Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

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

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample24.0ms (1.2%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

Compiler

Compiled 29 to 25 computations (13.8% saved)

simplify58.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	499	10
1	499	10

prune3.0ms (0.2%)

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: 8.5b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.0b	(/.f64 x0 (-.f64 1 x1))
7.7b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

rewrite21.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
6×	`associate-/r*_binary64`
5×	`distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/l*_binary64`
2×	`pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 55

Calls

2 calls:

13.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
6.0ms	(/.f64 x0 (-.f64 1 x1))

series14.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

8.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
6.0ms	(/.f64 x0 (-.f64 1 x1))

simplify71.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4971	931
1	4971	931

prune38.0ms (1.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	2	62

Merged error: 6.9b

Counts

62 → 2

Compiler

Compiled 872 to 526 computations (39.7% saved)

localize12.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
0.5b	(/.f64 (.f64 x0 (-.f64 (/.f64 x0 (.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
1.0b	(/.f64 x0 (-.f64 1 x1))
6.2b	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)

rewrite67.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64`
51×	`add-sqr-sqrt_binary64`
23×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64` `distribute-lft-out--_binary64`
10×	`associate-/r*_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`swap-sqr_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
4×	`associate-r/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `frac-times_binary64`
3×	`sub-neg_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `diff-log_binary64` `pow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `pow-sqr_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 128

Calls

4 calls:

28.0ms	(/.f64 (.f64 x0 (-.f64 (/.f64 x0 (.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
17.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
11.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
6.0ms	(/.f64 x0 (-.f64 1 x1))

series53.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(/.f64 (.f64 x0 (-.f64 (/.f64 x0 (.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
18.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
6.0ms	(/.f64 x0 (-.f64 1 x1))
2.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))

simplify112.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4951	2563
1	4951	2563

prune127.0ms (6.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	140	2	142

Merged error: 5.4b

Counts

142 → 2

Compiler

Compiled 3825 to 2423 computations (36.7% saved)

localize15.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 x1 (+.f64 x1 -2))
0.5b	(/.f64 (.f64 x0 (-.f64 (/.f64 x0 (+.f64 1 (.f64 x1 (+.f64 x1 -2)))) x0)) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
1.0b	(/.f64 x0 (-.f64 1 x1))
6.2b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite50.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
23×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r*_binary64` `difference-of-squares_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
5×	`distribute-lft-out--_binary64`
4×	`associate-r_binary64` `associate-r/_binary64` `associate-/r/_binary64` `associate-/l_binary64`
3×	`flip3--_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 105

Calls

4 calls:

22.0ms	(/.f64 (.f64 x0 (-.f64 (/.f64 x0 (+.f64 1 (.f64 x1 (+.f64 x1 -2)))) x0)) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
10.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
7.0ms	(*.f64 x1 (+.f64 x1 -2))
6.0ms	(/.f64 x0 (-.f64 1 x1))

series66.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(/.f64 (.f64 x0 (-.f64 (/.f64 x0 (+.f64 1 (.f64 x1 (+.f64 x1 -2)))) x0)) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
21.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
6.0ms	(/.f64 x0 (-.f64 1 x1))
4.0ms	(*.f64 x1 (+.f64 x1 -2))

simplify84.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5267	2302

prune102.0ms (5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	117	2	119

Merged error: 4.5b

Counts

119 → 2

Compiler

Compiled 3302 to 2059 computations (37.6% saved)

localize16.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (.f64 x0 (log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (.f64 x1 (+.f64 x1 -2)))) x0)))) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
1.0b	(/.f64 x0 (-.f64 1 x1))
5.1b	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
6.2b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite58.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r*_binary64`
7×	`log-pow_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out--_binary64` `exp-prod_binary64`
5×	`pow1_binary64`
4×	`log-prod_binary64` `associate-/r/_binary64` `associate-/l*_binary64`
3×	`cbrt-undiv_binary64` `div-exp_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `exp-sum_binary64` `prod-exp_binary64` `log-div_binary64` `flip-+_binary64`

Counts

4 → 100

Calls

4 calls:

28.0ms	(/.f64 (.f64 x0 (log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (.f64 x1 (+.f64 x1 -2)))) x0)))) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
10.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
10.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
6.0ms	(/.f64 x0 (-.f64 1 x1))

series77.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(/.f64 (.f64 x0 (log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (.f64 x1 (+.f64 x1 -2)))) x0)))) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
20.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
20.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
6.0ms	(/.f64 x0 (-.f64 1 x1))

simplify81.0ms (4%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5748	2461

prune101.0ms (5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	112	2	114

Merged error: 3.5b

Counts

114 → 2

Compiler

Compiled 3297 to 2105 computations (36.2% saved)

regimes39.0ms (1.9%)

Compiler: Compiled 136 to 108 computations (20.6% saved)

bsearch8.0ms (0.4%)

Steps

Iters	Range		Point
7	0.000209	0.0186	0.00021208908081054686

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	108
1	59	108

end0.0ms (0%)

sample729.0ms (35.8%)

Algorithm

1×

intervals

Results

207.0ms	8000×	pre	80	true
162.0ms	8000×	body	80	valid

Compiler

Compiled 165 to 126 computations (23.6% saved)

Details

analyze3.0ms (0.2%)

sample24.0ms (1.2%)

simplify58.0ms (2.8%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

rewrite21.0ms (1%)

series14.0ms (0.7%)

simplify71.0ms (3.5%)

prune38.0ms (1.9%)

localize12.0ms (0.6%)

rewrite67.0ms (3.3%)

series53.0ms (2.6%)

simplify112.0ms (5.5%)

prune127.0ms (6.2%)

localize15.0ms (0.8%)

rewrite50.0ms (2.4%)

series66.0ms (3.2%)

simplify84.0ms (4.1%)

prune102.0ms (5%)

localize16.0ms (0.8%)

rewrite58.0ms (2.8%)

series77.0ms (3.8%)

simplify81.0ms (4%)

prune101.0ms (5%)

regimes39.0ms (1.9%)

bsearch8.0ms (0.4%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample729.0ms (35.8%)

Profiling