Details

analyze3.0ms (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
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample8.0ms (0%)

Algorithm

1×

intervals

Results

4.0ms

256×

body

128

valid

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify99.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	7
1	7	7

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 5 to 4 computations (20% saved)

localize3.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_4891`
1×	`add-exp-log_binary64_4890` `+-commutative_binary64_4782` `flip-+_binary64_4826` `add-cube-cbrt_binary64_4887` `add-cbrt-cube_binary64_4888` `*-un-lft-identity_binary64_4852` `add-sqr-sqrt_binary64_4874` `pow1_binary64_4913` `flip3-+_binary64_4855` `sum-log_binary64_4943`

Counts

1 → 11

Calls

2 calls:

4.0ms	(+.f64 (*.f64 x x) 1)
0.0ms	(+.f64 (*.f64 x x) 1)

series31.0ms (0%)

Counts

1 → 6

Calls

1 calls:

31.0ms

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

Compiler

Compiled 37 to 38 computations (-2.7% saved)

simplify93.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4939	148
1	4939	148

prune44.0ms (0.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	7	10	17
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	7	11	18

Error

Counts

18 → 11

Compiler

Compiled 200 to 133 computations (33.5% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_4891`
1×	`add-exp-log_binary64_4890` `+-commutative_binary64_4782` `flip-+_binary64_4826` `add-cube-cbrt_binary64_4887` `add-cbrt-cube_binary64_4888` `*-un-lft-identity_binary64_4852` `add-sqr-sqrt_binary64_4874` `pow1_binary64_4913` `flip3-+_binary64_4855` `sum-log_binary64_4943`

Counts

1 → 11

Calls

2 calls:

4.0ms	(+.f64 (*.f64 x x) 1)
0.0ms	(+.f64 (*.f64 x x) 1)

series33.0ms (0%)

Counts

1 → 6

Calls

1 calls:

33.0ms

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

Compiler

Compiled 55 to 56 computations (-1.8% saved)

simplify99.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4939	148
1	4939	148

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 (3.0ms)

Iter	Nodes	Cost
0	0	0

localize11.0ms (0%)

Local error

Found 2 expressions with local error:

9.8b	(/.f64 (+.f64 (pow.f64 x 4) -1) (-.f64 (*.f64 x x) 1))
9.8b	(/.f64 (+.f64 (pow.f64 x 4) -1) (-.f64 (*.f64 x x) 1))

rewrite21.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64_4858`
38×	`*-un-lft-identity_binary64_4852` `add-sqr-sqrt_binary64_4874`
21×	`difference-of-sqr--1_binary64_4823`
16×	`difference-of-squares_binary64_4821` `add-cube-cbrt_binary64_4887`
8×	`difference-of-sqr-1_binary64_4822`
7×	`distribute-lft-out_binary64_4803` `associate-/l*_binary64_4797` `unpow-prod-down_binary64_4931` `sqr-pow_binary64_4824`
6×	`associate-/r*_binary64_4796`
3×	`add-exp-log_binary64_4890` `add-cbrt-cube_binary64_4888`
2×	`associate-/l/_binary64_4799` `associate-/r/_binary64_4798`
1×	`flip3--_binary64_4856` `flip-+_binary64_4826` `div-inv_binary64_4849` `clear-num_binary64_4851` `add-log-exp_binary64_4891` `pow1_binary64_4913` `flip--_binary64_4827` `cbrt-undiv_binary64_4886` `flip3-+_binary64_4855` `frac-2neg_binary64_4863` `div-exp_binary64_4903`

Counts

1 → 71

Calls

2 calls:

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

series82.0ms (0.1%)

Counts

1 → 6

Calls

1 calls:

82.0ms

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

Compiler

Compiled 37 to 38 computations (-2.7% saved)

simplify88.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	6453	1652

localize8.0ms (0%)

Local error

Found 6 expressions with local error:

