Details

analyze68.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample21.0ms (0%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify130.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5126	25

prune2.0ms (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

0.2b

Counts

2 → 1

Compiler

Compiled 17 to 12 computations (29.4% saved)

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.0b	(.f64 4 (.f64 b b))
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
0.0b	(.f64 4 (.f64 b b))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log_binary64_2844` `pow1_binary64_2867`
8×	`add-cbrt-cube_binary64_2842`
7×	`add-sqr-sqrt_binary64_2828`
6×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
5×	`add-log-exp_binary64_2845`
3×	`associate-l_binary64_2747` `prod-exp_binary64_2855` `pow-unpow_binary64_2883` `cbrt-unprod_binary64_2839` `unpow-prod-down_binary64_2885` `pow-prod-down_binary64_2877`
1×	`pow-exp_binary64_2874` `-commutative_binary64_2737` `pow-pow_binary64_2878` `pow-to-exp_binary64_2875` `flip-+_binary64_2780` `sum-log_binary64_2897` `flip3-+_binary64_2809` `sqr-pow_binary64_2778` `associate-r*_binary64_2746` `unpow2_binary64_2871` `unswap-sqr_binary64_2774` `+-commutative_binary64_2736`

Counts

3 → 48

Calls

6 calls:

9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
6.0ms	(.f64 4 (.f64 b b))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
0.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series596.0ms (0.7%)

Counts

3 → 39

Calls

3 calls:

375.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
195.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
26.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 1044 to 913 computations (12.5% saved)

simplify71.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5040	1394

prune257.0ms (0.3%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	58	29	87
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	58	30	88

Error

Counts

88 → 30

Compiler

Compiled 1689 to 954 computations (43.5% saved)

localize14.0ms (0%)

Local error

Found 6 expressions with local error:

2.4b	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
0.0b	(.f64 4 (.f64 b b))
0.0b	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b)))
0.0b	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b)))
0.0b	(.f64 4 (.f64 b b))
2.4b	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))

rewrite45.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `pow1_binary64_2867`
18×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `pow-prod-down_binary64_2877`
12×	`add-log-exp_binary64_2845`
6×	`sum-log_binary64_2897`
5×	`add-sqr-sqrt_binary64_2828`
4×	`associate-l_binary64_2747` `*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
2×	`-commutative_binary64_2737` `associate-r*_binary64_2746`
1×	`associate-+l+_binary64_2739` `flip-+_binary64_2780` `flip3-+_binary64_2809` `unswap-sqr_binary64_2774` `+-commutative_binary64_2736`

Counts

3 → 61

Calls

6 calls:

21.0ms	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b)))
10.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
6.0ms	(.f64 4 (.f64 b b))
0.0ms	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b)))
0.0ms	(.f64 4 (.f64 b b))

series508.0ms (0.6%)

Counts

3 → 27

Calls

3 calls:

384.0ms	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b)))
95.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
28.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 900 to 781 computations (13.2% saved)

simplify63.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5483	1488

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

1.6b	(.f64 (.f64 b b) (+.f64 4 (+.f64 (.f64 b b) (.f64 (*.f64 a a) 2))))
0.0b	(.f64 (.f64 a a) 2)
0.0b	(+.f64 4 (+.f64 (.f64 b b) (.f64 (*.f64 a a) 2)))
0.0b	(.f64 (.f64 a a) 2)
0.0b	(+.f64 4 (+.f64 (.f64 b b) (.f64 (*.f64 a a) 2)))
1.6b	(.f64 (.f64 b b) (+.f64 4 (+.f64 (.f64 b b) (.f64 (*.f64 a a) 2))))

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `pow1_binary64_2867`
9×	`*-un-lft-identity_binary64_2806`
8×	`add-log-exp_binary64_2845`
7×	`add-sqr-sqrt_binary64_2828` `associate-r_binary64_2746`
6×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `pow-prod-down_binary64_2877`
5×	`add-cube-cbrt_binary64_2841`
3×	`sum-log_binary64_2897`
2×	`associate-l_binary64_2747` `distribute-lft-out_binary64_2757` `-commutative_binary64_2737` `flip-+_binary64_2780` `flip3-+_binary64_2809` `associate-r/_binary64_2748` `unswap-sqr_binary64_2774`
1×	`distribute-lft-in_binary64_2755` `associate-+r+_binary64_2738` `distribute-rgt-in_binary64_2756` `+-commutative_binary64_2736`

Counts

3 → 57

Calls

6 calls:

11.0ms	(.f64 (.f64 b b) (+.f64 4 (+.f64 (.f64 b b) (.f64 (*.f64 a a) 2))))
6.0ms	(+.f64 4 (+.f64 (.f64 b b) (.f64 (*.f64 a a) 2)))
6.0ms	(.f64 (.f64 a a) 2)
0.0ms	(+.f64 4 (+.f64 (.f64 b b) (.f64 (*.f64 a a) 2)))
0.0ms	(.f64 (.f64 b b) (+.f64 4 (+.f64 (.f64 b b) (.f64 (*.f64 a a) 2))))

series348.0ms (0.4%)

Counts

3 → 27

Calls

3 calls:

201.0ms	(.f64 (.f64 b b) (+.f64 4 (+.f64 (.f64 b b) (.f64 (*.f64 a a) 2))))
121.0ms	(+.f64 4 (+.f64 (.f64 b b) (.f64 (*.f64 a a) 2)))
25.0ms	(.f64 (.f64 a a) 2)

Compiler

Compiled 678 to 602 computations (11.2% saved)

simplify75.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4976	1406
1	4976	1406

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 b (+.f64 4 (.f64 (*.f64 a a) 2)))
0.1b	(.f64 b (.f64 b (+.f64 4 (.f64 (.f64 a a) 2))))
0.0b	(.f64 (.f64 a a) 2)
0.0b	(+.f64 4 (.f64 (.f64 a a) 2))
0.0b	(.f64 (.f64 a a) 2)
0.0b	(+.f64 4 (.f64 (.f64 a a) 2))
0.1b	(.f64 b (.f64 b (+.f64 4 (.f64 (.f64 a a) 2))))
0.1b	(.f64 b (+.f64 4 (.f64 (*.f64 a a) 2)))

rewrite29.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `pow1_binary64_2867`
11×	`add-sqr-sqrt_binary64_2828`
8×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
7×	`associate-l_binary64_2747` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `associate-r_binary64_2746` `pow-prod-down_binary64_2877`
6×	`add-log-exp_binary64_2845` `associate-*r/_binary64_2748`
5×	`distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756`
3×	`*-commutative_binary64_2737` `flip-+_binary64_2780` `flip3-+_binary64_2809`
2×	`unswap-sqr_binary64_2774`
1×	`sum-log_binary64_2897` `+-commutative_binary64_2736`

Counts

4 → 76

Calls

8 calls:

7.0ms	(.f64 b (.f64 b (+.f64 4 (.f64 (.f64 a a) 2))))
6.0ms	(.f64 (.f64 a a) 2)
6.0ms	(.f64 b (+.f64 4 (.f64 (*.f64 a a) 2)))
3.0ms	(+.f64 4 (.f64 (.f64 a a) 2))
0.0ms	(+.f64 4 (.f64 (.f64 a a) 2))

series314.0ms (0.4%)

Counts

4 → 27

Calls

4 calls:

132.0ms	(.f64 b (.f64 b (+.f64 4 (.f64 (.f64 a a) 2))))
114.0ms	(.f64 b (+.f64 4 (.f64 (*.f64 a a) 2)))
42.0ms	(+.f64 4 (.f64 (.f64 a a) 2))
25.0ms	(.f64 (.f64 a a) 2)

Compiler

Compiled 771 to 687 computations (10.9% saved)

simplify70.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5091	1380

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

22.0b	(cbrt.f64 (*.f64 64 (pow.f64 b 6)))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.0b	(*.f64 64 (pow.f64 b 6))
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (cbrt.f64 (*.f64 64 (pow.f64 b 6))))
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (cbrt.f64 (*.f64 64 (pow.f64 b 6))))
0.0b	(*.f64 64 (pow.f64 b 6))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
22.0b	(cbrt.f64 (*.f64 64 (pow.f64 b 6)))

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2828`
11×	`*-un-lft-identity_binary64_2806`
10×	`add-exp-log_binary64_2844`
9×	`add-cube-cbrt_binary64_2841`
7×	`unpow-prod-down_binary64_2885` `associate-r_binary64_2746`
6×	`add-cbrt-cube_binary64_2842` `add-log-exp_binary64_2845`
5×	`pow1_binary64_2867`
3×	`associate-l_binary64_2747` `prod-exp_binary64_2855` `pow-unpow_binary64_2883` `sqr-pow_binary64_2778` `unswap-sqr_binary64_2774`
2×	`pow-exp_binary64_2874` `pow-to-exp_binary64_2875`
1×	`pow1/3_binary64_2888` `distribute-lft-out_binary64_2757` `*-commutative_binary64_2737` `pow-pow_binary64_2878` `cbrt-unprod_binary64_2839` `flip-+_binary64_2780` `sum-log_binary64_2897` `flip3-+_binary64_2809` `unpow2_binary64_2871` `cbrt-prod_binary64_2837` `+-commutative_binary64_2736`

