Details

analyze888.0ms (22.8%)

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
2.3%	97.4%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
24.9%	74.9%	0.2%	13
33.3%	66.5%	0.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample22.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	31×	body	80	invalid

Compiler

Compiled 23 to 26 computations (-13% saved)

simplify163.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (149.0ms)

Iter	Nodes	Cost
0	4984	16
1	4984	16

prune6.0ms (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: 0.9b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
1.5b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

rewrite34.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
27×	`add-cube-cbrt_binary64`
22×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-/l_binary64`
4×	`associate-/r/_binary64`
3×	`flip3--_binary64` `associate-l_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 113

Calls

3 calls:

16.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
9.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
4.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

series61.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

32.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
19.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
10.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

simplify75.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4996	2068
1	4996	2068

prune107.0ms (2.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	113	9	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	9	123

Merged error: 0b

Counts

123 → 9

Compiler

Compiled 2412 to 544 computations (77.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))))
0.0b	(/.f64 z (-.f64 z a))
0.0b	(/.f64 t (-.f64 z a))
1.5b	(*.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))))

rewrite62.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64`
62×	`add-sqr-sqrt_binary64`
48×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
20×	`distribute-lft-out--_binary64`
18×	`associate-r_binary64`
14×	`difference-of-squares_binary64`
10×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/r/_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-/l*_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`sub-neg_binary64` `associate-*r/_binary64` `div-inv_binary64`
3×	`distribute-rgt-out--_binary64` `associate-l_binary64`
2×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `sub-div_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 126

Calls

4 calls:

35.0ms	(*.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))))
8.0ms	(+.f64 x (*.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))))
6.0ms	(/.f64 t (-.f64 z a))
6.0ms	(/.f64 z (-.f64 z a))

series84.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

39.0ms	(*.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))))
32.0ms	(+.f64 x (*.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))))
8.0ms	(/.f64 t (-.f64 z a))
6.0ms	(/.f64 z (-.f64 z a))

simplify98.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5077	2159

prune83.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	142	5	147

Merged error: 0b

Counts

147 → 5

Compiler

Compiled 3043 to 664 computations (78.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 z a))
0.0b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))))
0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
1.5b	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))))

rewrite48.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
32×	`add-exp-log_binary64` `times-frac_binary64`
25×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`
20×	`add-cbrt-cube_binary64`
13×	`prod-exp_binary64`
12×	`pow1_binary64`
8×	`associate-r/_binary64` `associate-l*_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`cbrt-unprod_binary64`
6×	`add-log-exp_binary64` `flip3--_binary64` `div-exp_binary64` `flip--_binary64`
5×	`associate-/r*_binary64`
4×	`pow-prod-down_binary64` `associate-/r/_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`1-exp_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `rec-exp_binary64` `associate-/l*_binary64`
2×	`un-div-inv_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `pow-flip_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 130

Calls

4 calls:

17.0ms	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))))
15.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
6.0ms	(/.f64 1 (-.f64 z a))
5.0ms	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))))

series65.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))))
18.0ms	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))))
10.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
5.0ms	(/.f64 1 (-.f64 z a))

simplify73.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5084	1917

prune83.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	142	5	147

Merged error: 0b

Counts

147 → 5

Compiler

Compiled 2517 to 846 computations (66.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.5b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
5.8b	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
5.8b	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
5.8b	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

rewrite47.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
31×	`associate-r_binary64`
26×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64`
3×	`cbrt-div_binary64` `pow1/3_binary64` `associate-l_binary64` `cbrt-prod_binary64`
2×	`cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

16.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
9.0ms	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
9.0ms	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
9.0ms	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

series150.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
45.0ms	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
42.0ms	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
18.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

simplify85.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	6146	1348

prune46.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	92	5	97

Merged error: 0b

Counts

97 → 5

Compiler

Compiled 3618 to 419 computations (88.4% saved)

regimes349.0ms (9%)

Compiler: Compiled 679 to 490 computations (27.8% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	19
1	35	19

end0.0ms (0%)

sample1.2s (31.2%)

Algorithm

1×

intervals

Results

295.0ms	7999×	body	80	valid
29.0ms	739×	body	80	invalid
0.0ms	1×	body	320	valid

Compiler

Compiled 127 to 96 computations (24.4% saved)

Details

analyze888.0ms (22.8%)

sample22.0ms (0.6%)

simplify163.0ms (4.2%)

prune6.0ms (0.2%)

localize8.0ms (0.2%)

rewrite34.0ms (0.9%)

series61.0ms (1.6%)

simplify75.0ms (1.9%)

prune107.0ms (2.7%)

localize12.0ms (0.3%)

rewrite62.0ms (1.6%)

series84.0ms (2.2%)

simplify98.0ms (2.5%)

prune83.0ms (2.1%)

localize9.0ms (0.2%)

rewrite48.0ms (1.2%)

series65.0ms (1.7%)

simplify73.0ms (1.9%)

prune83.0ms (2.1%)

localize13.0ms (0.3%)

rewrite47.0ms (1.2%)

series150.0ms (3.9%)

simplify85.0ms (2.2%)

prune46.0ms (1.2%)

regimes349.0ms (9%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.2s (31.2%)

Profiling