Details

analyze233.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

sample18.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
0.0ms	13×	body	80	invalid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	110	11
1	110	11

prune3.0ms

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: 5.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

3.7b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
4.0b	(.f64 y (+.f64 1 (.f64 z z)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac_binary64`
26×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
12×	`div-exp_binary64`
6×	`cbrt-undiv_binary64`
5×	`prod-exp_binary64`
4×	`pow1_binary64` `associate-*r/_binary64`
3×	`cbrt-unprod_binary64` `associate-r_binary64` `associate-l_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `add-log-exp_binary64` `1-exp_binary64` `associate-/r/_binary64` `rec-exp_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

2 → 74

Calls

2 calls:

10.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
6.0ms	(.f64 y (+.f64 1 (.f64 z z)))

series28.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
11.0ms	(.f64 y (+.f64 1 (.f64 z z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5072	883

prune107.0ms

Filtered

51 candidates to 80 candidates (-56.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	71	9	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	9	81

Merged error: 4.2b

Counts

81 → 9

localize7.0ms

Local error

Found 3 expressions with local error:

0.4b	(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
3.4b	(.f64 (.f64 y (+.f64 1 (*.f64 z z))) x)
4.0b	(.f64 y (+.f64 1 (.f64 z z)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
19×	`add-cbrt-cube_binary64`
16×	`pow1_binary64`
13×	`prod-exp_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
6×	`associate-r_binary64` `associate-*r/_binary64` `div-exp_binary64`
4×	`associate-l_binary64` `associate-*l/_binary64`
3×	`flip3-+_binary64` `add-log-exp_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `associate-/l*_binary64` `times-frac_binary64` `pow-flip_binary64` `flip-+_binary64`
2×	`associate-/r/_binary64` `*-commutative_binary64`
1×	`associate-/r*_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

3 → 77

Calls

3 calls:

8.0ms	(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
7.0ms	(.f64 (.f64 y (+.f64 1 (*.f64 z z))) x)
6.0ms	(.f64 y (+.f64 1 (.f64 z z)))

series41.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
15.0ms	(.f64 (.f64 y (+.f64 1 (*.f64 z z))) x)
11.0ms	(.f64 y (+.f64 1 (.f64 z z)))

simplify51.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5214	833

prune81.0ms

Filtered

49 candidates to 86 candidates (-75.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	86	9	95

Merged error: 4.2b

Counts

95 → 9

localize7.0ms

Local error

Found 3 expressions with local error:

0.3b	(/.f64 1 (.f64 y (+.f64 1 (.f64 z z))))
3.5b	(/.f64 (/.f64 1 (.f64 y (+.f64 1 (.f64 z z)))) x)
4.0b	(.f64 y (+.f64 1 (.f64 z z)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac_binary64`
35×	`add-exp-log_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`add-cbrt-cube_binary64`
15×	`div-exp_binary64`
12×	`associate-r/_binary64` `associate-/l_binary64`
10×	`associate-/r/_binary64`
8×	`pow1_binary64`
7×	`cbrt-undiv_binary64` `prod-exp_binary64`
6×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
4×	`associate-/r*_binary64` `1-exp_binary64` `rec-exp_binary64`
3×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-flip_binary64`
1×	`associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `*-commutative_binary64`

Counts

3 → 112

Calls

3 calls:

6.0ms	(/.f64 1 (.f64 y (+.f64 1 (.f64 z z))))
12.0ms	(/.f64 (/.f64 1 (.f64 y (+.f64 1 (.f64 z z)))) x)
6.0ms	(.f64 y (+.f64 1 (.f64 z z)))

series39.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/.f64 1 (.f64 y (+.f64 1 (.f64 z z))))
14.0ms	(/.f64 (/.f64 1 (.f64 y (+.f64 1 (.f64 z z)))) x)
11.0ms	(.f64 y (+.f64 1 (.f64 z z)))

simplify69.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4937	1479
1	4937	1479

prune141.0ms

Filtered

75 candidates to 121 candidates (-61.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	123	7	130

Merged error: 4.2b

Counts

130 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
3.7b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
14.3b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
14.3b	(sqrt.f64 (+.f64 1 (*.f64 z z)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log_binary64`
31×	`times-frac_binary64`
30×	`add-cbrt-cube_binary64`
28×	`sqrt-div_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`div-exp_binary64`
16×	`associate-*r/_binary64`
15×	`prod-exp_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
13×	`associate-/l*_binary64`
11×	`pow1_binary64`
9×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-prod_binary64`
8×	`associate-/r/_binary64` `frac-times_binary64`
6×	`associate-r_binary64`
4×	`add-log-exp_binary64` `associate-*l/_binary64`
3×	`pow-prod-down_binary64` `1-exp_binary64` `rec-exp_binary64` `div-inv_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`associate-/l/_binary64` `associate-/r_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 123

Calls

4 calls:

11.0ms	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
15.0ms	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
5.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
17.0ms	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

simplify73.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4934	1670
1	4934	1670

prune114.0ms

Filtered

89 candidates to 135 candidates (-51.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	135	7	142

Merged error: 4.2b

Counts

142 → 7

regimes450.0ms

Accuracy

82.6% (0.3b remaining)

Error of 5.1b against oracle of 4.9b and baseline of 6.5b

bsearch28.0ms

Steps

Iters	Range		Point
7	1.1463584575932138e+49	7.367082629787665e+50	1.3704778646666072e+49
9	-3.321851767765178e+105	-6.820087354091445e+99	-3.2719025730029142e+103

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	31
1	24	31

end0.0ms

sample477.0ms

Algorithm

intervals

Results

288.0ms	8000×	body	80	valid
14.0ms	408×	body	80	invalid

Details

analyze233.0ms

sample18.0ms

simplify7.0ms

prune3.0ms

localize8.0ms

rewrite21.0ms

series28.0ms

simplify54.0ms

prune107.0ms

localize7.0ms

rewrite24.0ms

series41.0ms

simplify51.0ms

prune81.0ms

localize7.0ms

rewrite28.0ms

series39.0ms

simplify69.0ms

prune141.0ms

localize9.0ms

rewrite39.0ms

series35.0ms

simplify73.0ms

prune114.0ms

regimes450.0ms

bsearch28.0ms

simplify2.0ms

end0.0ms

sample477.0ms

Profiling