Details

analyze37.0ms (0%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
43.7%	56.2%	0.1%	5
46.8%	53.1%	0.1%	6
78%	21.9%	0.1%	7
82.7%	17.2%	0.1%	8
89%	10.9%	0.1%	9
91.3%	8.6%	0.1%	10
94.4%	5.5%	0.1%	11
95.6%	4.3%	0.1%	12
97.2%	2.7%	0.1%	13
97.8%	2.1%	0.1%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample12.0ms (0%)

Algorithm

1×

intervals

Results

6.0ms

256×

body

128

valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify101.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	10
1	10	10

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 7 to 6 computations (14.3% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 x y) (+.f64 y 1))
0.0b	(/.f64 (+.f64 x y) (+.f64 y 1))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64_9285`
16×	`times-frac_binary64_9291`
11×	`add-sqr-sqrt_binary64_9307` `add-cube-cbrt_binary64_9320`
10×	`distribute-lft-out_binary64_9236`
4×	`associate-/l_binary64_9230` `associate-/r_binary64_9229`
3×	`add-cbrt-cube_binary64_9321` `add-exp-log_binary64_9323`
2×	`associate-/l/_binary64_9232` `flip-+_binary64_9259` `associate-/r/_binary64_9231` `flip3-+_binary64_9288`
1×	`clear-num_binary64_9284` `div-exp_binary64_9336` `cbrt-undiv_binary64_9319` `pow1_binary64_9346` `frac-2neg_binary64_9296` `add-log-exp_binary64_9324` `div-inv_binary64_9282`

Counts

1 → 40

Calls

2 calls:

8.0ms	(/.f64 (+.f64 x y) (+.f64 y 1))
0.0ms	(/.f64 (+.f64 x y) (+.f64 y 1))

series97.0ms (0.1%)

Counts

1 → 18

Calls

1 calls:

97.0ms

(/.f64 (+.f64 x y) (+.f64 y 1))

Compiler

Compiled 261 to 215 computations (17.6% saved)

simplify76.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4948	978
1	4948	978

prune177.0ms (0.2%)

Pruning

36 alts after pruning (35 fresh and 1 done)

	Pruned	Kept	Total
New	23	35	58
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	23	36	59

Error

Counts

59 → 36

Compiler

Compiled 1053 to 641 computations (39.1% saved)

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 y (+.f64 y 1))
0.0b	(/.f64 x (+.f64 y 1))
0.0b	(/.f64 x (+.f64 y 1))
0.0b	(/.f64 y (+.f64 y 1))

rewrite15.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_9285`
24×	`times-frac_binary64_9291`
20×	`add-sqr-sqrt_binary64_9307` `add-cube-cbrt_binary64_9320`
8×	`distribute-lft-out_binary64_9236` `associate-/r*_binary64_9229`
6×	`add-cbrt-cube_binary64_9321` `associate-/l*_binary64_9230` `add-exp-log_binary64_9323`
4×	`associate-/r/_binary64_9231`
2×	`clear-num_binary64_9284` `div-exp_binary64_9336` `cbrt-undiv_binary64_9319` `pow1_binary64_9346` `flip-+_binary64_9259` `frac-2neg_binary64_9296` `add-log-exp_binary64_9324` `flip3-+_binary64_9288` `div-inv_binary64_9282`

Counts

2 → 66

Calls

4 calls:

5.0ms	(/.f64 y (+.f64 y 1))
5.0ms	(/.f64 x (+.f64 y 1))
0.0ms	(/.f64 x (+.f64 y 1))
0.0ms	(/.f64 y (+.f64 y 1))

series98.0ms (0.1%)

Counts

2 → 27

Calls

2 calls:

67.0ms	(/.f64 x (+.f64 y 1))
31.0ms	(/.f64 y (+.f64 y 1))

Compiler

Compiled 436 to 346 computations (20.6% saved)

simplify78.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4952	1173
1	4952	1173

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 y (+.f64 y 1))
0.0b	(/.f64 y (+.f64 y 1))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64_9285`
12×	`times-frac_binary64_9291`
10×	`add-sqr-sqrt_binary64_9307` `add-cube-cbrt_binary64_9320`
4×	`distribute-lft-out_binary64_9236` `associate-/r*_binary64_9229`
3×	`add-cbrt-cube_binary64_9321` `associate-/l*_binary64_9230` `add-exp-log_binary64_9323`
2×	`associate-/r/_binary64_9231`
1×	`clear-num_binary64_9284` `div-exp_binary64_9336` `cbrt-undiv_binary64_9319` `pow1_binary64_9346` `flip-+_binary64_9259` `frac-2neg_binary64_9296` `add-log-exp_binary64_9324` `flip3-+_binary64_9288` `div-inv_binary64_9282`