Counts

4 → 64

Calls

8 calls:

9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (cbrt.f64 (*.f64 64 (pow.f64 b 6))))
6.0ms	(*.f64 64 (pow.f64 b 6))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
3.0ms	(cbrt.f64 (*.f64 64 (pow.f64 b 6)))
0.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (cbrt.f64 (*.f64 64 (pow.f64 b 6))))

series596.0ms (0.7%)

Counts

4 → 36

Calls

4 calls:

401.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (cbrt.f64 (*.f64 64 (pow.f64 b 6))))
116.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
41.0ms	(cbrt.f64 (*.f64 64 (pow.f64 b 6)))
38.0ms	(*.f64 64 (pow.f64 b 6))

Compiler

Compiled 1043 to 936 computations (10.3% saved)

simplify54.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5887	1532

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 2)
0.2b	(.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (*.f64 b b))) 2))
0.0b	(.f64 4 (.f64 b b))
0.0b	(+.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 2)) (.f64 4 (*.f64 b b)))
0.4b	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 2)
0.6b	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4)
9.7b	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
9.7b	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))

rewrite27.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806` `unpow-prod-down_binary64_2885` `add-cube-cbrt_binary64_2841` `cbrt-prod_binary64_2837`
6×	`add-exp-log_binary64_2844` `pow-unpow_binary64_2883` `pow1_binary64_2867`
4×	`cbrt-div_binary64_2838` `pow1/3_binary64_2888` `add-cbrt-cube_binary64_2842` `pow-pow_binary64_2878` `add-log-exp_binary64_2845`
2×	`pow-exp_binary64_2874` `pow-to-exp_binary64_2875` `flip-+_binary64_2780` `flip3-+_binary64_2809` `sqr-pow_binary64_2778`
1×	`unpow2_binary64_2871`

Counts

4 → 69

Calls

8 calls:

6.0ms	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 2)
5.0ms	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4)
4.0ms	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
4.0ms	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
0.0ms	(+.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 2)) (.f64 4 (*.f64 b b)))

series643.0ms (0.8%)

Counts

4 → 36

Calls

4 calls:

262.0ms	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4)
224.0ms	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 2)
79.0ms	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
78.0ms	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 2136 to 1680 computations (21.3% saved)

simplify68.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4934	1700
1	4934	1700

prune4.7s (5.7%)

Pruning

170 alts after pruning (165 fresh and 5 done)

	Pruned	Kept	Total
New	334	146	480
Fresh	5	19	24
Picked	0	0	0
Done	1	5	6
Total	340	170	510

Error

Counts

510 → 170

Compiler

Compiled 11927 to 7111 computations (40.4% saved)

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

2.4b	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
0.4b	(.f64 (cbrt.f64 (.f64 b (.f64 b 4))) (cbrt.f64 (.f64 b (*.f64 b 4))))
0.2b	(.f64 (.f64 (cbrt.f64 (.f64 b (.f64 b 4))) (cbrt.f64 (.f64 b (.f64 b 4)))) (cbrt.f64 (.f64 b (.f64 b 4))))
0.0b	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 (.f64 (cbrt.f64 (.f64 b (.f64 b 4))) (cbrt.f64 (.f64 b (.f64 b 4)))) (cbrt.f64 (.f64 b (.f64 b 4)))))
2.4b	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
24.2b	(cbrt.f64 (.f64 b (.f64 b 4)))
24.2b	(cbrt.f64 (.f64 b (.f64 b 4)))
24.2b	(cbrt.f64 (.f64 b (.f64 b 4)))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `pow1_binary64_2867`
15×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `pow-prod-down_binary64_2877`
4×	`add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806` `add-log-exp_binary64_2845` `add-cube-cbrt_binary64_2841`
3×	`pow1/3_binary64_2888` `cbrt-prod_binary64_2837`
1×	`associate-l_binary64_2747` `-commutative_binary64_2737` `associate-r*_binary64_2746`

Counts

4 → 55

Calls

8 calls:

10.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
6.0ms	(cbrt.f64 (.f64 b (.f64 b 4)))
4.0ms	(cbrt.f64 (.f64 b (.f64 b 4)))
4.0ms	(cbrt.f64 (.f64 b (.f64 b 4)))
0.0ms	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 (.f64 (cbrt.f64 (.f64 b (.f64 b 4))) (cbrt.f64 (.f64 b (.f64 b 4)))) (cbrt.f64 (.f64 b (.f64 b 4)))))

series420.0ms (0.5%)

Counts

4 → 15

Calls

4 calls:

108.0ms	(cbrt.f64 (.f64 b (.f64 b 4)))
107.0ms	(cbrt.f64 (.f64 b (.f64 b 4)))
104.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
100.0ms	(cbrt.f64 (.f64 b (.f64 b 4)))

Compiler

Compiled 1236 to 978 computations (20.9% saved)

simplify61.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5038	817

localize4.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 b b) (*.f64 b b))
0.0b	(-.f64 (.f64 (.f64 b b) (*.f64 b b)) 1)
0.0b	(-.f64 (.f64 (.f64 b b) (*.f64 b b)) 1)
0.2b	(.f64 (.f64 b b) (*.f64 b b))

rewrite26.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`pow1_binary64_2867`
36×	`pow-prod-up_binary64_2876`
23×	`pow-prod-down_binary64_2877`
22×	`pow-sqr_binary64_2779`
18×	`pow-plus_binary64_2869`
14×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
13×	`pow2_binary64_2887`
8×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
4×	`add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806` `add-log-exp_binary64_2845`
3×	`cancel-sign-sub-inv_binary64_2772` `add-cube-cbrt_binary64_2841`
2×	`difference-of-squares_binary64_2775`
1×	`associate-l_binary64_2747` `-commutative_binary64_2737` `flip3--_binary64_2810` `diff-log_binary64_2898` `sub-neg_binary64_2799` `swap-sqr_binary64_2773` `difference-of-sqr-1_binary64_2776` `flip--_binary64_2781` `associate-r*_binary64_2746` `unswap-sqr_binary64_2774`

Counts

2 → 80

Calls

4 calls:

11.0ms	(-.f64 (.f64 (.f64 b b) (*.f64 b b)) 1)
9.0ms	(.f64 (.f64 b b) (*.f64 b b))
0.0ms	(-.f64 (.f64 (.f64 b b) (*.f64 b b)) 1)
0.0ms	(.f64 (.f64 b b) (*.f64 b b))

series85.0ms (0.1%)

Counts

2 → 9

Calls

2 calls:

57.0ms	(-.f64 (.f64 (.f64 b b) (*.f64 b b)) 1)
28.0ms	(.f64 (.f64 b b) (*.f64 b b))

Compiler

Compiled 67 to 83 computations (-23.9% saved)

simplify89.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4958	390
1	4958	390

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 (.f64 a a) 2) (.f64 (.f64 a a) 2)) (.f64 4 (.f64 (.f64 a a) 2)))
0.0b	(.f64 (.f64 a a) 2)
0.0b	(.f64 (.f64 a a) 2)
0.0b	(.f64 (.f64 a a) 2)
0.2b	(.f64 (.f64 (.f64 a a) 2) (.f64 (*.f64 a a) 2))
0.7b	(.f64 b (.f64 b (+.f64 64 (*.f64 (pow.f64 a 6) 8))))
1.9b	(/.f64 (.f64 b (.f64 b (+.f64 64 (.f64 (pow.f64 a 6) 8)))) (+.f64 (.f64 4 4) (-.f64 (.f64 (.f64 (.f64 a a) 2) (.f64 (.f64 a a) 2)) (.f64 4 (.f64 (.f64 a a) 2)))))
2.6b	(.f64 b (+.f64 64 (.f64 (pow.f64 a 6) 8)))

rewrite73.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

125×	`pow1_binary64_2867`
70×	`pow-prod-down_binary64_2877`
56×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
34×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
11×	`add-sqr-sqrt_binary64_2828`
10×	`associate-*r/_binary64_2748`
9×	`pow-sqr_binary64_2779` `*-un-lft-identity_binary64_2806` `pow-prod-up_binary64_2876` `add-cube-cbrt_binary64_2841`
7×	`associate-l_binary64_2747`
5×	`distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756` `associate-r_binary64_2746`
4×	`flip-+_binary64_2780` `add-log-exp_binary64_2845` `flip3-+_binary64_2809`
3×	`times-frac_binary64_2812` `div-exp_binary64_2857` `-commutative_binary64_2737` `cbrt-undiv_binary64_2840` `associate-/r_binary64_2750` `pow-plus_binary64_2869`
2×	`associate-/l/_binary64_2753` `associate-/r/_binary64_2752`
1×	`div-inv_binary64_2803` `swap-sqr_binary64_2773` `pow2_binary64_2887` `clear-num_binary64_2805` `associate-/l*_binary64_2751` `unswap-sqr_binary64_2774` `frac-2neg_binary64_2817`

Counts

4 → 133

Calls

8 calls:

25.0ms	(/.f64 (.f64 b (.f64 b (+.f64 64 (.f64 (pow.f64 a 6) 8)))) (+.f64 (.f64 4 4) (-.f64 (.f64 (.f64 (.f64 a a) 2) (.f64 (.f64 a a) 2)) (.f64 4 (.f64 (.f64 a a) 2)))))
13.0ms	(.f64 (.f64 (.f64 a a) 2) (.f64 (*.f64 a a) 2))
7.0ms	(.f64 b (.f64 b (+.f64 64 (*.f64 (pow.f64 a 6) 8))))
6.0ms	(.f64 b (+.f64 64 (.f64 (pow.f64 a 6) 8)))
0.0ms	(.f64 (.f64 a a) 2)

series823.0ms (1%)

Counts

4 → 28

Calls

4 calls:

363.0ms	(/.f64 (.f64 b (.f64 b (+.f64 64 (.f64 (pow.f64 a 6) 8)))) (+.f64 (.f64 4 4) (-.f64 (.f64 (.f64 (.f64 a a) 2) (.f64 (.f64 a a) 2)) (.f64 4 (.f64 (.f64 a a) 2)))))
228.0ms	(.f64 b (.f64 b (+.f64 64 (*.f64 (pow.f64 a 6) 8))))
196.0ms	(.f64 b (+.f64 64 (.f64 (pow.f64 a 6) 8)))
36.0ms	(.f64 (.f64 (.f64 a a) 2) (.f64 (*.f64 a a) 2))

Compiler

Compiled 1721 to 1385 computations (19.5% saved)

simplify82.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4948	2637
1	4948	2637

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4)
0.4b	(pow.f64 (cbrt.f64 (*.f64 a a)) 2)
0.0b	(.f64 4 (.f64 b b))
0.0b	(+.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (cbrt.f64 (.f64 a a)) 2)) (.f64 4 (.f64 b b)))
0.6b	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4)
1.8b	(.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (cbrt.f64 (.f64 a a)) 2))
9.7b	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
25.1b	(cbrt.f64 (*.f64 a a))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_2828`
34×	`unpow-prod-down_binary64_2885`
20×	`cbrt-prod_binary64_2837` `unswap-sqr_binary64_2774`
17×	`add-exp-log_binary64_2844`
13×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
12×	`sqr-pow_binary64_2778`
10×	`associate-l_binary64_2747`
9×	`prod-exp_binary64_2855` `associate-r_binary64_2746`
7×	`pow-exp_binary64_2874` `pow-to-exp_binary64_2875`
6×	`add-cbrt-cube_binary64_2842`
5×	`unpow2_binary64_2871` `pow1_binary64_2867`
4×	`add-log-exp_binary64_2845`
3×	`pow1/3_binary64_2888` `pow-unpow_binary64_2883`
2×	`cbrt-div_binary64_2838` `pow-pow_binary64_2878`
1×	`*-commutative_binary64_2737` `cbrt-unprod_binary64_2839` `flip-+_binary64_2780` `flip3-+_binary64_2809`

Counts

4 → 100

Calls

8 calls:

14.0ms	(.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (cbrt.f64 (.f64 a a)) 2))
6.0ms	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4)
4.0ms	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
2.0ms	(cbrt.f64 (*.f64 a a))
0.0ms	(+.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (cbrt.f64 (.f64 a a)) 2)) (.f64 4 (.f64 b b)))

series638.0ms (0.8%)

Counts

4 → 33

Calls

4 calls:

295.0ms	(.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (cbrt.f64 (.f64 a a)) 2))
185.0ms	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4)
80.0ms	(cbrt.f64 (*.f64 a a))
78.0ms	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 1653 to 1401 computations (15.2% saved)

simplify69.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5356	2968

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

22.0b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 64) (cbrt.f64 64)) (*.f64 (pow.f64 b 6) (cbrt.f64 64))))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.0b	(.f64 (.f64 (cbrt.f64 64) (cbrt.f64 64)) (*.f64 (pow.f64 b 6) (cbrt.f64 64)))
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (cbrt.f64 (.f64 (.f64 (cbrt.f64 64) (cbrt.f64 64)) (*.f64 (pow.f64 b 6) (cbrt.f64 64)))))
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (cbrt.f64 (.f64 (.f64 (cbrt.f64 64) (cbrt.f64 64)) (*.f64 (pow.f64 b 6) (cbrt.f64 64)))))
0.0b	(.f64 (.f64 (cbrt.f64 64) (cbrt.f64 64)) (*.f64 (pow.f64 b 6) (cbrt.f64 64)))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
22.0b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 64) (cbrt.f64 64)) (*.f64 (pow.f64 b 6) (cbrt.f64 64))))

