Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample20.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms	58×	body	640	valid
4.0ms	136×	body	80	valid
3.0ms	40×	body	320	valid
1.0ms	22×	body	160	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify25.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	77	16
1	77	16

prune6.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.5b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
2.1b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

rewrite56.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64`
72×	`add-sqr-sqrt_binary64`
69×	`times-frac_binary64`
32×	`add-cube-cbrt_binary64`
27×	`distribute-lft-out--_binary64`
17×	`difference-of-squares_binary64`
11×	`associate-/r*_binary64` `add-exp-log_binary64`
10×	`distribute-lft-out_binary64`
7×	`add-cbrt-cube_binary64`
6×	`associate-/r/_binary64` `associate-/l*_binary64` `div-inv_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`difference-of-sqr-1_binary64` `div-exp_binary64`
3×	`insert-posit16` `flip--_binary64`
2×	`flip3--_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-flip_binary64` `flip-+_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `frac-sub_binary64`

Counts

3 → 127

Calls

3 calls:

35.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
7.0ms	(/.f64 1 (-.f64 x 1))
7.0ms	(/.f64 1 (+.f64 x 1))

series118.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

83.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
19.0ms	(/.f64 1 (-.f64 x 1))
15.0ms	(/.f64 1 (+.f64 x 1))

simplify109.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4854	2154
1	4854	2154

prune144.0ms (4.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	135	2	137

Merged error: 0.3b

Counts

137 → 2

Compiler

Compiled 2361 to 1947 computations (17.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.3b	(/.f64 -2 (+.f64 -1 (*.f64 x x)))

rewrite7.0ms (0.2%)

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` `insert-posit16` `flip-+_binary64`

Counts

1 → 30

Calls

1 calls:

6.0ms

(/.f64 -2 (+.f64 -1 (*.f64 x x)))

series37.0ms (1.2%)

Counts

1 → 3

Calls

1 calls:

37.0ms

(/.f64 -2 (+.f64 -1 (*.f64 x x)))

simplify115.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	5273	569

prune38.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	31	4	35

Merged error: 0.2b

Counts

35 → 4

Compiler

Compiled 526 to 359 computations (31.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1 (.f64 (cbrt.f64 (+.f64 -1 (.f64 x x))) (cbrt.f64 (+.f64 -1 (*.f64 x x)))))
14.9b	(cbrt.f64 (+.f64 -1 (*.f64 x x)))
14.9b	(cbrt.f64 (+.f64 -1 (*.f64 x x)))
14.9b	(cbrt.f64 (+.f64 -1 (*.f64 x x)))

rewrite27.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-div_binary64`
15×	`add-exp-log_binary64`
12×	`pow1_binary64`
9×	`flip3-+_binary64` `*-un-lft-identity_binary64` `pow1/3_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `pow-flip_binary64` `flip-+_binary64` `cbrt-prod_binary64`
8×	`associate-/r/_binary64`
7×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `div-exp_binary64` `insert-posit16` `frac-times_binary64`
3×	`prod-exp_binary64` `associate-/l*_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `rec-exp_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`associate-/r*_binary64` `cbrt-unprod_binary64` `pow-plus_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow2_binary64`

Counts

4 → 86

Calls

4 calls:

14.0ms	(/.f64 1 (.f64 (cbrt.f64 (+.f64 -1 (.f64 x x))) (cbrt.f64 (+.f64 -1 (*.f64 x x)))))
3.0ms	(cbrt.f64 (+.f64 -1 (*.f64 x x)))
3.0ms	(cbrt.f64 (+.f64 -1 (*.f64 x x)))
3.0ms	(cbrt.f64 (+.f64 -1 (*.f64 x x)))

series403.0ms (13.1%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(/.f64 1 (.f64 (cbrt.f64 (+.f64 -1 (.f64 x x))) (cbrt.f64 (+.f64 -1 (*.f64 x x)))))
100.0ms	(cbrt.f64 (+.f64 -1 (*.f64 x x)))
96.0ms	(cbrt.f64 (+.f64 -1 (*.f64 x x)))
90.0ms	(cbrt.f64 (+.f64 -1 (*.f64 x x)))