Counts

1 → 33

Calls

2 calls:

5.0ms	(/.f64 y (+.f64 y 1))
0.0ms	(/.f64 y (+.f64 y 1))

series29.0ms (0%)

Counts

1 → 12

Calls

1 calls:

29.0ms

(/.f64 y (+.f64 y 1))

Compiler

Compiled 96 to 98 computations (-2.1% saved)

simplify73.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4943	555
1	4943	555

localize13.0ms (0%)

Local error

Found 6 expressions with local error:

29.2b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (*.f64 (+.f64 y 1) (-.f64 x y)))
2.3b	(-.f64 (.f64 x x) (.f64 y y))
0.0b	(*.f64 (+.f64 y 1) (-.f64 x y))
0.0b	(*.f64 (+.f64 y 1) (-.f64 x y))
2.3b	(-.f64 (.f64 x x) (.f64 y y))
29.2b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (*.f64 (+.f64 y 1) (-.f64 x y)))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_9307` `*-un-lft-identity_binary64_9285`
10×	`add-cbrt-cube_binary64_9321` `add-exp-log_binary64_9323`
9×	`add-cube-cbrt_binary64_9320`
8×	`frac-times_binary64_9295` `flip--_binary64_9260` `flip3--_binary64_9289` `associate-/r/_binary64_9231`
7×	`cancel-sign-sub-inv_binary64_9251`
6×	`flip-+_binary64_9259` `flip3-+_binary64_9288`
5×	`associate-r_binary64_9225` `pow1_binary64_9346` `add-log-exp_binary64_9324`
4×	`associate-l/_binary64_9228` `distribute-lft-in_binary64_9234` `distribute-rgt-in_binary64_9235` `associate-l_binary64_9226` `times-frac_binary64_9291` `associate-r/_binary64_9227` `associate-/l*_binary64_9230` `difference-of-squares_binary64_9254`
3×	`sub-neg_binary64_9278`
2×	`associate-/l/_binary64_9232` `cbrt-unprod_binary64_9318` `prod-exp_binary64_9334` `div-exp_binary64_9336` `cbrt-undiv_binary64_9319`
1×	`clear-num_binary64_9284` `div-sub_binary64_9290` `pow-prod-down_binary64_9356` `unswap-sqr_binary64_9253` `frac-2neg_binary64_9296` `-commutative_binary64_9216` `distribute-lft-out_binary64_9236` `diff-log_binary64_9377` `distribute-lft-out--_binary64_9237` `associate-/r_binary64_9229` `div-inv_binary64_9282`

Counts

3 → 84

Calls

6 calls:

12.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (*.f64 (+.f64 y 1) (-.f64 x y)))
9.0ms	(*.f64 (+.f64 y 1) (-.f64 x y))
4.0ms	(-.f64 (.f64 x x) (.f64 y y))
0.0ms	(*.f64 (+.f64 y 1) (-.f64 x y))
0.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (*.f64 (+.f64 y 1) (-.f64 x y)))

series345.0ms (0.4%)

Counts

3 → 45

Calls

3 calls:

149.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (*.f64 (+.f64 y 1) (-.f64 x y)))
101.0ms	(*.f64 (+.f64 y 1) (-.f64 x y))
95.0ms	(-.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 1010 to 761 computations (24.7% saved)

simplify90.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4983	1938
1	4983	1938

localize8.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 (sqrt.f64 (+.f64 x y)) (+.f64 y 1)))
0.1b	(/.f64 (sqrt.f64 (+.f64 x y)) (+.f64 y 1))
0.0b	(sqrt.f64 (+.f64 x y))
0.0b	(sqrt.f64 (+.f64 x y))
0.0b	(sqrt.f64 (+.f64 x y))
0.0b	(sqrt.f64 (+.f64 x y))
0.1b	(/.f64 (sqrt.f64 (+.f64 x y)) (+.f64 y 1))
0.2b	(*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 (sqrt.f64 (+.f64 x y)) (+.f64 y 1)))