rewrite41.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64_2844`
18×	`prod-exp_binary64_2855`
10×	`add-cbrt-cube_binary64_2842` `pow1_binary64_2867`
8×	`*-un-lft-identity_binary64_2806` `cbrt-unprod_binary64_2839`
6×	`add-sqr-sqrt_binary64_2828` `add-log-exp_binary64_2845` `add-cube-cbrt_binary64_2841`
3×	`pow-exp_binary64_2874` `pow-unpow_binary64_2883` `pow-to-exp_binary64_2875` `unpow-prod-down_binary64_2885` `pow-prod-down_binary64_2877`
1×	`associate-l_binary64_2747` `pow1/3_binary64_2888` `distribute-lft-out_binary64_2757` `-commutative_binary64_2737` `pow-pow_binary64_2878` `flip-+_binary64_2780` `sum-log_binary64_2897` `flip3-+_binary64_2809` `sqr-pow_binary64_2778` `associate-r*_binary64_2746` `unpow2_binary64_2871` `cbrt-prod_binary64_2837` `+-commutative_binary64_2736`

Counts

4 → 63

Calls

8 calls:

11.0ms	(.f64 (.f64 (cbrt.f64 64) (cbrt.f64 64)) (*.f64 (pow.f64 b 6) (cbrt.f64 64)))
9.0ms	(cbrt.f64 (.f64 (.f64 (cbrt.f64 64) (cbrt.f64 64)) (*.f64 (pow.f64 b 6) (cbrt.f64 64))))
9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (cbrt.f64 (.f64 (.f64 (cbrt.f64 64) (cbrt.f64 64)) (*.f64 (pow.f64 b 6) (cbrt.f64 64)))))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (cbrt.f64 (.f64 (.f64 (cbrt.f64 64) (cbrt.f64 64)) (*.f64 (pow.f64 b 6) (cbrt.f64 64)))))

series649.0ms (0.8%)

Counts

4 → 36

Calls

4 calls:

404.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (cbrt.f64 (.f64 (.f64 (cbrt.f64 64) (cbrt.f64 64)) (*.f64 (pow.f64 b 6) (cbrt.f64 64)))))
125.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
82.0ms	(.f64 (.f64 (cbrt.f64 64) (cbrt.f64 64)) (*.f64 (pow.f64 b 6) (cbrt.f64 64)))
39.0ms	(cbrt.f64 (.f64 (.f64 (cbrt.f64 64) (cbrt.f64 64)) (*.f64 (pow.f64 b 6) (cbrt.f64 64))))

Compiler

Compiled 1187 to 1080 computations (9% saved)

simplify46.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5303	1555

prune11.4s (13.9%)

Pruning

310 alts after pruning (300 fresh and 10 done)

	Pruned	Kept	Total
New	405	147	552
Fresh	7	153	160
Picked	0	0	0
Done	0	10	10
Total	412	310	722

Error

Counts

722 → 310

Compiler

Compiled 18815 to 12458 computations (33.8% saved)

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

1.0b	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
0.3b	(.f64 (.f64 b b) (cbrt.f64 4))
0.2b	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))
0.0b	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4))))
0.2b	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))
0.3b	(.f64 (.f64 b b) (cbrt.f64 4))
1.0b	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
2.4b	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))

rewrite55.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`pow1_binary64_2867`
53×	`add-exp-log_binary64_2844`
39×	`add-cbrt-cube_binary64_2842`
35×	`pow-prod-down_binary64_2877`
34×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
24×	`add-sqr-sqrt_binary64_2828`
20×	`cbrt-prod_binary64_2837`
14×	`-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841` `associate-r*_binary64_2746`
9×	`associate-l_binary64_2747`
6×	`pow1/3_binary64_2888` `swap-sqr_binary64_2773` `unswap-sqr_binary64_2774`
4×	`*-commutative_binary64_2737` `add-log-exp_binary64_2845`
2×	`pow-sqr_binary64_2779` `pow-prod-up_binary64_2876`
1×	`pow2_binary64_2887` `pow-plus_binary64_2869`

Counts

4 → 119

Calls

8 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))
10.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
9.0ms	(.f64 (.f64 b b) (cbrt.f64 4))
7.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
0.0ms	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4))))

series203.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

96.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
64.0ms	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))
42.0ms	(.f64 (.f64 b b) (cbrt.f64 4))
0.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))

Compiler

Compiled 744 to 636 computations (14.5% saved)

simplify101.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4928	1246
1	4928	1246

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

2.4b	(.f64 (.f64 b b) (.f64 (.f64 a a) 2))
0.0b	(.f64 (.f64 a a) 2)
0.0b	(.f64 (.f64 a a) 2)
2.4b	(.f64 (.f64 b b) (.f64 (.f64 a a) 2))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `pow1_binary64_2867`
18×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `pow-prod-down_binary64_2877`
4×	`add-sqr-sqrt_binary64_2828` `associate-r_binary64_2746`
3×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
2×	`associate-l_binary64_2747` `*-commutative_binary64_2737` `add-log-exp_binary64_2845`
1×	`unswap-sqr_binary64_2774`