simplify108.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4906	1598
1	4906	1598

prune159.0ms (5.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	97	5	102

Merged error: 0.2b

Counts

102 → 5

Compiler

Compiled 2910 to 1968 computations (32.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 1 (cbrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (cbrt.f64 (+.f64 -1 (*.f64 x x)))))
14.9b	(cbrt.f64 (+.f64 -1 (*.f64 x x)))
14.9b	(cbrt.f64 (+.f64 -1 (*.f64 x x)))
14.9b	(cbrt.f64 (+.f64 -1 (*.f64 x x)))

rewrite54.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

129×	`add-sqr-sqrt_binary64`
112×	`times-frac_binary64`
81×	`*-un-lft-identity_binary64`
65×	`cbrt-prod_binary64`
59×	`add-cube-cbrt_binary64`
44×	`add-exp-log_binary64`
26×	`swap-sqr_binary64`
25×	`unswap-sqr_binary64`
24×	`associate-r_binary64` `associate-l_binary64`
19×	`pow1_binary64`
16×	`prod-exp_binary64` `div-exp_binary64`
14×	`cbrt-div_binary64` `pow-flip_binary64`
12×	`add-cbrt-cube_binary64`
9×	`pow1/3_binary64`
8×	`1-exp_binary64` `associate-/r/_binary64` `inv-pow_binary64` `rec-exp_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`pow-prod-up_binary64` `div-inv_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `pow-sqr_binary64` `insert-posit16`
1×	`associate-r/_binary64` `pow-plus_binary64` `un-div-inv_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 190

Calls

4 calls:

29.0ms	(.f64 (/.f64 1 (cbrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (cbrt.f64 (+.f64 -1 (*.f64 x x)))))
3.0ms	(cbrt.f64 (+.f64 -1 (*.f64 x x)))
3.0ms	(cbrt.f64 (+.f64 -1 (*.f64 x x)))
3.0ms	(cbrt.f64 (+.f64 -1 (*.f64 x x)))

series400.0ms (13%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(.f64 (/.f64 1 (cbrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (cbrt.f64 (+.f64 -1 (*.f64 x x)))))
93.0ms	(cbrt.f64 (+.f64 -1 (*.f64 x x)))
92.0ms	(cbrt.f64 (+.f64 -1 (*.f64 x x)))
92.0ms	(cbrt.f64 (+.f64 -1 (*.f64 x x)))

simplify154.0ms (5%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4964	4706
1	4964	4706

prune350.0ms (11.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	202	5	207

Merged error: 0.2b

Counts

207 → 5

Compiler

Compiled 6310 to 4321 computations (31.5% saved)

regimes13.0ms (0.4%)

Compiler: Compiled 95 to 74 computations (22.1% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	10
1	8	10

end0.0ms (0%)

sample702.0ms (22.8%)

Algorithm

1×

intervals

Results

203.0ms	1907×	body	640	valid
133.0ms	4225×	body	80	valid
106.0ms	1235×	body	320	valid
35.0ms	633×	body	160	valid

Compiler

Compiled 112 to 90 computations (19.6% saved)

Details

analyze4.0ms (0.1%)

sample20.0ms (0.6%)

simplify25.0ms (0.8%)

prune6.0ms (0.2%)

localize7.0ms (0.2%)

rewrite56.0ms (1.8%)

series118.0ms (3.8%)

simplify109.0ms (3.5%)

prune144.0ms (4.7%)

localize4.0ms (0.1%)

rewrite7.0ms (0.2%)

series37.0ms (1.2%)

simplify115.0ms (3.7%)

prune38.0ms (1.2%)

localize10.0ms (0.3%)

rewrite27.0ms (0.9%)

series403.0ms (13.1%)

simplify108.0ms (3.5%)

prune159.0ms (5.1%)

localize10.0ms (0.3%)

rewrite54.0ms (1.7%)

series400.0ms (13%)

simplify154.0ms (5%)

prune350.0ms (11.4%)

regimes13.0ms (0.4%)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

end0.0ms (0%)

sample702.0ms (22.8%)

Profiling