Details

analyze69.0ms (2.2%)

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%	62.4%	12.6%	6
25%	40.6%	34.4%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample13.0ms (0.4%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify179.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	13
1	24	13

prune5.0ms (0.1%)

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

Merged error: 0.0b

Counts

2 → 2

Compiler

Compiled 49 to 37 computations (24.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
0.0b	(*.f64 x (+.f64 x 2))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_13861` `*-un-lft-identity_binary64_13839`
4×	`associate-r_binary64_13779` `pow1_binary64_13900` `add-log-exp_binary64_13878` `add-cube-cbrt_binary64_13874` `add-exp-log_binary64_13877` `add-cbrt-cube_binary64_13875`
3×	`associate-l_binary64_13780`
2×	`associate-+l+_binary64_13772` `flip3-+_binary64_13842` `distribute-lft-in_binary64_13788` `flip-+_binary64_13813` `associate-*r/_binary64_13781` `distribute-rgt-in_binary64_13789`
1×	`unswap-sqr_binary64_13807` `+-commutative_binary64_13769` `cbrt-unprod_binary64_13872` `distribute-lft-out_binary64_13790` `sum-log_binary64_13930` `*-commutative_binary64_13770` `pow-prod-down_binary64_13910` `prod-exp_binary64_13888`

Counts

2 → 36

Calls

2 calls:

8.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
7.0ms	(*.f64 x (+.f64 x 2))

series103.0ms (3.2%)

Counts

2 → 6

Calls

2 calls:

60.0ms	(*.f64 x (+.f64 x 2))
42.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))

simplify69.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5451	509

prune44.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Merged error: 0b

Counts

44 → 4

Compiler

Compiled 777 to 451 computations (42% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 x 4) (*.f64 x 8))
0.0b	(+.f64 (/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2)))) (*.f64 y y))
0.0b	(+.f64 (.f64 x x) (-.f64 (.f64 2 2) (*.f64 x 2)))
10.3b	(/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2))))

rewrite48.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-log-exp_binary64_13878`
12×	`add-sqr-sqrt_binary64_13861` `add-cube-cbrt_binary64_13874` `*-un-lft-identity_binary64_13839`
9×	`times-frac_binary64_13845`
6×	`add-exp-log_binary64_13877` `add-cbrt-cube_binary64_13875`
5×	`flip3-+_binary64_13842` `flip-+_binary64_13813`
4×	`pow1_binary64_13900` `sum-log_binary64_13930`
3×	`associate-/l_binary64_13784` `+-commutative_binary64_13769` `associate-/r_binary64_13783`
2×	`associate-/l/_binary64_13786` `associate-/r/_binary64_13785` `associate-+r+_binary64_13771`
1×	`div-exp_binary64_13890` `sub-neg_binary64_13832` `associate-+r-_binary64_13773` `cancel-sign-sub-inv_binary64_13805` `cbrt-undiv_binary64_13873` `diff-log_binary64_13931` `clear-num_binary64_13838` `div-inv_binary64_13836` `frac-2neg_binary64_13850`

Counts

4 → 68

Calls

4 calls:

16.0ms	(+.f64 (/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2)))) (*.f64 y y))
13.0ms	(/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2))))
7.0ms	(+.f64 (.f64 x x) (-.f64 (.f64 2 2) (*.f64 x 2)))
5.0ms	(+.f64 (pow.f64 x 4) (*.f64 x 8))

series439.0ms (13.6%)

Counts

4 → 12

Calls

4 calls:

199.0ms	(/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2))))
110.0ms	(+.f64 (pow.f64 x 4) (*.f64 x 8))
108.0ms	(+.f64 (/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2)))) (*.f64 y y))
21.0ms	(+.f64 (.f64 x x) (-.f64 (.f64 2 2) (*.f64 x 2)))

simplify79.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4934	1972
1	4934	1972

prune121.0ms (3.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	80	4	84

Merged error: 0b

Counts

84 → 4

Compiler

Compiled 2508 to 1691 computations (32.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
0.0b	(*.f64 x (+.f64 x 2))
0.0b	(*.f64 x (+.f64 x 2))
0.1b	(.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))))

rewrite53.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_13861`
24×	`pow1_binary64_13900`
21×	`sqrt-prod_binary64_13855` `*-un-lft-identity_binary64_13839`
17×	`add-cube-cbrt_binary64_13874`
14×	`associate-r_binary64_13779` `sqrt-div_binary64_13856`
12×	`associate-l_binary64_13780`
10×	`add-exp-log_binary64_13877` `add-cbrt-cube_binary64_13875`
9×	`sqrt-pow1_binary64_13857` `flip3-+_binary64_13842` `pow1/2_binary64_13919` `flip-+_binary64_13813`
8×	`swap-sqr_binary64_13806`
6×	`unswap-sqr_binary64_13807` `associate-*r/_binary64_13781`
5×	`pow-prod-up_binary64_13909` `pow-prod-down_binary64_13910`
4×	`add-log-exp_binary64_13878` `frac-times_binary64_13849`
3×	`rem-sqrt-square_binary64_13852` `pow-sqr_binary64_13812` `cbrt-unprod_binary64_13872` `*-commutative_binary64_13770` `prod-exp_binary64_13888`
2×	`distribute-lft-in_binary64_13788` `distribute-lft-out_binary64_13790` `associate-*l/_binary64_13782` `distribute-rgt-in_binary64_13789`
1×	`sqr-abs_binary64_13854` `pow-plus_binary64_13902` `sqrt-unprod_binary64_13859` `pow2_binary64_13920` `rem-square-sqrt_binary64_13851`

