Details

analyze1.2s (21.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
18.4%	81.3%	0.2%	13
29.5%	70.3%	0.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	27×	body	128	invalid

Compiler

Compiled 23 to 26 computations (-13% saved)

simplify332.0ms (5.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (216.0ms)

Iter	Nodes	Cost
0	4787	16
1	4787	16

prune2.0ms (0%)

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: 9.6b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
0.0b	(*.f64 (-.f64 y z) t)
9.9b	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_14763` `*-un-lft-identity_binary64_14741`
10×	`add-exp-log_binary64_14779` `add-cbrt-cube_binary64_14777`
7×	`add-cube-cbrt_binary64_14776`
5×	`associate-/r_binary64_14685` `times-frac_binary64_14747` `add-log-exp_binary64_14780` `associate-l*_binary64_14682` `pow1_binary64_14802`
4×	`associate-*l/_binary64_14684`
3×	`distribute-lft-out--_binary64_14693` `flip--_binary64_14716` `associate-r_binary64_14681` `difference-of-squares_binary64_14710` `flip3--_binary64_14745`
2×	`cbrt-undiv_binary64_14775` `cbrt-unprod_binary64_14774` `associate-/l/_binary64_14688` `associate-/r/_binary64_14687` `div-exp_binary64_14792` `prod-exp_binary64_14790`
1×	`unswap-sqr_binary64_14709` `frac-2neg_binary64_14752` `div-inv_binary64_14738` `pow-prod-down_binary64_14812` `distribute-lft-out_binary64_14692` `+-commutative_binary64_14671` `associate-/l_binary64_14686` `-commutative_binary64_14672` `flip-+_binary64_14715` `sum-log_binary64_14832` `clear-num_binary64_14740` `flip3-+_binary64_14744`

Counts

3 → 63

Calls

3 calls:

15.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
8.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
8.0ms	(*.f64 (-.f64 y z) t)

series248.0ms (4.3%)

Counts

3 → 9

Calls

3 calls:

128.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
81.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
38.0ms	(*.f64 (-.f64 y z) t)

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5983	1014

prune97.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	6	73

Merged error: 0.0b

Counts

73 → 6

Compiler

Compiled 1208 to 323 computations (73.3% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
6.2b	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 t (cbrt.f64 (-.f64 a z))))

rewrite97.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64_14763`
38×	`*-un-lft-identity_binary64_14741`
36×	`times-frac_binary64_14747`
32×	`cbrt-prod_binary64_14772`
30×	`associate-r_binary64_14681`
25×	`add-exp-log_binary64_14779`
24×	`add-cube-cbrt_binary64_14776`
20×	`cbrt-div_binary64_14773`
18×	`add-cbrt-cube_binary64_14777`
17×	`associate-l_binary64_14682`
10×	`associate-/r/_binary64_14687` `flip--_binary64_14716` `flip3--_binary64_14745`
8×	`cbrt-unprod_binary64_14774` `prod-exp_binary64_14790`
7×	`distribute-lft-out--_binary64_14693` `cbrt-undiv_binary64_14775` `div-exp_binary64_14792` `difference-of-squares_binary64_14710`
6×	`unswap-sqr_binary64_14709` `pow1_binary64_14802`
5×	`frac-times_binary64_14751`
4×	`add-log-exp_binary64_14780`
3×	`pow1/3_binary64_14823` `associate-r/_binary64_14683` `associate-l/_binary64_14684`
2×	`div-inv_binary64_14738`
1×	`pow-prod-down_binary64_14812` `*-commutative_binary64_14672`

Counts

4 → 122

Calls

4 calls:

53.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 t (cbrt.f64 (-.f64 a z))))
6.0ms	(cbrt.f64 (-.f64 a z))
6.0ms	(cbrt.f64 (-.f64 a z))
6.0ms	(cbrt.f64 (-.f64 a z))

series591.0ms (10.3%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt.f64 (-.f64 a z))
165.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 t (cbrt.f64 (-.f64 a z))))
132.0ms	(cbrt.f64 (-.f64 a z))
116.0ms	(cbrt.f64 (-.f64 a z))

simplify84.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5336	2952

prune137.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	135	5	140

Merged error: 0b

Counts

140 → 5

Compiler

Compiled 3762 to 744 computations (80.2% saved)

localize18.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (pow.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t) 1))
0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
1.3b	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64_14763`
73×	`*-un-lft-identity_binary64_14741`
51×	`times-frac_binary64_14747`
31×	`associate-l_binary64_14682`
27×	`add-cube-cbrt_binary64_14776`
22×	`distribute-lft-out--_binary64_14693` `difference-of-squares_binary64_14710`
10×	`add-exp-log_binary64_14779` `add-cbrt-cube_binary64_14777`
5×	`associate-/r_binary64_14685` `add-log-exp_binary64_14780` `associate-/l_binary64_14686` `pow1_binary64_14802`
4×	`associate-/r/_binary64_14687`
3×	`flip--_binary64_14716` `associate-r_binary64_14681` `flip3--_binary64_14745`
2×	`unswap-sqr_binary64_14709` `div-inv_binary64_14738` `cbrt-undiv_binary64_14775` `cbrt-unprod_binary64_14774` `associate-/l/_binary64_14688` `div-exp_binary64_14792` `prod-exp_binary64_14790`
1×	`div-sub_binary64_14746` `frac-2neg_binary64_14752` `pow-prod-down_binary64_14812` `distribute-lft-out_binary64_14692` `+-commutative_binary64_14671` `associate-l/_binary64_14684` `-commutative_binary64_14672` `flip-+_binary64_14715` `sum-log_binary64_14832` `clear-num_binary64_14740` `flip3-+_binary64_14744`

