Details

analyze318.0ms (7.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample76.0ms (1.8%)

Algorithm

1×

intervals

Results

37.0ms	78×	body	1280	valid
14.0ms	48×	body	640	valid
11.0ms	31×	body	2560	valid
4.0ms	26×	body	320	valid
3.0ms	62×	body	80	valid
1.0ms	11×	body	160	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify15.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

prune3.0ms (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: 54.3b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

1.1b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.4b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
16.3b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64`
3×	`flip3-+_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`distribute-lft-out_binary64` `log-div_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 42

Calls

3 calls:

7.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series16.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

8.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
5.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify68.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5010	862

prune60.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0.0b

Counts

52 → 4

Compiler

Compiled 812 to 538 computations (33.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
20.7b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
13×	`add-exp-log_binary64`
10×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `unpow-prod-down_binary64`
7×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
6×	`prod-exp_binary64`
4×	`sqr-pow_binary64` `cube-prod_binary64`
3×	`pow1_binary64`
2×	`pow-to-exp_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

3 → 69

Calls

3 calls:

7.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
6.0ms	(*.f64 3/40 (pow.f64 x 5))

series16.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

6.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
5.0ms	(*.f64 3/40 (pow.f64 x 5))
4.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify80.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5004	1008

prune67.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	77	5	82

Merged error: 0.0b

Counts

82 → 5

Compiler

Compiled 1459 to 1133 computations (22.3% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/16 (pow.f64 x 5))
0.4b	(/.f64 1/8 (pow.f64 x 3))
14.3b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
17.7b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite88.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
71×	`times-frac_binary64`
68×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
26×	`unpow-prod-down_binary64`
19×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
14×	`cube-prod_binary64`
11×	`log-prod_binary64`
10×	`sqr-pow_binary64` `difference-of-squares_binary64`
9×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-sub_binary64`
5×	`pow1_binary64` `log-div_binary64`
4×	`distribute-lft-out_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sum-log_binary64`

Counts

4 → 159

Calls

4 calls:

36.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
35.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
6.0ms	(/.f64 1/8 (pow.f64 x 3))
5.0ms	(/.f64 1/16 (pow.f64 x 5))

series25.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
6.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
5.0ms	(/.f64 1/16 (pow.f64 x 5))
4.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify102.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5317	3623

prune196.0ms (4.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	171	5	176

Merged error: 0.0b

Counts

176 → 5

Compiler

Compiled 4121 to 3275 computations (20.5% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.4b	(/.f64 1/8 (pow.f64 x 3))
11.4b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`associate-/r*_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
8×	`add-exp-log_binary64`
6×	`log-prod_binary64`
4×	`distribute-lft-out_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`pow1_binary64` `associate-/l*_binary64` `div-exp_binary64`
2×	`add-log-exp_binary64` `distribute-lft-out--_binary64` `log-div_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

2 → 82

Calls

2 calls:

22.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

series12.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

8.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
4.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify76.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5049	1420

prune68.0ms (1.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	88	5	93

Merged error: 0.0b

Counts

93 → 5

Compiler

Compiled 1752 to 1285 computations (26.7% saved)

regimes31.0ms (0.8%)

Compiler: Compiled 72 to 61 computations (15.3% saved)

bsearch26.0ms (0.6%)

Steps

Iters	Range		Point
9	0.04411607610495515	177787.32042252456	0.9667608709422276
9	-1493439.6319824792	-0.00423940421494459	-1.0832968729492856

Compiler

Compiled 1 to 1 computations (0% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample2.7s (64.8%)

Algorithm

1×

intervals

Results

1.2s	2307×	body	1280	valid
467.0ms	1558×	body	640	valid
305.0ms	825×	body	2560	valid
143.0ms	775×	body	320	valid
101.0ms	2164×	body	80	valid
40.0ms	371×	body	160	valid

Compiler

Compiled 155 to 125 computations (19.4% saved)

Details

analyze318.0ms (7.7%)

sample76.0ms (1.8%)

simplify15.0ms (0.4%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

rewrite19.0ms (0.5%)

series16.0ms (0.4%)

simplify68.0ms (1.6%)

prune60.0ms (1.5%)

localize9.0ms (0.2%)

rewrite20.0ms (0.5%)

series16.0ms (0.4%)

simplify80.0ms (1.9%)

prune67.0ms (1.6%)

localize12.0ms (0.3%)

rewrite88.0ms (2.1%)

series25.0ms (0.6%)

simplify102.0ms (2.5%)

prune196.0ms (4.8%)

localize11.0ms (0.3%)

rewrite31.0ms (0.7%)

series12.0ms (0.3%)

simplify76.0ms (1.8%)

prune68.0ms (1.7%)

regimes31.0ms (0.8%)

bsearch26.0ms (0.6%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.7s (64.8%)

Profiling