Details

analyze253.0ms (6.4%)

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 23 to 18 computations (21.7% saved)

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
6.0ms	258×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify198.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4924	19
1	4924	19

prune5.0ms (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

Error

0.1b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite52.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-r_binary64`
10×	`associate-l_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`pow1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64`
6×	`add-log-exp_binary64` `associate-*r/_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-out--_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64` `cbrt-unprod_binary64` `prod-exp_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` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 113

Calls

4 calls:

18.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
8.0ms	(*.f64 m (-.f64 1 m))
7.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series108.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
27.0ms	(*.f64 m (-.f64 1 m))
24.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
15.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

simplify72.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5061	2142

prune145.0ms (3.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	120	6	126

Error

Counts

126 → 6

Compiler

Compiled 2528 to 1731 computations (31.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite64.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`frac-times_binary64`
28×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
22×	`flip3--_binary64` `flip--_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-*l/_binary64`
14×	`associate-r_binary64`
13×	`flip3-+_binary64` `add-cube-cbrt_binary64` `flip-+_binary64`
12×	`associate-*r/_binary64` `cancel-sign-sub-inv_binary64`
11×	`pow1_binary64` `sqrt-prod_binary64`
8×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64`
6×	`add-log-exp_binary64` `difference-of-squares_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`pow-prod-down_binary64` `distribute-lft-out_binary64`
3×	`associate-/r*_binary64` `distribute-lft-out--_binary64` `times-frac_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`difference-of-sqr-1_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 134

Calls

4 calls:

23.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
16.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
7.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
4.0ms	(+.f64 1 (sqrt.f64 m))

series119.0ms (3%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
41.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
22.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
11.0ms	(+.f64 1 (sqrt.f64 m))

simplify90.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4995	4311
1	4995	4311

prune195.0ms (4.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	146	6	152

Error

Counts

152 → 6

Compiler

Compiled 4365 to 2837 computations (35% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) (-.f64 1 m))
0.3b	(/.f64 m (sqrt.f64 v))
0.3b	(/.f64 (-.f64 1 m) (sqrt.f64 v))
0.4b	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))

rewrite86.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

150×	`add-sqr-sqrt_binary64`
120×	`times-frac_binary64`
118×	`*-un-lft-identity_binary64`
76×	`add-cube-cbrt_binary64`
66×	`sqrt-prod_binary64`
46×	`associate-r_binary64`
28×	`difference-of-squares_binary64`
25×	`associate-l_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`distribute-lft-out--_binary64`
12×	`associate-/r*_binary64`
10×	`unswap-sqr_binary64`
9×	`associate-/l*_binary64`
8×	`pow1_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `div-exp_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64` `frac-times_binary64`
4×	`add-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-inv_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`div-sub_binary64`

Counts

4 → 230

Calls

4 calls:

28.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
22.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) (-.f64 1 m))
7.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
4.0ms	(/.f64 m (sqrt.f64 v))

series130.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) (-.f64 1 m))
34.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
30.0ms	(/.f64 m (sqrt.f64 v))
22.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))

simplify77.0ms (2%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5677	4737

prune248.0ms (6.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	242	0	242
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	242	6	248

Error

Counts

248 → 6

Compiler

Compiled 5947 to 2904 computations (51.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) (cbrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
0.6b	(cbrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))
0.6b	(cbrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))
0.6b	(cbrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`cbrt-prod_binary64`
30×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
21×	`times-frac_binary64`
11×	`pow1_binary64`
10×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
9×	`pow1/3_binary64`
7×	`cbrt-div_binary64` `div-inv_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `associate-r/_binary64` `pow-plus_binary64` `prod-exp_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 103

Calls

4 calls:

10.0ms	(.f64 (cbrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) (cbrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
7.0ms	(cbrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))
5.0ms	(cbrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))
5.0ms	(cbrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))

series324.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(.f64 (cbrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) (cbrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
81.0ms	(cbrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))
73.0ms	(cbrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))
73.0ms	(cbrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))

simplify115.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4850	2383
1	4850	2383

prune191.0ms (4.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	115	6	121

Error

Counts

121 → 6

Compiler

Compiled 4226 to 2844 computations (32.7% saved)

regimes165.0ms (4.2%)

Accuracy

Total 0.1b remaining (97.4%)

Threshold costs 0.1b (97.4%)

Compiler

Compiled 2013 to 1593 computations (20.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	19
1	33	19

end0.0ms (0%)

sample1.2s (30.5%)

Algorithm

1×

intervals

Results

274.0ms	8000×	body	128	valid
164.0ms	8061×	pre	128	true
2.0ms	61×	body	128	invalid

Compiler

Compiled 697 to 552 computations (20.8% saved)

Details

analyze253.0ms (6.4%)

sample24.0ms (0.6%)

simplify198.0ms (5%)

prune5.0ms (0.1%)

localize9.0ms (0.2%)

rewrite52.0ms (1.3%)

series108.0ms (2.7%)

simplify72.0ms (1.8%)

prune145.0ms (3.7%)

localize13.0ms (0.3%)

rewrite64.0ms (1.6%)

series119.0ms (3%)

simplify90.0ms (2.3%)

prune195.0ms (4.9%)

localize9.0ms (0.2%)

rewrite86.0ms (2.2%)

series130.0ms (3.3%)

simplify77.0ms (2%)

prune248.0ms (6.3%)

localize12.0ms (0.3%)

rewrite39.0ms (1%)

series324.0ms (8.2%)

simplify115.0ms (2.9%)

prune191.0ms (4.8%)

regimes165.0ms (4.2%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (30.5%)

Profiling