Details

analyze924.0ms

Algorithm

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
2.3%	97.4%	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
33.3%	66.5%	0.2%	14

sample27.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	16×	body	80	invalid

simplify106.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4982	11
1	4982	11

prune4.0ms

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: 1.2b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
1.3b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

rewrite31.0ms

Algorithm

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:

4.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
8.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
14.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

series62.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
13.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
19.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

simplify42.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4994	1366
1	4994	1366

prune127.0ms

Filtered

83 candidates to 122 candidates (-47.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	116	7	123

Merged error: 0b

Counts

123 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 z a))
0.0b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))))
0.3b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
1.3b	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
32×	`add-exp-log_binary64` `times-frac_binary64`
25×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`
20×	`add-cbrt-cube_binary64`
13×	`prod-exp_binary64`
12×	`pow1_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` `div-exp_binary64` `flip--_binary64`
5×	`associate-/r*_binary64`
4×	`pow-prod-down_binary64` `associate-/r/_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`1-exp_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `rec-exp_binary64` `associate-/l*_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 → 130

Calls

4 calls:

6.0ms	(/.f64 1 (-.f64 z a))
4.0ms	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))))
14.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
15.0ms	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 1 (-.f64 z a))
30.0ms	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))))
9.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
17.0ms	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))))

simplify42.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5082	1285

prune112.0ms

Filtered

87 candidates to 142 candidates (-63.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	142	7	149

Merged error: 0b

Counts

149 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 z a))
0.6b	(cbrt.f64 (-.f64 z a))
0.6b	(cbrt.f64 (-.f64 z a))
5.7b	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64`
50×	`times-frac_binary64`
46×	`associate-r_binary64`
42×	`cbrt-prod_binary64`
28×	`add-cube-cbrt_binary64`
25×	`add-exp-log_binary64`
20×	`cbrt-div_binary64`
18×	`add-cbrt-cube_binary64`
16×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
15×	`associate-l_binary64`
10×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_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 → 136

Calls

4 calls:

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

series99.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt.f64 (-.f64 z a))
24.0ms	(cbrt.f64 (-.f64 z a))
24.0ms	(cbrt.f64 (-.f64 z a))
25.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))))

simplify50.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5099	2207

prune138.0ms

Filtered

113 candidates to 148 candidates (-31.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	149	6	155

Merged error: 0b

Counts

155 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 y (-.f64 z a))
0.0b	(+.f64 x (pow.f64 (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)) 1))
9.6b	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-l_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-r*_binary64`
4×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
3×	`associate-/l*_binary64`
2×	`sub-neg_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 97

Calls

3 calls:

6.0ms	(/.f64 y (-.f64 z a))
7.0ms	(+.f64 x (pow.f64 (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)) 1))
13.0ms	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))

series61.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(/.f64 y (-.f64 z a))
29.0ms	(+.f64 x (pow.f64 (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)) 1))
24.0ms	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))

simplify45.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4970	1088
1	4970	1088

prune88.0ms

Filtered

79 candidates to 106 candidates (-34.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	106	6	112

Merged error: 0b

Counts

112 → 6

regimes617.0ms

Accuracy

52.3% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 1.4b

bsearch40.0ms

Steps

Iters	Range		Point
8	1.3232535649681044e-73	4.343296980394084e-71	1.4975338283952657e-71
10	-6.960932538110582e-204	-1.540174954509379e-217	-4.4037374926802204e-213

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	33
1	47	33

end0.0ms

sample615.0ms

Algorithm

intervals

Results

306.0ms	7998×	body	80	valid
29.0ms	704×	body	80	invalid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	640	valid

Details

analyze924.0ms

sample27.0ms

simplify106.0ms

prune4.0ms

localize8.0ms

rewrite31.0ms

series62.0ms

simplify42.0ms

prune127.0ms

localize10.0ms

rewrite44.0ms

series61.0ms

simplify42.0ms

prune112.0ms

localize12.0ms

rewrite51.0ms

series99.0ms

simplify50.0ms

prune138.0ms

localize10.0ms

rewrite29.0ms

series61.0ms

simplify45.0ms

prune88.0ms

regimes617.0ms

bsearch40.0ms

simplify2.0ms

end0.0ms

sample615.0ms

Profiling