Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 8 to 6 computations (25% saved)

sample10.0ms (0.4%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	10
1	7	10

prune2.0ms (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: 14.5b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

14.5b

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

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64`
3×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
2×	`associate-/r/_binary64`
1×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

1 → 29

Calls

1 calls:

7.0ms

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

series52.0ms (1.9%)

Counts

1 → 3

Calls

1 calls:

52.0ms

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

simplify58.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5174	550

prune94.0ms (3.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Merged error: 0b

Counts

33 → 3

Compiler

Compiled 1521 to 953 computations (37.3% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (+.f64 (.f64 x x) 1)))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
14.4b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.4b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite73.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64`
164×	`add-sqr-sqrt_binary64`
162×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
156×	`sqrt-prod_binary64`
27×	`associate-/l*_binary64`
22×	`sqrt-div_binary64`
18×	`associate-/r/_binary64`
12×	`associate-/r*_binary64`
11×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
9×	`div-inv_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64`

Counts

4 → 262

Calls

4 calls:

19.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (+.f64 (.f64 x x) 1)))
8.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series198.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
56.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (+.f64 (.f64 x x) 1)))
42.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
33.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify177.0ms (6.5%)

Algorithm

1×	egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4904	8525
1	4904	8525

prune339.0ms (12.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	274	3	277

Merged error: 0b

Counts

277 → 3

Compiler

Compiled 6873 to 3970 computations (42.2% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (*.f64 x x) 1)
3.1b	(/.f64 x (+.f64 (pow.f64 x 4) -1))
21.0b	(.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)) (-.f64 (.f64 x x) 1))

rewrite48.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
43×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64`
27×	`associate-l_binary64`
21×	`difference-of-sqr--1_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`cancel-sign-sub-inv_binary64`
7×	`associate-/r*_binary64` `distribute-lft-out_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64`
6×	`associate-r_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-times_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

3 → 123

Calls

3 calls:

23.0ms	(.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)) (-.f64 (.f64 x x) 1))
8.0ms	(/.f64 x (+.f64 (pow.f64 x 4) -1))
5.0ms	(-.f64 (*.f64 x x) 1)

series290.0ms (10.7%)

Counts

3 → 9

Calls

3 calls:

147.0ms	(/.f64 x (+.f64 (pow.f64 x 4) -1))
93.0ms	(.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)) (-.f64 (.f64 x x) 1))
50.0ms	(-.f64 (*.f64 x x) 1)

simplify67.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4869	2168
1	4869	2168

prune131.0ms (4.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	132	3	135

Merged error: 0b

Counts

135 → 3

Compiler

Compiled 2553 to 1671 computations (34.5% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5)))
0.3b	(pow.f64 (/.f64 1 x) 3)
0.3b	(/.f64 1 (pow.f64 x 5))
16.6b	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))

rewrite98.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`*-un-lft-identity_binary64`
69×	`add-sqr-sqrt_binary64`
67×	`times-frac_binary64`
52×	`add-cube-cbrt_binary64`
41×	`unpow-prod-down_binary64`
32×	`cancel-sign-sub-inv_binary64`
29×	`cube-prod_binary64`
15×	`add-exp-log_binary64`
13×	`div-inv_binary64`
11×	`add-log-exp_binary64` `distribute-lft-out_binary64`
9×	`add-cbrt-cube_binary64`
8×	`difference-of-squares_binary64`
7×	`associate-/r*_binary64` `sqr-pow_binary64`
6×	`pow1_binary64`
5×	`distribute-lft-out--_binary64` `pow-exp_binary64`
4×	`cube-div_binary64` `rec-exp_binary64` `div-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `pow-pow_binary64` `associate-/l*_binary64` `frac-sub_binary64`
2×	`flip3-+_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `inv-pow_binary64` `rem-cube-cbrt_binary64` `pow-flip_binary64` `flip-+_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

4 → 179

Calls

4 calls:

45.0ms	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))
25.0ms	(+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5)))
6.0ms	(/.f64 1 (pow.f64 x 5))
5.0ms	(pow.f64 (/.f64 1 x) 3)

series237.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5)))
53.0ms	(/.f64 1 (pow.f64 x 5))
43.0ms	(pow.f64 (/.f64 1 x) 3)
38.0ms	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))

simplify97.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4850	2868
1	4850	2868

prune242.0ms (8.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	191	3	194

Merged error: 0b

Counts

194 → 3

Compiler

Compiled 3848 to 3060 computations (20.5% saved)

regimes27.0ms (1%)

Compiler: Compiled 45 to 35 computations (22.2% saved)

bsearch33.0ms (1.2%)

Steps

Iters	Range		Point
10	5.1060082024678407e-05	111837815101329.58	456.806429230397
9	-44823214768636.43	-75956.50512593919	-20496344444626.17

Compiler

Compiled 1 to 1 computations (0% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	75
1	40	75

end0.0ms (0%)

sample390.0ms (14.4%)

Algorithm

1×

intervals

Results

168.0ms

8000×

body

128

valid

Compiler

Compiled 109 to 86 computations (21.1% saved)

Details

analyze1.0ms (0%)

sample10.0ms (0.4%)

simplify8.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite9.0ms (0.3%)

series52.0ms (1.9%)

simplify58.0ms (2.1%)

prune94.0ms (3.5%)

localize6.0ms (0.2%)

rewrite73.0ms (2.7%)

series198.0ms (7.3%)

simplify177.0ms (6.5%)

prune339.0ms (12.5%)

localize8.0ms (0.3%)

rewrite48.0ms (1.8%)

series290.0ms (10.7%)

simplify67.0ms (2.5%)

prune131.0ms (4.8%)

localize11.0ms (0.4%)

rewrite98.0ms (3.6%)

series237.0ms (8.7%)

simplify97.0ms (3.6%)

prune242.0ms (8.9%)

regimes27.0ms (1%)

bsearch33.0ms (1.2%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample390.0ms (14.4%)

Profiling