rewrite52.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`*-un-lft-identity_binary64_9285`
60×	`add-sqr-sqrt_binary64_9307` `times-frac_binary64_9291`
53×	`sqrt-prod_binary64_9301`
42×	`add-cube-cbrt_binary64_9320`
34×	`associate-r_binary64_9225`
27×	`distribute-lft-out_binary64_9236`
11×	`add-cbrt-cube_binary64_9321` `add-exp-log_binary64_9323`
10×	`sqrt-div_binary64_9302`
8×	`pow1_binary64_9346`
7×	`associate-l_binary64_9226` `flip-+_binary64_9259` `associate-/l*_binary64_9230` `flip3-+_binary64_9288`
6×	`unswap-sqr_binary64_9253`
4×	`add-log-exp_binary64_9324` `associate-/r/_binary64_9231` `associate-/r*_binary64_9229`
2×	`associate-/l/_binary64_9232` `cbrt-unprod_binary64_9318` `associate-*l/_binary64_9228` `frac-times_binary64_9295` `prod-exp_binary64_9334` `div-exp_binary64_9336` `cbrt-undiv_binary64_9319` `rem-sqrt-square_binary64_9298` `sqrt-pow1_binary64_9303` `pow1/2_binary64_9365` `div-inv_binary64_9282`
1×	`clear-num_binary64_9284` `pow-prod-down_binary64_9356` `frac-2neg_binary64_9296` `associate-r/_binary64_9227` `-commutative_binary64_9216`

Counts

4 → 152

Calls

8 calls:

20.0ms	(*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 (sqrt.f64 (+.f64 x y)) (+.f64 y 1)))
8.0ms	(/.f64 (sqrt.f64 (+.f64 x y)) (+.f64 y 1))
3.0ms	(sqrt.f64 (+.f64 x y))
3.0ms	(sqrt.f64 (+.f64 x y))
0.0ms	(sqrt.f64 (+.f64 x y))

series263.0ms (0.3%)

Counts

4 → 46

Calls

4 calls:

91.0ms	(*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 (sqrt.f64 (+.f64 x y)) (+.f64 y 1)))
81.0ms	(/.f64 (sqrt.f64 (+.f64 x y)) (+.f64 y 1))
47.0ms	(sqrt.f64 (+.f64 x y))
44.0ms	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 1279 to 1020 computations (20.3% saved)

simplify131.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4914	3384
1	4914	3384

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b	(cbrt.f64 (+.f64 x y))
0.5b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))
0.3b	(.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (/.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y 1)))
0.1b	(/.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y 1))
0.5b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))
0.6b	(cbrt.f64 (+.f64 x y))
0.6b	(cbrt.f64 (+.f64 x y))
0.6b	(cbrt.f64 (+.f64 x y))

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64_9316`
35×	`*-un-lft-identity_binary64_9285`
23×	`add-sqr-sqrt_binary64_9307`
18×	`cbrt-div_binary64_9317`
15×	`add-cube-cbrt_binary64_9320`
11×	`pow1_binary64_9346`
9×	`swap-sqr_binary64_9252` `flip-+_binary64_9259` `pow1/3_binary64_9367` `distribute-lft-out_binary64_9236` `flip3-+_binary64_9288`
7×	`associate-l_binary64_9226` `associate-r_binary64_9225`
6×	`add-exp-log_binary64_9323`
4×	`frac-times_binary64_9295` `unswap-sqr_binary64_9253` `add-cbrt-cube_binary64_9321` `add-log-exp_binary64_9324`
2×	`associate-l/_binary64_9228` `pow-prod-down_binary64_9356` `pow-prod-up_binary64_9355` `associate-r/_binary64_9227` `pow-sqr_binary64_9258`
1×	`cbrt-unprod_binary64_9318` `prod-exp_binary64_9334` `pow-plus_binary64_9348` `*-commutative_binary64_9216` `pow2_binary64_9366`

Counts

4 → 95

Calls

8 calls:

11.0ms	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))
3.0ms	(cbrt.f64 (+.f64 x y))
3.0ms	(cbrt.f64 (+.f64 x y))
3.0ms	(cbrt.f64 (+.f64 x y))
0.0ms	(/.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y 1))

series493.0ms (0.6%)

Counts

4 → 51

Calls

4 calls:

152.0ms	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))
115.0ms	(cbrt.f64 (+.f64 x y))
114.0ms	(cbrt.f64 (+.f64 x y))
112.0ms	(cbrt.f64 (+.f64 x y))

Compiler

Compiled 2412 to 1866 computations (22.6% saved)

simplify73.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4936	2073
1	4936	2073

prune5.6s (6.4%)

Pruning

224 alts after pruning (220 fresh and 4 done)

	Pruned	Kept	Total
New	410	201	611
Fresh	11	19	30
Picked	0	0	0
Done	2	4	6
Total	423	224	647

Error

Counts

647 → 224

Compiler

Compiled 11987 to 6186 computations (48.4% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 y (+.f64 y 1))
0.0b	(/.f64 x (+.f64 y 1))
0.0b	(/.f64 x (+.f64 y 1))
0.0b	(/.f64 y (+.f64 y 1))

