Details

analyze270.0ms (7.6%)

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)

sample25.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
6.0ms	257×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify275.0ms (7.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4905	19
1	4905	19

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 26 to 22 computations (15.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite59.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
12×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64`
10×	`associate-l_binary64`
8×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64`
7×	`pow1_binary64`
6×	`associate-*r/_binary64` `difference-of-squares_binary64`
4×	`sub-neg_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64` `add-log-exp_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` `unswap-sqr_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

3 → 95

Calls

3 calls:

21.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
11.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
9.0ms	(*.f64 m (-.f64 1 m))

series194.0ms (5.5%)

Counts

3 → 9

Calls

3 calls:

76.0ms	(*.f64 m (-.f64 1 m))
66.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
52.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

simplify66.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4942	1776
1	4942	1776

prune228.0ms (6.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	5	105

Merged error: 0b

Counts

105 → 5

Compiler

Compiled 3926 to 2898 computations (26.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite97.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

171×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
139×	`*-un-lft-identity_binary64`
83×	`add-cube-cbrt_binary64`
40×	`difference-of-squares_binary64`
30×	`associate-/r*_binary64`
18×	`distribute-lft-out--_binary64`
13×	`associate-l_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
6×	`associate-r_binary64` `cancel-sign-sub-inv_binary64` `associate-/l*_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`add-log-exp_binary64` `difference-of-sqr-1_binary64`
2×	`sub-neg_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

3 → 202

Calls

3 calls:

51.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
12.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
7.0ms	(/.f64 v (-.f64 1 m))

series163.0ms (4.6%)

Counts

3 → 9

Calls

3 calls:

58.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
55.0ms	(/.f64 v (-.f64 1 m))
50.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))

simplify89.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4960	4468
1	4960	4468

prune241.0ms (6.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	211	5	216

Merged error: 0b

Counts

216 → 5

Compiler

Compiled 4985 to 3112 computations (37.6% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64` `associate-l_binary64`
12×	`associate-r_binary64` `cancel-sign-sub-inv_binary64`
10×	`times-frac_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64`
6×	`pow1_binary64` `frac-times_binary64`
4×	`sub-neg_binary64` `associate-*r/_binary64` `difference-of-squares_binary64`
3×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-*l/_binary64`
2×	`pow-prod-down_binary64` `add-log-exp_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`
1×	`cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 84

Calls

2 calls:

18.0ms	(.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 1) (-.f64 1 m))
13.0ms	(*.f64 (/.f64 m v) (-.f64 1 m))

series92.0ms (2.6%)

Counts

2 → 6

Calls

2 calls:

48.0ms	(*.f64 (/.f64 m v) (-.f64 1 m))
44.0ms	(.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 1) (-.f64 1 m))

simplify65.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4968	1735
1	4968	1735

prune88.0ms (2.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	90	5	95

Merged error: 0b

Counts

95 → 5

Compiler

Compiled 1906 to 1146 computations (39.9% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 m m) (.f64 1 m))
0.0b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 (pow.f64 m 3)))
0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
2.6b	(/.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 (pow.f64 m 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (*.f64 1 m))))

rewrite96.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
24×	`cancel-sign-sub-inv_binary64`
16×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64`
12×	`associate-r_binary64`
10×	`associate-/l/_binary64` `difference-of-squares_binary64`
8×	`unpow-prod-down_binary64` `cube-prod_binary64` `frac-times_binary64`
7×	`associate-/r_binary64` `associate-l*_binary64` `times-frac_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-*r/_binary64`
4×	`cbrt-undiv_binary64` `sqr-pow_binary64` `div-exp_binary64` `associate-*l/_binary64`
3×	`cbrt-unprod_binary64` `prod-exp_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `distribute-lft-out_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `flip-+_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-prod-down_binary64` `distribute-rgt-out_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 133

Calls

4 calls:

35.0ms	(/.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 (pow.f64 m 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (*.f64 1 m))))
27.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 (pow.f64 m 3)))
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
5.0ms	(+.f64 (.f64 m m) (.f64 1 m))

series266.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(/.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 (pow.f64 m 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (*.f64 1 m))))
67.0ms	(+.f64 (.f64 m m) (.f64 1 m))
61.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
46.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 (pow.f64 m 3)))

simplify110.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5082	3726

prune256.0ms (7.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	145	5	150

Merged error: 0b

Counts

150 → 5

Compiler

Compiled 4972 to 3399 computations (31.6% saved)

regimes32.0ms (0.9%)

Compiler: Compiled 198 to 164 computations (17.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	19
1	30	19

end0.0ms (0%)

sample747.0ms (21.1%)

Algorithm

1×

intervals

Results

291.0ms	8000×	body	128	valid
168.0ms	8059×	pre	128	true
2.0ms	59×	body	128	invalid

Compiler

Compiled 133 to 109 computations (18% saved)

Details

analyze270.0ms (7.6%)

sample25.0ms (0.7%)

simplify275.0ms (7.7%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite59.0ms (1.7%)

series194.0ms (5.5%)

simplify66.0ms (1.9%)

prune228.0ms (6.4%)

localize7.0ms (0.2%)

rewrite97.0ms (2.7%)

series163.0ms (4.6%)

simplify89.0ms (2.5%)

prune241.0ms (6.8%)

localize10.0ms (0.3%)

rewrite40.0ms (1.1%)

series92.0ms (2.6%)

simplify65.0ms (1.8%)

prune88.0ms (2.5%)

localize17.0ms (0.5%)

rewrite96.0ms (2.7%)

series266.0ms (7.5%)

simplify110.0ms (3.1%)

prune256.0ms (7.2%)

regimes32.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample747.0ms (21.1%)

Profiling