13.0b	(cbrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3))
0.1b	(pow.f64 (+.f64 (*.f64 x x) 1) 3)
0.0b	(+.f64 (*.f64 x x) 1)
0.0b	(+.f64 (*.f64 x x) 1)
0.1b	(pow.f64 (+.f64 (*.f64 x x) 1) 3)
13.0b	(cbrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64_4883`
9×	`add-cube-cbrt_binary64_4887` `*-un-lft-identity_binary64_4852` `add-sqr-sqrt_binary64_4874`
6×	`cube-prod_binary64_4880` `unpow-prod-down_binary64_4931`
5×	`add-log-exp_binary64_4891`
4×	`add-exp-log_binary64_4890` `add-cbrt-cube_binary64_4888` `pow1_binary64_4913` `cube-div_binary64_4881`
3×	`flip-+_binary64_4826` `pow-unpow_binary64_4929` `flip3-+_binary64_4855`
2×	`cube-mult_binary64_4882` `cbrt-div_binary64_4884` `unpow3_binary64_4918` `sqr-pow_binary64_4824`
1×	`+-commutative_binary64_4782` `pow-pow_binary64_4924` `rem-cube-cbrt_binary64_4875` `pow1/3_binary64_4934` `pow-to-exp_binary64_4921` `pow-exp_binary64_4920` `rem-cbrt-cube_binary64_4876` `sum-log_binary64_4943`

Counts

3 → 59

Calls

6 calls:

6.0ms	(cbrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3))
6.0ms	(pow.f64 (+.f64 (*.f64 x x) 1) 3)
4.0ms	(+.f64 (*.f64 x x) 1)
0.0ms	(+.f64 (*.f64 x x) 1)
0.0ms	(pow.f64 (+.f64 (*.f64 x x) 1) 3)

series124.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

53.0ms	(pow.f64 (+.f64 (*.f64 x x) 1) 3)
37.0ms	(+.f64 (*.f64 x x) 1)
35.0ms	(cbrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3))

Compiler

Compiled 239 to 229 computations (4.2% saved)

simplify53.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4947	974
1	4947	974

localize10.0ms (0%)

Local error

Found 2 expressions with local error:

12.9b	(/.f64 (+.f64 1 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))))
12.9b	(/.f64 (+.f64 1 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))))

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64_4852`
16×	`times-frac_binary64_4858`
11×	`add-cube-cbrt_binary64_4887` `add-sqr-sqrt_binary64_4874`
10×	`distribute-lft-out_binary64_4803`
4×	`associate-/l_binary64_4797` `associate-/r_binary64_4796`
3×	`add-exp-log_binary64_4890` `add-cbrt-cube_binary64_4888`
2×	`flip-+_binary64_4826` `associate-/l/_binary64_4799` `associate-/r/_binary64_4798` `flip3-+_binary64_4855`
1×	`div-inv_binary64_4849` `clear-num_binary64_4851` `add-log-exp_binary64_4891` `pow1_binary64_4913` `cbrt-undiv_binary64_4886` `frac-2neg_binary64_4863` `div-exp_binary64_4903`

Counts

1 → 40

Calls

2 calls:

13.0ms	(/.f64 (+.f64 1 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))))
0.0ms	(/.f64 (+.f64 1 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))))

series118.0ms (0.2%)

Counts

1 → 6

Calls

1 calls:

117.0ms

(/.f64 (+.f64 1 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))))

Compiler

Compiled 37 to 38 computations (-2.7% saved)

simplify81.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	6052	1321

prune1.3s (1.7%)

Pruning

96 alts after pruning (90 fresh and 6 done)

	Pruned	Kept	Total
New	138	85	223
Fresh	0	5	5
Picked	0	0	0
Done	0	6	6
Total	138	96	234

Error

Counts

234 → 96

Compiler

Compiled 4016 to 2939 computations (26.8% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_4891`
1×	`add-exp-log_binary64_4890` `+-commutative_binary64_4782` `flip-+_binary64_4826` `add-cube-cbrt_binary64_4887` `add-cbrt-cube_binary64_4888` `*-un-lft-identity_binary64_4852` `add-sqr-sqrt_binary64_4874` `pow1_binary64_4913` `flip3-+_binary64_4855` `sum-log_binary64_4943`

Counts

1 → 11

Calls

2 calls:

4.0ms	(+.f64 (*.f64 x x) 1)
0.0ms	(+.f64 (*.f64 x x) 1)

series31.0ms (0%)

Counts

1 → 6

Calls

1 calls:

31.0ms

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

Compiler

Compiled 73 to 74 computations (-1.4% saved)

simplify84.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4939	148
1	4939	148

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

5.5b	(/.f64 (/.f64 (+.f64 (pow.f64 x 4) -1) (+.f64 x 1)) (-.f64 x (sqrt.f64 1)))
4.2b	(/.f64 (+.f64 (pow.f64 x 4) -1) (+.f64 x 1))
4.2b	(/.f64 (+.f64 (pow.f64 x 4) -1) (+.f64 x 1))
5.5b	(/.f64 (/.f64 (+.f64 (pow.f64 x 4) -1) (+.f64 x 1)) (-.f64 x (sqrt.f64 1)))

rewrite91.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

490×	`times-frac_binary64_4858`
453×	`*-un-lft-identity_binary64_4852`
395×	`add-sqr-sqrt_binary64_4874`
146×	`add-cube-cbrt_binary64_4887`
111×	`difference-of-sqr--1_binary64_4823`
105×	`difference-of-squares_binary64_4821`
101×	`distribute-lft-out_binary64_4803`
70×	`sqrt-prod_binary64_4868`
41×	`associate-/l*_binary64_4797`
37×	`unpow-prod-down_binary64_4931` `sqr-pow_binary64_4824`
35×	`distribute-lft-out--_binary64_4804`
20×	`associate-/r/_binary64_4798`
11×	`associate-/r*_binary64_4796`
10×	`flip-+_binary64_4826` `div-inv_binary64_4849` `flip3-+_binary64_4855`
9×	`add-exp-log_binary64_4890` `add-cbrt-cube_binary64_4888`
4×	`cbrt-undiv_binary64_4886` `div-exp_binary64_4903`
3×	`associate-/l/_binary64_4799`
2×	`clear-num_binary64_4851` `add-log-exp_binary64_4891` `pow1_binary64_4913` `frac-2neg_binary64_4863`
1×	`flip3--_binary64_4856` `flip--_binary64_4827`

Counts

2 → 351

Calls

4 calls:

23.0ms	(/.f64 (/.f64 (+.f64 (pow.f64 x 4) -1) (+.f64 x 1)) (-.f64 x (sqrt.f64 1)))
10.0ms	(/.f64 (+.f64 (pow.f64 x 4) -1) (+.f64 x 1))
0.0ms	(/.f64 (+.f64 (pow.f64 x 4) -1) (+.f64 x 1))
0.0ms	(/.f64 (/.f64 (+.f64 (pow.f64 x 4) -1) (+.f64 x 1)) (-.f64 x (sqrt.f64 1)))

series137.0ms (0.2%)

Counts

2 → 18

Calls

2 calls:

100.0ms	(/.f64 (/.f64 (+.f64 (pow.f64 x 4) -1) (+.f64 x 1)) (-.f64 x (sqrt.f64 1)))
37.0ms	(/.f64 (+.f64 (pow.f64 x 4) -1) (+.f64 x 1))

Compiler

Compiled 179 to 156 computations (12.8% saved)