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_9285`
24×	`times-frac_binary64_9291`
20×	`add-sqr-sqrt_binary64_9307` `add-cube-cbrt_binary64_9320`
8×	`distribute-lft-out_binary64_9236` `associate-/r*_binary64_9229`
6×	`add-cbrt-cube_binary64_9321` `associate-/l*_binary64_9230` `add-exp-log_binary64_9323`
4×	`associate-/r/_binary64_9231`
2×	`clear-num_binary64_9284` `div-exp_binary64_9336` `cbrt-undiv_binary64_9319` `pow1_binary64_9346` `flip-+_binary64_9259` `frac-2neg_binary64_9296` `add-log-exp_binary64_9324` `flip3-+_binary64_9288` `div-inv_binary64_9282`

Counts

2 → 66

Calls

4 calls:

7.0ms	(/.f64 x (+.f64 y 1))
5.0ms	(/.f64 y (+.f64 y 1))
0.0ms	(/.f64 x (+.f64 y 1))
0.0ms	(/.f64 y (+.f64 y 1))

series102.0ms (0.1%)

Counts

2 → 27

Calls

2 calls:

70.0ms	(/.f64 x (+.f64 y 1))
32.0ms	(/.f64 y (+.f64 y 1))

Compiler

Compiled 496 to 406 computations (18.1% saved)

simplify78.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4952	1173
1	4952	1173

localize3.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 y (*.f64 y y))
0.0b	(-.f64 y (*.f64 y y))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_9324`
2×	`add-sqr-sqrt_binary64_9307` `*-un-lft-identity_binary64_9285`
1×	`cancel-sign-sub-inv_binary64_9251` `sub-neg_binary64_9278` `distribute-rgt-out--_binary64_9239` `flip--_binary64_9260` `flip3--_binary64_9289` `pow1_binary64_9346` `add-cbrt-cube_binary64_9321` `difference-of-squares_binary64_9254` `diff-log_binary64_9377` `add-exp-log_binary64_9323` `add-cube-cbrt_binary64_9320`

Counts

1 → 14

Calls

2 calls:

3.0ms	(-.f64 y (*.f64 y y))
0.0ms	(-.f64 y (*.f64 y y))

series36.0ms (0%)

Counts

1 → 6

Calls

1 calls:

36.0ms

(-.f64 y (*.f64 y y))

Compiler

Compiled 41 to 44 computations (-7.3% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4887	189
1	4887	189

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

1.7b	(log.f64 (exp.f64 (/.f64 x (+.f64 y 1))))
0.0b	(exp.f64 (/.f64 x (+.f64 y 1)))
0.0b	(/.f64 y (+.f64 y 1))
0.0b	(/.f64 x (+.f64 y 1))
0.0b	(/.f64 x (+.f64 y 1))
0.0b	(/.f64 y (+.f64 y 1))
0.0b	(exp.f64 (/.f64 x (+.f64 y 1)))
1.7b	(log.f64 (exp.f64 (/.f64 x (+.f64 y 1))))

rewrite35.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_9285`
48×	`times-frac_binary64_9291`
39×	`add-sqr-sqrt_binary64_9307` `add-cube-cbrt_binary64_9320`
36×	`exp-prod_binary64_9337`
19×	`log-pow_binary64_9374`
14×	`distribute-lft-out_binary64_9236`
8×	`add-cbrt-cube_binary64_9321` `associate-/r/_binary64_9231` `add-exp-log_binary64_9323` `associate-/r*_binary64_9229`
6×	`associate-/l*_binary64_9230`
5×	`pow1_binary64_9346` `add-log-exp_binary64_9324`
4×	`flip-+_binary64_9259` `flip3-+_binary64_9288` `div-inv_binary64_9282`
3×	`log-prod_binary64_9371`
2×	`clear-num_binary64_9284` `div-exp_binary64_9336` `cbrt-undiv_binary64_9319` `frac-2neg_binary64_9296`
1×	`rem-exp-log_binary64_9325` `rem-log-exp_binary64_9326`

Counts

4 → 122

Calls

8 calls:

7.0ms	(/.f64 y (+.f64 y 1))
7.0ms	(log.f64 (exp.f64 (/.f64 x (+.f64 y 1))))
6.0ms	(exp.f64 (/.f64 x (+.f64 y 1)))
5.0ms	(/.f64 x (+.f64 y 1))
0.0ms	(/.f64 x (+.f64 y 1))

series332.0ms (0.4%)

Counts

4 → 51

Calls

4 calls:

173.0ms	(log.f64 (exp.f64 (/.f64 x (+.f64 y 1))))
76.0ms	(exp.f64 (/.f64 x (+.f64 y 1)))
50.0ms	(/.f64 x (+.f64 y 1))
33.0ms	(/.f64 y (+.f64 y 1))

Compiler

Compiled 1148 to 914 computations (20.4% saved)

