Details

analyze991.0ms (29.6%)

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
18.4%	81.3%	0.2%	13
29.5%	70.3%	0.2%	14

sample22.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	20×	body	80	invalid

simplify141.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	4786	11
1	4786	11

prune8.0ms (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: 12.1b

Counts

2 → 1

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
0.0b	(*.f64 (-.f64 y z) t)
12.5b	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-cube-cbrt_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`associate-*l/_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 63

Calls

3 calls:

12.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
10.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
7.0ms	(*.f64 (-.f64 y z) t)

series58.0ms (1.7%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
19.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
8.0ms	(*.f64 (-.f64 y z) t)

simplify42.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5590	683

prune108.0ms (3.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	65	7	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	7	73

Merged error: 0.0b

Counts

73 → 7

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 t (-.f64 a z))))
0.0b	(/.f64 t (-.f64 a z))
10.3b	(*.f64 (-.f64 y z) (/.f64 t (-.f64 a z)))

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-l*_binary64`
4×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
3×	`associate-/l*_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 94

Calls

3 calls:

16.0ms	(*.f64 (-.f64 y z) (/.f64 t (-.f64 a z)))
6.0ms	(/.f64 t (-.f64 a z))
4.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 t (-.f64 a z))))

series58.0ms (1.7%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 t (-.f64 a z))))
19.0ms	(*.f64 (-.f64 y z) (/.f64 t (-.f64 a z)))
8.0ms	(/.f64 t (-.f64 a z))

simplify60.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4972	1059
1	4972	1059

prune125.0ms (3.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	102	8	110

Merged error: 0b

Counts

110 → 8

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
4.4b	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 t (cbrt.f64 (-.f64 a z))))

rewrite49.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
32×	`cbrt-prod_binary64`
30×	`associate-r_binary64`
25×	`add-exp-log_binary64`
24×	`add-cube-cbrt_binary64`
20×	`cbrt-div_binary64`
18×	`add-cbrt-cube_binary64`
17×	`associate-l_binary64`
10×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
6×	`pow1_binary64` `unswap-sqr_binary64`
5×	`frac-times_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r/_binary64` `pow1/3_binary64` `associate-l/_binary64`
2×	`div-inv_binary64`
1×	`pow-prod-down_binary64` `*-commutative_binary64`

Counts

4 → 122

Calls

4 calls:

33.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 t (cbrt.f64 (-.f64 a z))))
3.0ms	(cbrt.f64 (-.f64 a z))
3.0ms	(cbrt.f64 (-.f64 a z))
3.0ms	(cbrt.f64 (-.f64 a z))

series123.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 t (cbrt.f64 (-.f64 a z))))
31.0ms	(cbrt.f64 (-.f64 a z))
30.0ms	(cbrt.f64 (-.f64 a z))
29.0ms	(cbrt.f64 (-.f64 a z))

simplify61.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5572	1901

prune149.0ms (4.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	135	7	142

Merged error: 0b

Counts

142 → 7

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (pow.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t) 1))
0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
1.6b	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
73×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-l_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-r_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` `distribute-lft-out_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 114

Calls

3 calls:

13.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
9.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
5.0ms	(+.f64 x (pow.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t) 1))

series73.0ms (2.2%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(+.f64 x (pow.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t) 1))
30.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
11.0ms	(/.f64 (-.f64 y z) (-.f64 a z))

simplify42.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5032	1389

prune144.0ms (4.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	124	6	130

Merged error: 0b

Counts

130 → 6

regimes365.0ms (10.9%)

Accuracy

Total 1.2b remaining (99.4%)

Threshold costs 0b (0%)

bsearch31.0ms (0.9%)

Steps

Iters	Range		Point
7	121791759275.7593	4776541126796.931	128923762327.44762
7	-1.2048579292101348e-301	-4.861867457427471e-303	-5.212099959314552e-302

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	47
1	54	47

end0.0ms (0%)

sample569.0ms (17%)

Algorithm

1×

intervals

Results

294.0ms	7999×	body	80	valid
24.0ms	695×	body	80	invalid
0.0ms	1×	body	160	valid

Details

analyze991.0ms (29.6%)

sample22.0ms (0.7%)

simplify141.0ms (4.2%)

prune8.0ms (0.2%)

localize8.0ms (0.2%)

rewrite31.0ms (0.9%)

series58.0ms (1.7%)

simplify42.0ms (1.2%)

prune108.0ms (3.2%)

localize8.0ms (0.2%)

rewrite29.0ms (0.9%)

series58.0ms (1.7%)

simplify60.0ms (1.8%)

prune125.0ms (3.7%)

localize12.0ms (0.4%)

rewrite49.0ms (1.5%)

series123.0ms (3.7%)

simplify61.0ms (1.8%)

prune149.0ms (4.5%)

localize10.0ms (0.3%)

rewrite32.0ms (0.9%)

series73.0ms (2.2%)

simplify42.0ms (1.2%)

prune144.0ms (4.3%)

regimes365.0ms (10.9%)

bsearch31.0ms (0.9%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample569.0ms (17%)

Profiling