simplify155.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

369 → 369

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5465	11541

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

2.0b	(exp.f64 (log.f64 (+.f64 (*.f64 x x) 1)))
1.2b	(log.f64 (+.f64 (*.f64 x x) 1))
0.1b	(pow.f64 (exp.f64 (log.f64 (+.f64 (*.f64 x x) 1))) 3)
0.0b	(+.f64 (*.f64 x x) 1)
0.1b	(pow.f64 (exp.f64 (log.f64 (+.f64 (*.f64 x x) 1))) 3)
1.2b	(log.f64 (+.f64 (*.f64 x x) 1))
2.0b	(exp.f64 (log.f64 (+.f64 (*.f64 x x) 1)))
13.0b	(cbrt.f64 (pow.f64 (exp.f64 (log.f64 (+.f64 (*.f64 x x) 1))) 3))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cube-cbrt_binary64_4887` `log-prod_binary64_4938` `*-un-lft-identity_binary64_4852` `cbrt-prod_binary64_4883` `add-sqr-sqrt_binary64_4874`
15×	`exp-sum_binary64_4898`
12×	`cube-prod_binary64_4880` `unpow-prod-down_binary64_4931`
8×	`exp-prod_binary64_4904` `pow1_binary64_4913` `log-div_binary64_4939`
6×	`exp-diff_binary64_4900`
5×	`add-exp-log_binary64_4890` `pow-pow_binary64_4924` `add-cbrt-cube_binary64_4888`
4×	`flip-+_binary64_4826` `add-log-exp_binary64_4891` `cube-div_binary64_4881` `flip3-+_binary64_4855`
3×	`pow-unpow_binary64_4929` `log-pow_binary64_4941`
2×	`cube-mult_binary64_4882` `cbrt-div_binary64_4884` `unpow3_binary64_4918` `sqr-pow_binary64_4824`
1×	`rem-exp-log_binary64_4892` `rem-cube-cbrt_binary64_4875` `pow1/3_binary64_4934` `pow-to-exp_binary64_4921` `pow-exp_binary64_4920` `rem-log-exp_binary64_4893` `rem-cbrt-cube_binary64_4876`

Counts

4 → 95

Calls

8 calls:

7.0ms	(pow.f64 (exp.f64 (log.f64 (+.f64 (*.f64 x x) 1))) 3)
7.0ms	(cbrt.f64 (pow.f64 (exp.f64 (log.f64 (+.f64 (*.f64 x x) 1))) 3))
5.0ms	(exp.f64 (log.f64 (+.f64 (*.f64 x x) 1)))
4.0ms	(log.f64 (+.f64 (*.f64 x x) 1))
0.0ms	(+.f64 (*.f64 x x) 1)

series479.0ms (0.6%)

Counts

4 → 29

Calls

4 calls:

144.0ms	(cbrt.f64 (pow.f64 (exp.f64 (log.f64 (+.f64 (*.f64 x x) 1))) 3))
136.0ms	(pow.f64 (exp.f64 (log.f64 (+.f64 (*.f64 x x) 1))) 3)
128.0ms	(exp.f64 (log.f64 (+.f64 (*.f64 x x) 1)))
71.0ms	(log.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 646 to 603 computations (6.7% saved)

simplify113.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4835	1593
1	4835	1593

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(pow.f64 (+.f64 (*.f64 x x) 1) 3)
0.0b	(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (+.f64 (.f64 x x) 1) 3))) (cbrt.f64 (sqrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3))))
0.0b	(+.f64 (*.f64 x x) 1)
0.0b	(+.f64 (*.f64 x x) 1)
5.9b	(cbrt.f64 (sqrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3)))
5.9b	(cbrt.f64 (sqrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3)))
7.2b	(sqrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3))
7.2b	(sqrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3))

rewrite34.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`sqrt-prod_binary64_4868`
30×	`cbrt-prod_binary64_4883`
24×	`add-sqr-sqrt_binary64_4874`
18×	`add-cube-cbrt_binary64_4887` `*-un-lft-identity_binary64_4852`
14×	`cube-prod_binary64_4880` `unpow-prod-down_binary64_4931`
8×	`rem-sqrt-square_binary64_4865` `sqrt-div_binary64_4869` `cube-div_binary64_4881`
6×	`sqr-pow_binary64_4824`
4×	`add-exp-log_binary64_4890` `flip-+_binary64_4826` `cube-mult_binary64_4882` `add-cbrt-cube_binary64_4888` `cbrt-div_binary64_4884` `add-log-exp_binary64_4891` `pow1_binary64_4913` `unpow3_binary64_4918` `flip3-+_binary64_4855`
2×	`pow1/2_binary64_4932` `sqrt-pow1_binary64_4870` `pow1/3_binary64_4934`

Counts

4 → 104

Calls

8 calls:

6.0ms	(cbrt.f64 (sqrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3)))
6.0ms	(cbrt.f64 (sqrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3)))
6.0ms	(sqrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3))
6.0ms	(sqrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3))
0.0ms	(+.f64 (*.f64 x x) 1)

series187.0ms (0.3%)