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4981	2117
1	4981	2117

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 1 (*.f64 (cbrt.f64 (+.f64 y 1)) (cbrt.f64 (+.f64 y 1))))
0.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 y 1)) (cbrt.f64 (+.f64 y 1)))) (/.f64 x (cbrt.f64 (+.f64 y 1))))
0.1b	(/.f64 x (cbrt.f64 (+.f64 y 1)))
0.0b	(/.f64 y (+.f64 y 1))
0.2b	(*.f64 (cbrt.f64 (+.f64 y 1)) (cbrt.f64 (+.f64 y 1)))
0.3b	(cbrt.f64 (+.f64 y 1))
0.3b	(cbrt.f64 (+.f64 y 1))
0.3b	(cbrt.f64 (+.f64 y 1))

rewrite30.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64_9316`
35×	`*-un-lft-identity_binary64_9285`
23×	`add-sqr-sqrt_binary64_9307`
18×	`cbrt-div_binary64_9317`
15×	`add-cube-cbrt_binary64_9320`
11×	`pow1_binary64_9346`
9×	`swap-sqr_binary64_9252` `flip-+_binary64_9259` `pow1/3_binary64_9367` `distribute-lft-out_binary64_9236` `flip3-+_binary64_9288`
7×	`associate-l_binary64_9226` `associate-r_binary64_9225`
6×	`add-exp-log_binary64_9323`
4×	`frac-times_binary64_9295` `unswap-sqr_binary64_9253` `add-cbrt-cube_binary64_9321` `add-log-exp_binary64_9324`
2×	`associate-l/_binary64_9228` `pow-prod-down_binary64_9356` `pow-prod-up_binary64_9355` `associate-r/_binary64_9227` `pow-sqr_binary64_9258`
1×	`cbrt-unprod_binary64_9318` `prod-exp_binary64_9334` `pow-plus_binary64_9348` `*-commutative_binary64_9216` `pow2_binary64_9366`

Counts

4 → 95

Calls

8 calls:

11.0ms	(*.f64 (cbrt.f64 (+.f64 y 1)) (cbrt.f64 (+.f64 y 1)))
3.0ms	(cbrt.f64 (+.f64 y 1))
3.0ms	(cbrt.f64 (+.f64 y 1))
3.0ms	(cbrt.f64 (+.f64 y 1))
0.0ms	(/.f64 y (+.f64 y 1))

series223.0ms (0.3%)

Counts

4 → 39

Calls

4 calls:

65.0ms	(*.f64 (cbrt.f64 (+.f64 y 1)) (cbrt.f64 (+.f64 y 1)))
54.0ms	(cbrt.f64 (+.f64 y 1))
53.0ms	(cbrt.f64 (+.f64 y 1))
51.0ms	(cbrt.f64 (+.f64 y 1))

Compiler

Compiled 1385 to 1185 computations (14.4% saved)

simplify129.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4852	1870
1	4852	1870

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 y 1)) (cbrt.f64 (+.f64 y 1)))) (/.f64 (sqrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 y 1))))
0.1b	(/.f64 (sqrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 y 1)))
0.0b	(sqrt.f64 (+.f64 x y))
0.0b	(sqrt.f64 (+.f64 x y))
0.2b	(*.f64 (cbrt.f64 (+.f64 y 1)) (cbrt.f64 (+.f64 y 1)))
0.3b	(cbrt.f64 (+.f64 y 1))
0.3b	(cbrt.f64 (+.f64 y 1))
0.3b	(cbrt.f64 (+.f64 y 1))

rewrite30.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64_9316`
35×	`*-un-lft-identity_binary64_9285`
23×	`add-sqr-sqrt_binary64_9307`
18×	`cbrt-div_binary64_9317`
15×	`add-cube-cbrt_binary64_9320`
11×	`pow1_binary64_9346`
9×	`swap-sqr_binary64_9252` `flip-+_binary64_9259` `pow1/3_binary64_9367` `distribute-lft-out_binary64_9236` `flip3-+_binary64_9288`
7×	`associate-l_binary64_9226` `associate-r_binary64_9225`
6×	`add-exp-log_binary64_9323`
4×	`frac-times_binary64_9295` `unswap-sqr_binary64_9253` `add-cbrt-cube_binary64_9321` `add-log-exp_binary64_9324`
2×	`associate-l/_binary64_9228` `pow-prod-down_binary64_9356` `pow-prod-up_binary64_9355` `associate-r/_binary64_9227` `pow-sqr_binary64_9258`
1×	`cbrt-unprod_binary64_9318` `prod-exp_binary64_9334` `pow-plus_binary64_9348` `*-commutative_binary64_9216` `pow2_binary64_9366`

Counts

4 → 95

Calls

8 calls:

11.0ms	(*.f64 (cbrt.f64 (+.f64 y 1)) (cbrt.f64 (+.f64 y 1)))
3.0ms	(cbrt.f64 (+.f64 y 1))
3.0ms	(cbrt.f64 (+.f64 y 1))
3.0ms	(cbrt.f64 (+.f64 y 1))
0.0ms	(sqrt.f64 (+.f64 x y))

series219.0ms (0.3%)

Counts

4 → 39

Calls

4 calls:

66.0ms	(*.f64 (cbrt.f64 (+.f64 y 1)) (cbrt.f64 (+.f64 y 1)))
53.0ms	(cbrt.f64 (+.f64 y 1))
51.0ms	(cbrt.f64 (+.f64 y 1))
50.0ms	(cbrt.f64 (+.f64 y 1))

Compiler

Compiled 1469 to 1143 computations (22.2% saved)

simplify124.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4852	1870
1	4852	1870

prune14.2s (16.3%)

Pruning

390 alts after pruning (382 fresh and 8 done)

	Pruned	Kept	Total
New	353	201	554
Fresh	34	181	215
Picked	0	0	0
Done	1	8	9
Total	388	390	778

Error

Counts

778 → 390

Compiler

Compiled 18707 to 13008 computations (30.5% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 y (+.f64 y 1))
0.0b	(/.f64 x (+.f64 y 1))
0.0b	(/.f64 x (+.f64 y 1))
0.0b	(/.f64 y (+.f64 y 1))

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_9285`
24×	`times-frac_binary64_9291`
20×	`add-sqr-sqrt_binary64_9307` `add-cube-cbrt_binary64_9320`
8×	`distribute-lft-out_binary64_9236` `associate-/r*_binary64_9229`
6×	`add-cbrt-cube_binary64_9321` `associate-/l*_binary64_9230` `add-exp-log_binary64_9323`
4×	`associate-/r/_binary64_9231`
2×	`clear-num_binary64_9284` `div-exp_binary64_9336` `cbrt-undiv_binary64_9319` `pow1_binary64_9346` `flip-+_binary64_9259` `frac-2neg_binary64_9296` `add-log-exp_binary64_9324` `flip3-+_binary64_9288` `div-inv_binary64_9282`

Counts

2 → 66

Calls

4 calls:

6.0ms	(/.f64 y (+.f64 y 1))
5.0ms	(/.f64 x (+.f64 y 1))
0.0ms	(/.f64 x (+.f64 y 1))
0.0ms	(/.f64 y (+.f64 y 1))

series108.0ms (0.1%)

Counts

2 → 27

Calls

2 calls:

74.0ms	(/.f64 x (+.f64 y 1))
34.0ms	(/.f64 y (+.f64 y 1))

Compiler

Compiled 556 to 466 computations (16.2% saved)

simplify91.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4952	1173
1	4952	1173

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

3.1b	(+.f64 (pow.f64 x 3) (pow.f64 y 3))
1.4b	(+.f64 (.f64 x x) (.f64 y (-.f64 y x)))
0.0b	(.f64 (+.f64 y 1) (+.f64 (.f64 x x) (*.f64 y (-.f64 y x))))
0.0b	(*.f64 y (-.f64 y x))
0.0b	(.f64 (+.f64 y 1) (+.f64 (.f64 x x) (*.f64 y (-.f64 y x))))
1.4b	(+.f64 (.f64 x x) (.f64 y (-.f64 y x)))
3.1b	(+.f64 (pow.f64 x 3) (pow.f64 y 3))
39.6b	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (.f64 (+.f64 y 1) (+.f64 (.f64 x x) (*.f64 y (-.f64 y x)))))

rewrite61.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64_9285`
16×	`distribute-lft-out_binary64_9236`
15×	`flip-+_binary64_9259` `flip3-+_binary64_9288`
12×	`add-sqr-sqrt_binary64_9307` `unpow-prod-down_binary64_9364` `cube-prod_binary64_9313`
11×	`add-cbrt-cube_binary64_9321` `add-exp-log_binary64_9323`
10×	`add-cube-cbrt_binary64_9320`
9×	`times-frac_binary64_9291` `associate-/l*_binary64_9230`
8×	`associate-+r+_binary64_9217` `frac-times_binary64_9295` `add-log-exp_binary64_9324` `associate-/r/_binary64_9231`
6×	`cancel-sign-sub-inv_binary64_9251` `pow1_binary64_9346`
5×	`distribute-lft-in_binary64_9234` `distribute-rgt-in_binary64_9235`
4×	`associate-l/_binary64_9228` `associate-l_binary64_9226` `associate-r/_binary64_9227`
3×	`associate-r_binary64_9225` `sum-cubes_binary64_9286`
2×	`associate-/l/_binary64_9232` `cbrt-unprod_binary64_9318` `prod-exp_binary64_9334` `div-exp_binary64_9336` `sub-neg_binary64_9278` `cbrt-undiv_binary64_9319` `sum-log_binary64_9376` `+-commutative_binary64_9215`
1×	`clear-num_binary64_9284` `pow-prod-down_binary64_9356` `unswap-sqr_binary64_9253` `frac-2neg_binary64_9296` `-commutative_binary64_9216` `associate-/r_binary64_9229` `div-inv_binary64_9282`

