Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample23.0ms (0.8%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

Compiler

Compiled 29 to 25 computations (13.8% saved)

simplify74.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	473	10
1	473	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: 8.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.0b	(/.f64 x0 (-.f64 1 x1))
7.3b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

rewrite25.0ms (0.8%)

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` `insert-posit16` `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 → 57

Calls

2 calls:

16.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
7.0ms	(/.f64 x0 (-.f64 1 x1))

series124.0ms (4.1%)

Counts

2 → 6

Calls

2 calls:

66.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
58.0ms	(/.f64 x0 (-.f64 1 x1))

simplify113.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5131	949

prune50.0ms (1.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	2	64

Merged error: 6.6b

Counts

64 → 2

Compiler

Compiled 888 to 535 computations (39.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
5.8b	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)

rewrite60.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64` `times-frac_binary64`
18×	`difference-of-squares_binary64`
11×	`pow1_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64` `flip3--_binary64` `swap-sqr_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
6×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64`
4×	`insert-posit16` `frac-times_binary64`
3×	`sub-neg_binary64` `associate-/l*_binary64`
2×	`associate-r/_binary64` `associate-/r/_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `pow-prod-up_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 117

Calls

4 calls:

19.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
13.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
13.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
9.0ms	(/.f64 x0 (-.f64 1 x1))

series243.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
54.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
53.0ms	(/.f64 x0 (-.f64 1 x1))
16.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))

simplify135.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5129	1807

prune156.0ms (5.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	129	2	131

Merged error: 5.1b

Counts

131 → 2

Compiler

Compiled 3452 to 2154 computations (37.6% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 x1 (+.f64 x1 -2))
0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
5.8b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite45.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64` `pow1_binary64`
5×	`distribute-lft-out--_binary64`
4×	`associate-r_binary64` `insert-posit16`
3×	`associate-l_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 94

Calls

4 calls:

14.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
12.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
8.0ms	(*.f64 x1 (+.f64 x1 -2))
7.0ms	(/.f64 x0 (-.f64 1 x1))

series313.0ms (10.4%)

Counts

4 → 12

Calls

4 calls:

141.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
61.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
60.0ms	(/.f64 x0 (-.f64 1 x1))
51.0ms	(*.f64 x1 (+.f64 x1 -2))

simplify81.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4951	1580
1	4951	1580

prune128.0ms (4.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	106	2	108

Merged error: 4.1b

Counts

108 → 2

Compiler

Compiled 2944 to 1846 computations (37.3% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
4.6b	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
5.8b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite50.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64`
7×	`log-pow_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64` `exp-prod_binary64`
5×	`pow1_binary64`
4×	`log-prod_binary64` `insert-posit16`
3×	`associate-/l*_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `clear-num_binary64` `exp-sum_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 91

Calls

4 calls:

14.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
13.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
12.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
7.0ms	(/.f64 x0 (-.f64 1 x1))

series405.0ms (13.5%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
144.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
57.0ms	(/.f64 x0 (-.f64 1 x1))
54.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))

simplify108.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4965	1819
1	4965	1819

prune137.0ms (4.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	103	2	105

Merged error: 3.1b

Counts

105 → 2

Compiler

Compiled 3053 to 1975 computations (35.3% saved)

regimes20.0ms (0.7%)

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

bsearch15.0ms (0.5%)

Steps

Iters	Range		Point
7	0.000209	0.0186	0.00021208908081054686

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	59	108
1	59	108

end0.0ms (0%)

sample640.0ms (21.4%)

Algorithm

1×

intervals

Results

221.0ms	8000×	pre	80	true
169.0ms	8000×	body	80	valid

Compiler

Compiled 165 to 126 computations (23.6% saved)

Details

analyze3.0ms (0.1%)

sample23.0ms (0.8%)

simplify74.0ms (2.5%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite25.0ms (0.8%)

series124.0ms (4.1%)

simplify113.0ms (3.8%)

prune50.0ms (1.7%)

localize10.0ms (0.3%)

rewrite60.0ms (2%)

series243.0ms (8.1%)

simplify135.0ms (4.5%)

prune156.0ms (5.2%)

localize12.0ms (0.4%)

rewrite45.0ms (1.5%)

series313.0ms (10.4%)

simplify81.0ms (2.7%)

prune128.0ms (4.3%)

localize16.0ms (0.5%)

rewrite50.0ms (1.7%)

series405.0ms (13.5%)

simplify108.0ms (3.6%)

prune137.0ms (4.6%)

regimes20.0ms (0.7%)

bsearch15.0ms (0.5%)

simplify7.0ms (0.2%)

end0.0ms (0%)

sample640.0ms (21.4%)

Profiling