Details

analyze261.0ms (6.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 21 to 16 computations (23.8% saved)

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
6.0ms	257×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 27 computations (15.6% saved)

simplify308.0ms (7.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (127.0ms)

Iter	Nodes	Cost
0	4772	16
1	4772	16

prune4.0ms (0.1%)

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: 0.1b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
0.0b	(*.f64 m (-.f64 1 m))
0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

rewrite55.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

15.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
10.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
8.0ms	(*.f64 m (-.f64 1 m))

series210.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
60.0ms	(*.f64 m (-.f64 1 m))
57.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
32.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

simplify57.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4947	1419
1	4947	1419

prune107.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Merged error: 0.0b

Counts

100 → 7

Compiler

Compiled 1769 to 1185 computations (33% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 m (-.f64 1 m))
0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
0.4b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

rewrite56.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`pow1_binary64` `add-cube-cbrt_binary64`
11×	`associate-l_binary64`
7×	`sqrt-prod_binary64`
6×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-*l/_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `flip--_binary64`
3×	`associate-/r_binary64` `unswap-sqr_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
1×	`difference-of-sqr-1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 99

Calls

4 calls:

16.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
15.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
8.0ms	(*.f64 m (-.f64 1 m))
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series280.0ms (7%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
70.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
60.0ms	(*.f64 m (-.f64 1 m))
58.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify59.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5287	1775

prune113.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	111	7	118

Merged error: 0.0b

Counts

118 → 7

Compiler

Compiled 2351 to 1391 computations (40.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 1 m) v)
0.0b	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)
0.1b	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
0.7b	(*.f64 m (/.f64 (-.f64 1 m) v))

rewrite52.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`
37×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
25×	`associate-r_binary64`
14×	`difference-of-squares_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64`
7×	`distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64` `associate-/l*_binary64`
3×	`associate-/r*_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip--_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-*r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 114

Calls

4 calls:

12.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
12.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
9.0ms	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)
7.0ms	(/.f64 (-.f64 1 m) v)

series166.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
46.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
41.0ms	(/.f64 (-.f64 1 m) v)
32.0ms	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)

simplify72.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4950	1851
1	4950	1851

prune115.0ms (2.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	126	7	133

Merged error: 0.0b

Counts

133 → 7

Compiler

Compiled 2298 to 1474 computations (35.9% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
0.3b	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
0.3b	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
0.3b	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))

rewrite80.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`cbrt-prod_binary64`
55×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64`
18×	`cbrt-div_binary64`
16×	`difference-of-squares_binary64`
15×	`add-cube-cbrt_binary64`
14×	`swap-sqr_binary64`
11×	`pow1_binary64`
10×	`associate-r_binary64` `associate-l_binary64`
9×	`flip3--_binary64` `pow1/3_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

24.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
18.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
12.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
9.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))

series812.0ms (20.2%)

Counts

4 → 12

Calls

4 calls:

214.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
205.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
198.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
194.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))

simplify96.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5188	3783

prune262.0ms (6.5%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	127	7	134

Merged error: 0.0b

Counts

134 → 7

Compiler

Compiled 5411 to 3933 computations (27.3% saved)

regimes54.0ms (1.4%)

Compiler: Compiled 470 to 365 computations (22.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	16
1	31	16

end0.0ms (0%)

sample732.0ms (18.2%)

Algorithm

1×

intervals

Results

253.0ms	8000×	body	128	valid
161.0ms	8063×	pre	128	true
2.0ms	63×	body	128	invalid

Compiler

Compiled 180 to 140 computations (22.2% saved)

Details

analyze261.0ms (6.5%)

sample24.0ms (0.6%)

simplify308.0ms (7.7%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite55.0ms (1.4%)

series210.0ms (5.2%)

simplify57.0ms (1.4%)

prune107.0ms (2.7%)

localize9.0ms (0.2%)

rewrite56.0ms (1.4%)

series280.0ms (7%)

simplify59.0ms (1.5%)

prune113.0ms (2.8%)

localize7.0ms (0.2%)

rewrite52.0ms (1.3%)

series166.0ms (4.1%)

simplify72.0ms (1.8%)

prune115.0ms (2.9%)

localize12.0ms (0.3%)

rewrite80.0ms (2%)

series812.0ms (20.2%)

simplify96.0ms (2.4%)

prune262.0ms (6.5%)

regimes54.0ms (1.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample732.0ms (18.2%)

Profiling