Counts

4 → 34

Calls

4 calls:

60.0ms	(sqrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3))
52.0ms	(sqrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3))
38.0ms	(cbrt.f64 (sqrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3)))
36.0ms	(cbrt.f64 (sqrt.f64 (pow.f64 (+.f64 (*.f64 x x) 1) 3)))

Compiler

Compiled 858 to 734 computations (14.5% saved)

simplify117.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4876	2228
1	4876	2228

prune11.1s (14.9%)

Pruning

270 alts after pruning (259 fresh and 11 done)

	Pruned	Kept	Total
New	468	180	648
Fresh	6	79	85
Picked	0	0	0
Done	0	11	11
Total	474	270	744

Error

Counts

744 → 270

Compiler

Compiled 13755 to 10612 computations (22.8% saved)

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

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

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_4852`
26×	`add-sqr-sqrt_binary64_4874`
25×	`times-frac_binary64_4858`
21×	`add-cube-cbrt_binary64_4887`
18×	`associate-l_binary64_4793`
10×	`add-exp-log_binary64_4890` `add-cbrt-cube_binary64_4888`
8×	`distribute-lft-out_binary64_4803`
6×	`flip-+_binary64_4826` `flip3-+_binary64_4855`
5×	`add-log-exp_binary64_4891` `pow1_binary64_4913`
4×	`associate-r_binary64_4792` `associate-/r*_binary64_4796` `associate-/r/_binary64_4798`
3×	`associate-/l*_binary64_4797`
2×	`unswap-sqr_binary64_4820` `frac-times_binary64_4862` `cbrt-unprod_binary64_4885` `associate-*r/_binary64_4794` `associate-/l/_binary64_4799` `div-inv_binary64_4849` `prod-exp_binary64_4901` `cbrt-undiv_binary64_4886` `div-exp_binary64_4903`
1×	`+-commutative_binary64_4782` `distribute-lft-in_binary64_4801` `clear-num_binary64_4851` `distribute-rgt-in_binary64_4802` `associate-l/_binary64_4795` `pow-prod-down_binary64_4923` `frac-2neg_binary64_4863` `sum-log_binary64_4943` `-commutative_binary64_4783`

Counts

3 → 90

Calls

6 calls:

15.0ms	(.f64 (/.f64 (+.f64 1 (.f64 x x)) (+.f64 x 1)) (+.f64 x (sqrt.f64 1)))
7.0ms	(/.f64 (+.f64 1 (*.f64 x x)) (+.f64 x 1))
3.0ms	(+.f64 1 (*.f64 x x))
0.0ms	(+.f64 1 (*.f64 x x))
0.0ms	(.f64 (/.f64 (+.f64 1 (.f64 x x)) (+.f64 x 1)) (+.f64 x (sqrt.f64 1)))

series100.0ms (0.1%)

Counts

3 → 24

Calls

3 calls:

35.0ms	(/.f64 (+.f64 1 (*.f64 x x)) (+.f64 x 1))
33.0ms	(+.f64 1 (*.f64 x x))
31.0ms	(.f64 (/.f64 (+.f64 1 (.f64 x x)) (+.f64 x 1)) (+.f64 x (sqrt.f64 1)))

Compiler

Compiled 303 to 267 computations (11.9% saved)

simplify105.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4923	1672
1	4923	1672

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_4891`
1×	`add-exp-log_binary64_4890` `+-commutative_binary64_4782` `flip-+_binary64_4826` `add-cube-cbrt_binary64_4887` `add-cbrt-cube_binary64_4888` `*-un-lft-identity_binary64_4852` `add-sqr-sqrt_binary64_4874` `pow1_binary64_4913` `flip3-+_binary64_4855` `sum-log_binary64_4943`

Counts

1 → 11

Calls

2 calls:

4.0ms	(+.f64 (*.f64 x x) 1)
0.0ms	(+.f64 (*.f64 x x) 1)

series32.0ms (0%)

Counts

1 → 6

Calls

1 calls:

32.0ms

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

Compiler

Compiled 91 to 92 computations (-1.1% saved)

simplify82.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4939	148
1	4939	148