Counts

4 → 119

Calls

4 calls:

19.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))))
7.0ms	(*.f64 x (+.f64 x 2))
7.0ms	(*.f64 x (+.f64 x 2))
7.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))

series261.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
59.0ms	(*.f64 x (+.f64 x 2))
55.0ms	(*.f64 x (+.f64 x 2))
50.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))))

simplify80.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5092	2029

prune150.0ms (4.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	131	4	135

Merged error: 0b

Counts

135 → 4

Compiler

Compiled 3181 to 1822 computations (42.7% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x (-.f64 x 2))
0.1b	(pow.f64 (/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 4 (.f64 x (-.f64 x 2)))) 3)
10.3b	(/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 4 (.f64 x (-.f64 x 2))))
40.8b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 4 (.f64 x (-.f64 x 2)))) 3))

rewrite59.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64_13861`
48×	`*-un-lft-identity_binary64_13839`
46×	`add-cube-cbrt_binary64_13874`
45×	`times-frac_binary64_13845`
36×	`cbrt-prod_binary64_13870`
30×	`cube-prod_binary64_13867` `unpow-prod-down_binary64_13918`
11×	`add-exp-log_binary64_13877` `add-cbrt-cube_binary64_13875`
10×	`associate-/r/_binary64_13785`
7×	`pow1_binary64_13900`
6×	`flip3-+_binary64_13842` `cancel-sign-sub-inv_binary64_13805` `flip-+_binary64_13813`
5×	`associate-r_binary64_13779` `div-inv_binary64_13836`
4×	`add-log-exp_binary64_13878` `distribute-lft-in_binary64_13788` `distribute-rgt-in_binary64_13789`
3×	`associate-/l_binary64_13784` `associate-l_binary64_13780` `associate-/r_binary64_13783` `pow-unpow_binary64_13916`
2×	`div-exp_binary64_13890` `sub-neg_binary64_13832` `associate-/l/_binary64_13786` `cbrt-undiv_binary64_13873` `unpow3_binary64_13905` `pow-exp_binary64_13907` `cube-mult_binary64_13869` `rem-cube-cbrt_binary64_13862` `cube-div_binary64_13868` `associate-*r/_binary64_13781` `sqr-pow_binary64_13811`
1×	`rem-cbrt-cube_binary64_13863` `pow-to-exp_binary64_13908` `flip--_binary64_13814` `unswap-sqr_binary64_13807` `cbrt-div_binary64_13871` `cbrt-unprod_binary64_13872` `pow1/3_binary64_13921` `distribute-lft-out--_binary64_13791` `difference-of-squares_binary64_13808` `*-commutative_binary64_13770` `clear-num_binary64_13838` `pow-pow_binary64_13911` `pow-prod-down_binary64_13910` `prod-exp_binary64_13888` `frac-2neg_binary64_13850` `flip3--_binary64_13843`

Counts

4 → 157

Calls

4 calls:

12.0ms	(pow.f64 (/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 4 (.f64 x (-.f64 x 2)))) 3)
11.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 4 (.f64 x (-.f64 x 2)))) 3))
9.0ms	(/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 4 (.f64 x (-.f64 x 2))))
8.0ms	(*.f64 x (-.f64 x 2))

series466.0ms (14.4%)

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 4 (.f64 x (-.f64 x 2)))) 3))
180.0ms	(/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 4 (.f64 x (-.f64 x 2))))
52.0ms	(pow.f64 (/.f64 (+.f64 (pow.f64 x 4) (.f64 x 8)) (+.f64 4 (.f64 x (-.f64 x 2)))) 3)
49.0ms	(*.f64 x (-.f64 x 2))

simplify98.0ms (3%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5883	4906

prune290.0ms (9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	169	4	173

Merged error: 0b

Counts

173 → 4

Compiler

Compiled 5162 to 3667 computations (29% saved)

regimes35.0ms (1.1%)

Compiler: Compiled 235 to 185 computations (21.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms (0%)

sample497.0ms (15.4%)

Algorithm

1×

intervals

Results

241.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 107 to 83 computations (22.4% saved)

Details

analyze69.0ms (2.2%)

sample13.0ms (0.4%)

simplify179.0ms (5.6%)

prune5.0ms (0.1%)

localize6.0ms (0.2%)

rewrite17.0ms (0.5%)

series103.0ms (3.2%)

simplify69.0ms (2.1%)

prune44.0ms (1.4%)

localize14.0ms (0.4%)

rewrite48.0ms (1.5%)

series439.0ms (13.6%)

simplify79.0ms (2.5%)

prune121.0ms (3.8%)

localize11.0ms (0.3%)

rewrite53.0ms (1.6%)

series261.0ms (8.1%)

simplify80.0ms (2.5%)

prune150.0ms (4.7%)

localize15.0ms (0.5%)

rewrite59.0ms (1.8%)

series466.0ms (14.4%)

simplify98.0ms (3%)

prune290.0ms (9%)

regimes35.0ms (1.1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample497.0ms (15.4%)

Profiling