Details

analyze920.0ms (11.7%)

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
24.9%	74.9%	0.2%	13
26.2%	73.5%	0.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample22.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	17×	body	128	invalid

Compiler

Compiled 23 to 26 computations (-13% saved)

simplify150.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (143.0ms)

Iter	Nodes	Cost
0	5681	16

prune3.0ms (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: 1.8b

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 y (/.f64 (-.f64 z t) (-.f64 a t))))
0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
2.3b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

rewrite47.0ms (0.6%)

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:

17.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
10.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
4.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

series519.0ms (6.6%)

Counts

3 → 9

Calls

3 calls:

244.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
176.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
99.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	6268	2068

prune508.0ms (6.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	115	7	122
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	115	8	123

Merged error: 0b

Counts

123 → 8

Compiler

Compiled 6053 to 2840 computations (53.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 z (-.f64 a t))
0.0b	(+.f64 x (*.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t)))))
0.0b	(/.f64 t (-.f64 a t))
2.3b	(*.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))))

rewrite100.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`*-un-lft-identity_binary64`
122×	`add-sqr-sqrt_binary64`
108×	`times-frac_binary64`
84×	`cancel-sign-sub-inv_binary64`
64×	`add-cube-cbrt_binary64`
44×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-+r+_binary64`
32×	`distribute-lft-out--_binary64`
26×	`difference-of-squares_binary64`
18×	`associate-r_binary64`
16×	`associate-/r/_binary64`
10×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`div-inv_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-/l*_binary64`
4×	`sub-neg_binary64` `associate-*r/_binary64`
3×	`distribute-rgt-out--_binary64` `associate-l_binary64`
2×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_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 → 210

Calls

4 calls:

42.0ms	(*.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))))
18.0ms	(+.f64 x (*.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t)))))
9.0ms	(/.f64 t (-.f64 a t))
7.0ms	(/.f64 z (-.f64 a t))

series722.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

336.0ms	(+.f64 x (*.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t)))))
261.0ms	(*.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))))
66.0ms	(/.f64 z (-.f64 a t))
58.0ms	(/.f64 t (-.f64 a t))

simplify94.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5488	3882

prune204.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	223	7	230

Merged error: 0b

Counts

230 → 7

Compiler

Compiled 5512 to 1223 computations (77.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 a t))
0.0b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))
0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
2.3b	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))))

rewrite57.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
26×	`add-exp-log_binary64`
25×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`
20×	`add-cbrt-cube_binary64`
12×	`pow1_binary64`
10×	`prod-exp_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` `flip--_binary64`
5×	`associate-/r*_binary64`
4×	`pow-prod-down_binary64` `associate-/r/_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `rec-exp_binary64` `associate-/l*_binary64` `div-exp_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 → 127

Calls

4 calls:

18.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
16.0ms	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))))
7.0ms	(/.f64 1 (-.f64 a t))
5.0ms	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))

series581.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

269.0ms	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))
176.0ms	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))))
92.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
44.0ms	(/.f64 1 (-.f64 a t))

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5177	1884

prune118.0ms (1.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	139	7	146

Merged error: 0b

Counts

146 → 7

Compiler

Compiled 2608 to 943 computations (63.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 y (.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))))
3.6b	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
3.6b	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
3.6b	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))

rewrite79.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-sqr-sqrt_binary64`
98×	`*-un-lft-identity_binary64`
93×	`cbrt-prod_binary64`
75×	`times-frac_binary64`
38×	`add-cube-cbrt_binary64`
30×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
9×	`pow1_binary64` `add-exp-log_binary64`
7×	`cbrt-div_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r/_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `associate-l_binary64` `prod-exp_binary64` `div-inv_binary64` `flip--_binary64`
1×	`associate-r_binary64` `unswap-sqr_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 142

Calls

4 calls:

26.0ms	(.f64 y (.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))))
9.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
9.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
9.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))

series2.3s (29%)

Counts

4 → 12

Calls

4 calls:

613.0ms	(.f64 y (.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))))
558.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
557.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
553.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))

simplify115.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4861	3753
1	4861	3753

prune155.0ms (2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	154	7	161

Merged error: 0b

Counts

161 → 7

Compiler

Compiled 5817 to 908 computations (84.4% saved)

regimes175.0ms (2.2%)

Compiler: Compiled 1015 to 799 computations (21.3% saved)

bsearch37.0ms (0.5%)

Steps

Iters	Range		Point
10	1.1529899655089004e-110	7.910230204653643e-95	1.8357966397242195e-102
5	-2390355893516931.5	-789266040379027.0	-862252199741748.1

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	63
1	40	63

end0.0ms (0%)

sample788.0ms (10%)

Algorithm

1×

intervals

Results

311.0ms	7999×	body	128	valid
32.0ms	690×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 210 to 140 computations (33.3% saved)

Details

analyze920.0ms (11.7%)

sample22.0ms (0.3%)

simplify150.0ms (1.9%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite47.0ms (0.6%)

series519.0ms (6.6%)

simplify73.0ms (0.9%)

prune508.0ms (6.5%)

localize10.0ms (0.1%)

rewrite100.0ms (1.3%)

series722.0ms (9.2%)

simplify94.0ms (1.2%)

prune204.0ms (2.6%)

localize10.0ms (0.1%)

rewrite57.0ms (0.7%)

series581.0ms (7.4%)

simplify68.0ms (0.9%)

prune118.0ms (1.5%)

localize13.0ms (0.2%)

rewrite79.0ms (1%)

series2.3s (29%)

simplify115.0ms (1.5%)

prune155.0ms (2%)

regimes175.0ms (2.2%)

bsearch37.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample788.0ms (10%)

Profiling