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

5.5b	(/.f64 (/.f64 (+.f64 (pow.f64 x 4) -1) (sqrt.f64 (+.f64 -1 (.f64 x x)))) (sqrt.f64 (-.f64 (.f64 x x) 1)))
4.2b	(/.f64 (+.f64 (pow.f64 x 4) -1) (sqrt.f64 (+.f64 -1 (*.f64 x x))))
4.2b	(/.f64 (+.f64 (pow.f64 x 4) -1) (sqrt.f64 (+.f64 -1 (*.f64 x x))))
5.5b	(/.f64 (/.f64 (+.f64 (pow.f64 x 4) -1) (sqrt.f64 (+.f64 -1 (.f64 x x)))) (sqrt.f64 (-.f64 (.f64 x x) 1)))

rewrite154.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

894×	`times-frac_binary64_4858`
528×	`sqrt-prod_binary64_4868`
516×	`*-un-lft-identity_binary64_4852` `add-sqr-sqrt_binary64_4874`
333×	`add-cube-cbrt_binary64_4887`
201×	`difference-of-sqr--1_binary64_4823`
98×	`difference-of-squares_binary64_4821`
67×	`distribute-lft-out_binary64_4803` `unpow-prod-down_binary64_4931` `sqr-pow_binary64_4824`
55×	`associate-/l*_binary64_4797`
49×	`difference-of-sqr-1_binary64_4822`
24×	`sqrt-div_binary64_4869` `associate-/r/_binary64_4798`
15×	`associate-/r*_binary64_4796`
12×	`flip-+_binary64_4826` `div-inv_binary64_4849` `flip3-+_binary64_4855`
9×	`add-exp-log_binary64_4890` `add-cbrt-cube_binary64_4888`
4×	`cbrt-undiv_binary64_4886` `div-exp_binary64_4903`
3×	`associate-/l/_binary64_4799`
2×	`clear-num_binary64_4851` `add-log-exp_binary64_4891` `pow1_binary64_4913` `frac-2neg_binary64_4863`
1×	`flip3--_binary64_4856` `flip--_binary64_4827`

Counts

2 → 577

Calls

4 calls:

34.0ms	(/.f64 (/.f64 (+.f64 (pow.f64 x 4) -1) (sqrt.f64 (+.f64 -1 (.f64 x x)))) (sqrt.f64 (-.f64 (.f64 x x) 1)))
11.0ms	(/.f64 (+.f64 (pow.f64 x 4) -1) (sqrt.f64 (+.f64 -1 (*.f64 x x))))
0.0ms	(/.f64 (+.f64 (pow.f64 x 4) -1) (sqrt.f64 (+.f64 -1 (*.f64 x x))))
0.0ms	(/.f64 (/.f64 (+.f64 (pow.f64 x 4) -1) (sqrt.f64 (+.f64 -1 (.f64 x x)))) (sqrt.f64 (-.f64 (.f64 x x) 1)))

series138.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

90.0ms	(/.f64 (/.f64 (+.f64 (pow.f64 x 4) -1) (sqrt.f64 (+.f64 -1 (.f64 x x)))) (sqrt.f64 (-.f64 (.f64 x x) 1)))
48.0ms	(/.f64 (+.f64 (pow.f64 x 4) -1) (sqrt.f64 (+.f64 -1 (*.f64 x x))))

Compiler

Compiled 165 to 144 computations (12.7% saved)

simplify273.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

589 → 589

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5259	26297

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

16.2b	(/.f64 (pow.f64 (+.f64 1 (pow.f64 x 6)) 3) (pow.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))) 3))
13.0b	(cbrt.f64 (/.f64 (pow.f64 (+.f64 1 (pow.f64 x 6)) 3) (pow.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))) 3)))
0.0b	(pow.f64 (+.f64 1 (pow.f64 x 6)) 3)
0.0b	(pow.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))) 3)
0.0b	(pow.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))) 3)
0.0b	(pow.f64 (+.f64 1 (pow.f64 x 6)) 3)
13.0b	(cbrt.f64 (/.f64 (pow.f64 (+.f64 1 (pow.f64 x 6)) 3) (pow.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))) 3)))
16.2b	(/.f64 (pow.f64 (+.f64 1 (pow.f64 x 6)) 3) (pow.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))) 3))