Counts

2 → 47

Calls

4 calls:

10.0ms	(.f64 (.f64 b b) (.f64 (.f64 a a) 2))
6.0ms	(.f64 (.f64 a a) 2)
0.0ms	(.f64 (.f64 a a) 2)
0.0ms	(.f64 (.f64 b b) (.f64 (.f64 a a) 2))

series116.0ms (0.1%)

Counts

2 → 9

Calls

2 calls:

90.0ms	(.f64 (.f64 b b) (.f64 (.f64 a a) 2))
26.0ms	(.f64 (.f64 a a) 2)

Compiler

Compiled 198 to 192 computations (3% saved)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4938	618
1	4938	618

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

1.6b	(.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b))))
0.0b	(exp.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b))))))
0.0b	(.f64 (.f64 a a) 2)
0.0b	(+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b)))
0.0b	(+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b)))
0.0b	(exp.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b))))))
1.6b	(.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b))))
4.1b	(log.f64 (exp.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b)))))))

rewrite44.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-log-exp_binary64_2845`
10×	`pow1_binary64_2867`
9×	`add-sqr-sqrt_binary64_2828` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
8×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
6×	`exp-prod_binary64_2858`
4×	`sum-log_binary64_2897` `log-prod_binary64_2892` `log-pow_binary64_2895`
3×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `associate-r_binary64_2746` `pow-prod-down_binary64_2877`
2×	`exp-sum_binary64_2852` `flip-+_binary64_2780` `flip3-+_binary64_2809` `associate-*r/_binary64_2748` `rem-exp-log_binary64_2846`
1×	`associate-l_binary64_2747` `*-commutative_binary64_2737` `distribute-lft-in_binary64_2755` `associate-+r+_binary64_2738` `distribute-rgt-in_binary64_2756` `rem-log-exp_binary64_2847` `unswap-sqr_binary64_2774` `+-commutative_binary64_2736`

Counts

4 → 65

Calls

8 calls:

13.0ms	(.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b))))
9.0ms	(+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b)))
6.0ms	(exp.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b))))))
6.0ms	(log.f64 (exp.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b)))))))
0.0ms	(+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b)))

series1.1s (1.4%)

Counts

4 → 39

Calls

4 calls:

755.0ms	(log.f64 (exp.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b)))))))
157.0ms	(.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b))))
122.0ms	(exp.f64 (+.f64 (pow.f64 a 4) (.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b))))))
102.0ms	(+.f64 (.f64 (.f64 a a) 2) (+.f64 4 (*.f64 b b)))

Compiler

Compiled 1641 to 1453 computations (11.5% saved)

simplify63.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5031	2568

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
0.4b	(pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)
0.0b	(.f64 4 (.f64 b b))
0.0b	(+.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (.f64 4 (.f64 b b)))
0.7b	(cbrt.f64 a)
0.7b	(cbrt.f64 a)
1.8b	(.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) 2))
9.7b	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))

rewrite29.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_2828`
24×	`add-exp-log_binary64_2844`
19×	`unpow-prod-down_binary64_2885`
16×	`cbrt-prod_binary64_2837` `unswap-sqr_binary64_2774`
15×	`prod-exp_binary64_2855`
11×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
10×	`associate-l_binary64_2747` `pow-exp_binary64_2874` `sqr-pow_binary64_2778`
7×	`pow-to-exp_binary64_2875`
6×	`add-cbrt-cube_binary64_2842` `associate-r_binary64_2746`
5×	`unpow2_binary64_2871`
4×	`add-log-exp_binary64_2845` `pow1_binary64_2867`
3×	`pow1/3_binary64_2888`
2×	`cbrt-div_binary64_2838`
1×	`*-commutative_binary64_2737` `cbrt-unprod_binary64_2839` `flip-+_binary64_2780` `flip3-+_binary64_2809`

Counts

4 → 88

Calls

8 calls:

12.0ms	(.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) 2))
4.0ms	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
1.0ms	(cbrt.f64 a)
1.0ms	(cbrt.f64 a)
0.0ms	(+.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (.f64 4 (.f64 b b)))

series592.0ms (0.7%)

Counts

4 → 27

Calls

4 calls:

366.0ms	(.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) 2))
79.0ms	(cbrt.f64 a)
74.0ms	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
73.0ms	(cbrt.f64 a)

