15×	`sqrt-prod_binary64_94`
14×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
11×	`add-cube-cbrt_binary64_113`
10×	`unpow-prod-down_binary64_157`
8×	`distribute-lft-neg-in_binary64_35` `exp-prod_binary64_130` `distribute-rgt-neg-in_binary64_36`
6×	`difference-of-squares_binary64_47`
4×	`pow-exp_binary64_146`
3×	`add-log-exp_binary64_117` `add-exp-log_binary64_116`
2×	`add-cbrt-cube_binary64_114` `pow-to-exp_binary64_147` `sqr-pow_binary64_50` `pow1_binary64_139`
1×	`pow-sub_binary64_154` `neg-mul-1_binary64_74` `rem-exp-log_binary64_118` `pow-pow_binary64_150` `neg-sub0_binary64_73` `pow-neg_binary64_151`

Counts

2 → 58

Calls

4 calls:

8.0ms	(pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) 1) (neg.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))
4.0ms	(exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0ms	(exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0ms	(pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) 1) (neg.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))

series99.0ms (0.4%)

Counts

2 → 12

Calls

2 calls:

66.0ms	(pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) 1) (neg.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))
33.0ms	(exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

Compiler

Compiled 296 to 266 computations (10.1% saved)

simplify109.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4889	1278
1	4889	1278

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(cbrt.f64 (+.f64 x 1))
0.0b	(cbrt.f64 (+.f64 x 1))
0.0b	(cbrt.f64 (+.f64 x 1))
0.0b	(exp.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))
0.0b	(exp.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))
0.0b	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 x 1)))
0.0b	(pow.f64 (pow.f64 (exp.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 x 1))) (-.f64 x (sqrt.f64 1)))
0.0b	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))

rewrite48.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64_78`
33×	`add-sqr-sqrt_binary64_100`
28×	`cbrt-prod_binary64_109`
20×	`add-cube-cbrt_binary64_113`
14×	`pow-unpow_binary64_155`
13×	`unpow-prod-down_binary64_157`
12×	`cbrt-div_binary64_110` `pow1_binary64_139`
9×	`swap-sqr_binary64_45`
7×	`associate-l_binary64_19` `add-log-exp_binary64_117` `associate-r_binary64_18` `unpow-prod-up_binary64_156` `add-exp-log_binary64_116` `distribute-lft-out_binary64_29`
6×	`flip-+_binary64_52` `pow1/3_binary64_160` `cancel-sign-sub-inv_binary64_44` `flip3-+_binary64_81`
5×	`sqrt-prod_binary64_94` `pow-exp_binary64_146`
4×	`add-cbrt-cube_binary64_114` `frac-times_binary64_88` `pow-pow_binary64_150` `unswap-sqr_binary64_46`
3×	`pow-to-exp_binary64_147` `sqr-pow_binary64_50` `difference-of-squares_binary64_47`
2×	`pow-sqr_binary64_51` `exp-to-pow_binary64_140` `pow-prod-up_binary64_148` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `exp-prod_binary64_130` `associate-r/_binary64_20`
1×	`pow2_binary64_159` `pow-sub_binary64_154` `*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `distribute-lft-out--_binary64_30` `rem-exp-log_binary64_118` `pow-plus_binary64_141` `sub-neg_binary64_71`

Counts

4 → 121

Calls

8 calls:

12.0ms	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
8.0ms	(exp.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))
8.0ms	(pow.f64 (pow.f64 (exp.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 x 1))) (-.f64 x (sqrt.f64 1)))
7.0ms	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 x 1)))
0.0ms	(exp.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))

series516.0ms (1.9%)

Counts

4 → 36

Calls

4 calls:

249.0ms	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 x 1)))
122.0ms	(pow.f64 (pow.f64 (exp.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 x 1))) (-.f64 x (sqrt.f64 1)))
79.0ms	(exp.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))
65.0ms	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))

Compiler

Compiled 1402 to 1222 computations (12.8% saved)

simplify112.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4972	3610
1	4972	3610

prune7.7s (28.8%)

Pruning

282 alts after pruning (266 fresh and 16 done)

	Pruned	Kept	Total
New	278	117	395
Fresh	12	149	161
Picked	0	0	0
Done	0	16	16
Total	290	282	572

Error

Counts

572 → 282

Compiler

Compiled 5363 to 3758 computations (29.9% saved)

simplify336.0ms (1.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (151.0ms)

Iter	Nodes	Cost
0	5065	14641

regimes1.6s (5.8%)

Compiler: Compiled 20853 to 16115 computations (22.7% saved)

bsearch0.0ms (0%)

regimes123.0ms (0.5%)

Compiler: Compiled 983 to 842 computations (14.3% saved)

bsearch0.0ms (0%)

regimes32.0ms (0.1%)

Compiler: Compiled 166 to 138 computations (16.9% saved)

bsearch0.0ms (0%)

regimes27.0ms (0.1%)

Compiler: Compiled 118 to 102 computations (13.6% saved)

bsearch0.0ms (0%)

regimes23.0ms (0.1%)

Compiler: Compiled 74 to 68 computations (8.1% saved)

bsearch0.0ms (0%)

regimes20.0ms (0.1%)

Accuracy

Total 0.0b remaining (95%)

Threshold costs 0.0b (95%)

Compiler

Compiled 44 to 42 computations (4.5% saved)

bsearch4.0ms (0%)

Compiler: Compiled 48 to 38 computations (20.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	73
1	50	73

end1.0ms (0%)

sample7.4s (27.4%)

Algorithm

1×

intervals

Results

239.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 7097 to 5489 computations (22.7% saved)

Pareto

0.9648143638833722