rewrite150.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

425×	`*-un-lft-identity_binary64_4852`
392×	`times-frac_binary64_4858`
240×	`cube-prod_binary64_4880` `unpow-prod-down_binary64_4931`
202×	`cbrt-prod_binary64_4883`
185×	`add-cube-cbrt_binary64_4887` `add-sqr-sqrt_binary64_4874`
120×	`distribute-lft-out_binary64_4803`
60×	`cube-mult_binary64_4882` `unpow3_binary64_4918` `sqr-pow_binary64_4824`
18×	`add-exp-log_binary64_4890`
14×	`associate-/l_binary64_4797` `associate-/r_binary64_4796`
10×	`cube-div_binary64_4881`
9×	`div-exp_binary64_4903`
8×	`add-cbrt-cube_binary64_4888` `pow-to-exp_binary64_4921` `pow-exp_binary64_4920`
6×	`pow1_binary64_4913` `pow-unpow_binary64_4929`
5×	`flip-+_binary64_4826` `flip3-+_binary64_4855`
4×	`add-log-exp_binary64_4891` `associate-/r/_binary64_4798`
2×	`pow-pow_binary64_4924` `rem-cube-cbrt_binary64_4875` `associate-/l/_binary64_4799` `div-inv_binary64_4849`
1×	`clear-num_binary64_4851` `pow1/3_binary64_4934` `cbrt-div_binary64_4884` `cbrt-undiv_binary64_4886` `frac-2neg_binary64_4863`

Counts

4 → 513

Calls

8 calls:

31.0ms	(cbrt.f64 (/.f64 (pow.f64 (+.f64 1 (pow.f64 x 6)) 3) (pow.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))) 3)))
21.0ms	(/.f64 (pow.f64 (+.f64 1 (pow.f64 x 6)) 3) (pow.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))) 3))
8.0ms	(pow.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))) 3)
6.0ms	(pow.f64 (+.f64 1 (pow.f64 x 6)) 3)
0.0ms	(pow.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))) 3)

series603.0ms (0.8%)

Counts

4 → 42

Calls

4 calls:

309.0ms	(pow.f64 (+.f64 1 (pow.f64 x 6)) 3)
114.0ms	(/.f64 (pow.f64 (+.f64 1 (pow.f64 x 6)) 3) (pow.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))) 3))
112.0ms	(cbrt.f64 (/.f64 (pow.f64 (+.f64 1 (pow.f64 x 6)) 3) (pow.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))) 3)))
67.0ms	(pow.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))) 3)

Compiler

Compiled 701 to 616 computations (12.1% saved)

simplify221.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

555 → 555

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5549	21485

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (+.f64 1 (sqrt.f64 (pow.f64 x 4))) (sqrt.f64 (+.f64 x 1)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 1 (sqrt.f64 (pow.f64 x 4)))
0.1b	(*.f64 (/.f64 (+.f64 1 (sqrt.f64 (pow.f64 x 4))) (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 -1 (sqrt.f64 (pow.f64 x 4))) (sqrt.f64 (+.f64 x 1))))
3.4b	(/.f64 (*.f64 (/.f64 (+.f64 1 (sqrt.f64 (pow.f64 x 4))) (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 -1 (sqrt.f64 (pow.f64 x 4))) (sqrt.f64 (+.f64 x 1)))) (-.f64 x (sqrt.f64 1)))
20.4b	(sqrt.f64 (pow.f64 x 4))
20.4b	(sqrt.f64 (pow.f64 x 4))