Compiler

Compiled 1453 to 1210 computations (16.7% saved)

simplify65.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5085	2313

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 4 (.f64 b b))
0.0b	(-.f64 (.f64 a a) (.f64 b b))
0.0b	(-.f64 (pow.f64 a 4) (pow.f64 b 4))
0.0b	(+.f64 (.f64 (pow.f64 (/.f64 (cbrt.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4))) (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b)))) 4) (pow.f64 (cbrt.f64 (.f64 a a)) 2)) (.f64 4 (.f64 b b)))
2.8b	(/.f64 (cbrt.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4))) (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))))
9.7b	(cbrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
20.2b	(cbrt.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)))
25.1b	(cbrt.f64 (*.f64 a a))

rewrite71.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

203×	`cbrt-prod_binary64_2837`
166×	`add-sqr-sqrt_binary64_2828`
119×	`times-frac_binary64_2812`
100×	`difference-of-squares_binary64_2775`
94×	`*-un-lft-identity_binary64_2806`
72×	`unpow-prod-down_binary64_2885`
58×	`add-cube-cbrt_binary64_2841`
54×	`sqr-pow_binary64_2778`
18×	`distribute-lft-out--_binary64_2758`
17×	`associate-/l*_binary64_2751`
8×	`cbrt-div_binary64_2838`
7×	`associate-/r*_binary64_2750`
6×	`add-exp-log_binary64_2844`
4×	`add-cbrt-cube_binary64_2842` `flip3--_binary64_2810` `add-log-exp_binary64_2845` `flip--_binary64_2781` `pow1_binary64_2867`
3×	`pow1/3_binary64_2888`
2×	`associate-/l/_binary64_2753` `associate-/r/_binary64_2752`
1×	`div-inv_binary64_2803` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `clear-num_binary64_2805` `frac-2neg_binary64_2817`

Counts

4 → 206

Calls

8 calls:

19.0ms	(/.f64 (cbrt.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4))) (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))))
8.0ms	(cbrt.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)))
4.0ms	(cbrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
2.0ms	(cbrt.f64 (*.f64 a a))
0.0ms	(+.f64 (.f64 (pow.f64 (/.f64 (cbrt.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4))) (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b)))) 4) (pow.f64 (cbrt.f64 (.f64 a a)) 2)) (.f64 4 (.f64 b b)))

series489.0ms (0.6%)

Counts

4 → 25

Calls

4 calls:

154.0ms	(cbrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
143.0ms	(cbrt.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)))
105.0ms	(/.f64 (cbrt.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4))) (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))))
86.0ms	(cbrt.f64 (*.f64 a a))

Compiler

Compiled 1808 to 1480 computations (18.1% saved)

simplify145.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4868	8403
1	4868	8403

prune23.0s (27.9%)

Pruning

471 alts after pruning (457 fresh and 14 done)

	Pruned	Kept	Total
New	449	188	637
Fresh	26	269	295
Picked	0	0	0
Done	1	14	15
Total	476	471	947

Error

Counts

947 → 471

Compiler

Compiled 13731 to 7324 computations (46.7% saved)

simplify654.0ms (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5001	43594

regimes9.3s (11.3%)

Compiler: Compiled 140750 to 98238 computations (30.2% saved)

bsearch0.0ms (0%)

regimes857.0ms (1%)

Compiler: Compiled 10184 to 7734 computations (24.1% saved)

bsearch0.0ms (0%)

regimes421.0ms (0.5%)

Compiler: Compiled 4436 to 3426 computations (22.8% saved)

bsearch0.0ms (0%)

regimes147.0ms (0.2%)

Compiler: Compiled 1399 to 1069 computations (23.6% saved)

bsearch0.0ms (0%)

regimes109.0ms (0.1%)

Compiler: Compiled 920 to 720 computations (21.7% saved)

bsearch0.0ms (0%)

regimes77.0ms (0.1%)

Compiler: Compiled 512 to 432 computations (15.6% saved)

bsearch0.0ms (0%)

regimes30.0ms (0%)

Compiler: Compiled 79 to 83 computations (-5.1% saved)

bsearch0.0ms (0%)

regimes27.0ms (0%)

Compiler: Compiled 46 to 59 computations (-28.3% saved)

bsearch0.0ms (0%)

regimes15.0ms (0%)

Accuracy

Total 0.0b remaining (80.7%)

Threshold costs 0.0b (80.7%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch8.0ms (0%)

Compiler: Compiled 135 to 95 computations (29.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	198
1	78	198

end0.0ms (0%)

sample21.0s (25.4%)

Algorithm

1×

intervals

Results

335.0ms	8000×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 25224 to 17759 computations (29.6% saved)

Pareto

0.8849605115451353