Counts

3 → 114

Calls

3 calls:

15.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
9.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
5.0ms	(+.f64 x (pow.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t) 1))

series310.0ms (5.4%)

Counts

3 → 9

Calls

3 calls:

128.0ms	(+.f64 x (pow.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t) 1))
126.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
56.0ms	(/.f64 (-.f64 y z) (-.f64 a z))

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5102	2097

prune131.0ms (2.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	123	5	128

Merged error: 0b

Counts

128 → 5

Compiler

Compiled 2508 to 748 computations (70.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 a z)) t)))
0.0b	(/.f64 1 (-.f64 a z))
0.2b	(*.f64 (/.f64 1 (-.f64 a z)) t)
13.5b	(.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 a z)) t))

rewrite50.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64_14763`
42×	`*-un-lft-identity_binary64_14741`
32×	`times-frac_binary64_14747` `add-exp-log_binary64_14779`
26×	`associate-l_binary64_14682`
25×	`add-cube-cbrt_binary64_14776`
20×	`add-cbrt-cube_binary64_14777`
13×	`prod-exp_binary64_14790`
12×	`pow1_binary64_14802`
8×	`distribute-lft-out--_binary64_14693` `difference-of-squares_binary64_14710`
7×	`cbrt-unprod_binary64_14774`
6×	`add-log-exp_binary64_14780` `div-exp_binary64_14792` `associate-*l/_binary64_14684`
5×	`associate-/r*_binary64_14685`
4×	`pow-prod-down_binary64_14812` `associate-/r/_binary64_14687` `flip--_binary64_14716` `associate-r_binary64_14681` `flip3--_binary64_14745`
3×	`unswap-sqr_binary64_14709` `1-exp_binary64_14785` `cbrt-undiv_binary64_14775` `associate-/l*_binary64_14686` `rec-exp_binary64_14791`
2×	`div-inv_binary64_14738` `frac-times_binary64_14751` `*-commutative_binary64_14672`
1×	`frac-2neg_binary64_14752` `associate-*r/_binary64_14683` `+-commutative_binary64_14671` `flip-+_binary64_14715` `pow-flip_binary64_14815` `sum-log_binary64_14832` `inv-pow_binary64_14826` `clear-num_binary64_14740` `flip3-+_binary64_14744`

Counts

4 → 124

Calls

4 calls:

17.0ms	(*.f64 (/.f64 1 (-.f64 a z)) t)
14.0ms	(.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 a z)) t))
6.0ms	(/.f64 1 (-.f64 a z))
4.0ms	(+.f64 x (.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 a z)) t)))

series334.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

132.0ms	(.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 a z)) t))
112.0ms	(+.f64 x (.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 a z)) t)))
65.0ms	(*.f64 (/.f64 1 (-.f64 a z)) t)
24.0ms	(/.f64 1 (-.f64 a z))

simplify92.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5622	1719

prune121.0ms (2.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	136	5	141

Merged error: 0b

Counts

141 → 5

Compiler

Compiled 2331 to 786 computations (66.3% saved)

regimes342.0ms (6%)

Compiler: Compiled 2367 to 1946 computations (17.8% saved)

bsearch1.0ms (0%)

Compiler: Compiled 9 to 9 computations (0% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	70
1	42	70

end0.0ms (0%)

sample1.2s (21.1%)

Algorithm

1×

intervals

Results

379.0ms	7997×	body	128	valid
43.0ms	698×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 423 to 313 computations (26% saved)

Details

analyze1.2s (21.7%)

sample22.0ms (0.4%)

simplify332.0ms (5.8%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite36.0ms (0.6%)

series248.0ms (4.3%)

simplify75.0ms (1.3%)

prune97.0ms (1.7%)

localize15.0ms (0.3%)

rewrite97.0ms (1.7%)

series591.0ms (10.3%)

simplify84.0ms (1.5%)

prune137.0ms (2.4%)

localize18.0ms (0.3%)

rewrite39.0ms (0.7%)

series310.0ms (5.4%)

simplify83.0ms (1.4%)

prune131.0ms (2.3%)

localize10.0ms (0.2%)

rewrite50.0ms (0.9%)

series334.0ms (5.8%)

simplify92.0ms (1.6%)

prune121.0ms (2.1%)

regimes342.0ms (6%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (21.1%)

Profiling