rewrite117.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`*-un-lft-identity_binary64_4852`
95×	`add-sqr-sqrt_binary64_4874`
82×	`times-frac_binary64_4858`
67×	`sqrt-prod_binary64_4868`
44×	`add-cube-cbrt_binary64_4887`
41×	`associate-l_binary64_4793`
34×	`add-exp-log_binary64_4890` `add-cbrt-cube_binary64_4888` `associate-r_binary64_4792`
30×	`distribute-lft-out_binary64_4803`
13×	`cbrt-undiv_binary64_4886` `div-exp_binary64_4903`
9×	`unswap-sqr_binary64_4820`
8×	`cbrt-unprod_binary64_4885` `unpow-prod-down_binary64_4931` `prod-exp_binary64_4901`
7×	`associate-/r*_binary64_4796`
6×	`difference-of-squares_binary64_4821` `rem-sqrt-square_binary64_4865` `associate-/r/_binary64_4798` `pow1_binary64_4913`
4×	`add-log-exp_binary64_4891` `sqrt-div_binary64_4869` `sqr-pow_binary64_4824`
3×	`associate-/l/_binary64_4799` `div-inv_binary64_4849`
2×	`distribute-lft-out--_binary64_4804` `pow1/2_binary64_4932` `frac-times_binary64_4862` `flip-+_binary64_4826` `associate-r/_binary64_4794` `sqrt-pow1_binary64_4870` `associate-l/_binary64_4795` `flip3-+_binary64_4855`
1×	`flip3--_binary64_4856` `associate-/l_binary64_4797` `clear-num_binary64_4851` `flip--_binary64_4827` `pow-prod-down_binary64_4923` `frac-2neg_binary64_4863` `-commutative_binary64_4783`

Counts

4 → 182

Calls

8 calls:

47.0ms	(*.f64 (/.f64 (+.f64 1 (sqrt.f64 (pow.f64 x 4))) (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 -1 (sqrt.f64 (pow.f64 x 4))) (sqrt.f64 (+.f64 x 1))))
35.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 (sqrt.f64 (pow.f64 x 4))) (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 -1 (sqrt.f64 (pow.f64 x 4))) (sqrt.f64 (+.f64 x 1)))) (-.f64 x (sqrt.f64 1)))
3.0ms	(sqrt.f64 (pow.f64 x 4))
2.0ms	(sqrt.f64 (pow.f64 x 4))
0.0ms	(+.f64 1 (sqrt.f64 (pow.f64 x 4)))

series246.0ms (0.3%)

Counts

4 → 24

Calls

4 calls:

156.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 (sqrt.f64 (pow.f64 x 4))) (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 -1 (sqrt.f64 (pow.f64 x 4))) (sqrt.f64 (+.f64 x 1)))) (-.f64 x (sqrt.f64 1)))
43.0ms	(*.f64 (/.f64 (+.f64 1 (sqrt.f64 (pow.f64 x 4))) (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 -1 (sqrt.f64 (pow.f64 x 4))) (sqrt.f64 (+.f64 x 1))))
24.0ms	(sqrt.f64 (pow.f64 x 4))
23.0ms	(sqrt.f64 (pow.f64 x 4))

Compiler

Compiled 503 to 432 computations (14.1% saved)

simplify97.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4989	5748
1	4989	5748

prune32.0s (43%)

Pruning

561 alts after pruning (545 fresh and 16 done)

	Pruned	Kept	Total
New	1155	326	1481
Fresh	35	219	254
Picked	0	0	0
Done	0	16	16
Total	1190	561	1751

Error

Counts

1751 → 561

Compiler

Compiled 16621 to 12215 computations (26.5% saved)

simplify592.0ms (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4993	37749
1	4993	37749

regimes3.7s (4.9%)

Compiler: Compiled 40536 to 32182 computations (20.6% saved)

bsearch0.0ms (0%)

regimes39.0ms (0.1%)

Compiler: Compiled 26 to 28 computations (-7.7% saved)

bsearch0.0ms (0%)

Compiler: Compiled 3 to 2 computations (33.3% saved)

regimes10.0ms (0%)

Accuracy

Total 0.0b remaining (100%)

Threshold costs 0.0b (100%)

Compiler

Compiled 8 to 11 computations (-37.5% saved)

bsearch2.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	22
1	11	22

end0.0ms (0%)

sample20.7s (27.8%)

Algorithm

1×

intervals

Results

129.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 20318 to 16130 computations (20.6% saved)

Pareto

0.5302689604248855