Counts

4 → 108

Calls

8 calls:

22.0ms	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (.f64 (+.f64 y 1) (+.f64 (.f64 x x) (*.f64 y (-.f64 y x)))))
12.0ms	(+.f64 (pow.f64 x 3) (pow.f64 y 3))
10.0ms	(.f64 (+.f64 y 1) (+.f64 (.f64 x x) (*.f64 y (-.f64 y x))))
5.0ms	(+.f64 (.f64 x x) (.f64 y (-.f64 y x)))
0.0ms	(*.f64 y (-.f64 y x))

series649.0ms (0.7%)

Counts

4 → 69

Calls

4 calls:

174.0ms	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (.f64 (+.f64 y 1) (+.f64 (.f64 x x) (*.f64 y (-.f64 y x)))))
163.0ms	(+.f64 (pow.f64 x 3) (pow.f64 y 3))
158.0ms	(.f64 (+.f64 y 1) (+.f64 (.f64 x x) (*.f64 y (-.f64 y x))))
153.0ms	(+.f64 (.f64 x x) (.f64 y (-.f64 y x)))

Compiler

Compiled 1965 to 1519 computations (22.7% saved)

simplify120.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4975	3752
1	4975	3752

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (/.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 y 1))) (sqrt.f64 (+.f64 y 1)))
0.0b	(/.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 y 1)))
0.0b	(sqrt.f64 (+.f64 x y))
0.0b	(sqrt.f64 (+.f64 x y))
0.0b	(sqrt.f64 (+.f64 x y))
0.0b	(/.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 y 1)))
0.1b	(/.f64 (/.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 y 1))) (sqrt.f64 (+.f64 y 1)))
0.2b	(*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 (/.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 y 1))) (sqrt.f64 (+.f64 y 1))))

rewrite378.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

1590×	`times-frac_binary64_9291`
1393×	`sqrt-prod_binary64_9301`
1375×	`*-un-lft-identity_binary64_9285`
778×	`add-sqr-sqrt_binary64_9307`
697×	`add-cube-cbrt_binary64_9320`
391×	`associate-r_binary64_9225`
339×	`distribute-lft-out_binary64_9236`
62×	`associate-/l*_binary64_9230`
44×	`sqrt-div_binary64_9302`
36×	`associate-/r/_binary64_9231`
22×	`unswap-sqr_binary64_9253` `flip-+_binary64_9259` `flip3-+_binary64_9288`
20×	`add-cbrt-cube_binary64_9321` `add-exp-log_binary64_9323`
18×	`div-inv_binary64_9282`
14×	`associate-/r*_binary64_9229`
7×	`div-exp_binary64_9336` `cbrt-undiv_binary64_9319` `associate-l_binary64_9226` `pow1_binary64_9346`
5×	`sqrt-undiv_binary64_9306`
4×	`add-log-exp_binary64_9324`
3×	`associate-/l/_binary64_9232` `cbrt-unprod_binary64_9318` `prod-exp_binary64_9334`
2×	`clear-num_binary64_9284` `associate-*l/_binary64_9228` `frac-times_binary64_9295` `frac-2neg_binary64_9296`
1×	`pow-prod-down_binary64_9356` `associate-r/_binary64_9227` `-commutative_binary64_9216` `sqrt-unprod_binary64_9305` `rem-sqrt-square_binary64_9298` `sqrt-pow1_binary64_9303` `pow1/2_binary64_9365`

Counts

4 → 1000

Calls

8 calls:

134.0ms	(*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 (/.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 y 1))) (sqrt.f64 (+.f64 y 1))))
33.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 y 1))) (sqrt.f64 (+.f64 y 1)))
10.0ms	(/.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 y 1)))
3.0ms	(sqrt.f64 (+.f64 x y))
0.0ms	(sqrt.f64 (+.f64 x y))

series363.0ms (0.4%)

Counts

4 → 53

Calls

4 calls:

117.0ms	(/.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 y 1)))
106.0ms	(*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 (/.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 y 1))) (sqrt.f64 (+.f64 y 1))))
90.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 y 1))) (sqrt.f64 (+.f64 y 1)))
49.0ms	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 1806 to 1446 computations (19.9% saved)

simplify371.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1053 → 1053

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4966	31809
1	4966	31809

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (+.f64 y 1)) (cbrt.f64 (+.f64 y 1)))) (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y 1))))
0.0b	(/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y 1)))
0.0b	(/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (+.f64 y 1)) (cbrt.f64 (+.f64 y 1))))
0.0b	(/.f64 x (+.f64 y 1))
0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_9316`
23×	`add-sqr-sqrt_binary64_9307`
15×	`*-un-lft-identity_binary64_9285` `add-cube-cbrt_binary64_9320`
11×	`pow1_binary64_9346`
9×	`pow1/3_binary64_9367`
6×	`swap-sqr_binary64_9252` `associate-l_binary64_9226` `associate-r_binary64_9225` `add-exp-log_binary64_9323`
4×	`unswap-sqr_binary64_9253` `add-cbrt-cube_binary64_9321` `add-log-exp_binary64_9324`
2×	`pow-prod-down_binary64_9356` `pow-prod-up_binary64_9355` `pow-sqr_binary64_9258`
1×	`cbrt-unprod_binary64_9318` `prod-exp_binary64_9334` `pow-plus_binary64_9348` `*-commutative_binary64_9216` `pow2_binary64_9366`

Counts

4 → 73

Calls

8 calls:

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

series352.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
84.0ms	(cbrt.f64 y)
82.0ms	(cbrt.f64 y)
79.0ms	(cbrt.f64 y)

Compiler

Compiled 754 to 598 computations (20.7% saved)

simplify88.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4873	548
1	4873	548

prune29.6s (33.9%)

Pruning

556 alts after pruning (543 fresh and 13 done)

	Pruned	Kept	Total
New	1170	238	1408
Fresh	72	305	377
Picked	0	0	0
Done	0	13	13
Total	1242	556	1798

Error

Counts

1798 → 556

Compiler

Compiled 15423 to 8303 computations (46.2% saved)

simplify718.0ms (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4993	47178
1	4993	47178

regimes8.5s (9.7%)

Compiler: Compiled 69704 to 49013 computations (29.7% saved)

bsearch0.0ms (0%)

regimes105.0ms (0.1%)

Compiler: Compiled 471 to 449 computations (4.7% saved)

bsearch0.0ms (0%)

regimes81.0ms (0.1%)

Compiler: Compiled 98 to 114 computations (-16.3% saved)

bsearch23.0ms (0%)

Steps

Iters	Range		Point
8	8.951275089691592e-26	5.039133880677533e-21	4.9348703360248525e-21
6	-0.0005972207045617881	-0.00014211870981034057	-0.00016371713172152162

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes91.0ms (0.1%)

Compiler: Compiled 84 to 104 computations (-23.8% saved)

bsearch28.0ms (0%)

Steps

Iters	Range		Point
9	6.578146766914627e+18	9.127523733615497e+23	7.964679520541659e+21
9	-1.557137979392603e+40	-1.3289912796642235e+34	-1.6290916020610802e+37

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes107.0ms (0.1%)

Compiler: Compiled 32 to 52 computations (-62.5% saved)

bsearch45.0ms (0.1%)

Steps

Iters	Range		Point
3	1.758429223527947e+148	2.3260588167714206e+148	1.793906073105664e+148
9	9.648436980652349e-05	33.318685738147025	9.758469592823563e-05
9	1.295010377502728e-79	2.5372985246450584e-74	5.430151421803193e-75
10	-228714761080280.75	-12435.954290891914	-2057647.2520269328

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes92.0ms (0.1%)

Compiler: Compiled 22 to 42 computations (-90.9% saved)

bsearch35.0ms (0%)

Steps

Iters	Range		Point
9	9.648436980652349e-05	33.318685738147025	1.0114685826183083
9	1.295010377502728e-79	2.5372985246450584e-74	2.467067767939997e-77
8	-1.8301954562646827	-0.0005972207045617881	-0.99570101351035

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes36.0ms (0%)

Accuracy

Total 0.0b remaining (100%)

Threshold costs 0.0b (100%)

Compiler

Compiled 8 to 18 computations (-125% saved)

bsearch29.0ms (0%)

Steps

Iters	Range		Point
8	8.951275089691592e-26	5.039133880677533e-21	4.9348703360248525e-21
8	-1.8301954562646827	-0.0005972207045617881	-0.99570101351035

Compiler

Compiled 124 to 99 computations (20.2% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	86	164
1	86	164

end0.0ms (0%)

sample21.5s (24.6%)

Algorithm

1×

intervals

Results

195.0ms	7999×	body	128	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 23550 to 16592 computations (29.5% saved)

Pareto

0.20789987255932857