Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample42.0ms

Algorithm

intervals

Results

21.0ms	100×	body	1280	valid
5.0ms	8×	body	320	valid
5.0ms	120×	body	80	valid
4.0ms	23×	body	640	valid
0.0ms	5×	body	160	valid

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	442	12
1	442	12

prune2.0ms

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: 14.5b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
0.0b	(/.f64 1.0 (hypot.f64 1.0 x))
1.9b	(-.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`pow1_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-prod_binary64` `flip-+_binary64`

Counts

3 → 53

Calls

3 calls:

7.0ms	(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
3.0ms	(/.f64 1.0 (hypot.f64 1.0 x))
4.0ms	(-.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))

series42.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
6.0ms	(/.f64 1.0 (hypot.f64 1.0 x))
19.0ms	(-.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5548	714

prune73.0ms

Filtered

44 candidates to 62 candidates (-40.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	3	63

Merged error: 14.0b

Counts

63 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
0.0b	(/.f64 0.5 (hypot.f64 1.0 x))
0.0b	(/.f64 1.0 (hypot.f64 1.0 x))
1.5b	(-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
11×	`add-log-exp_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r_binary64` `associate-/l_binary64`
4×	`pow1_binary64`
3×	`diff-log_binary64` `distribute-lft-out--_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`flip3-+_binary64` `associate--l-_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 86

Calls

4 calls:

3.0ms	(+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
3.0ms	(/.f64 0.5 (hypot.f64 1.0 x))
3.0ms	(/.f64 1.0 (hypot.f64 1.0 x))
10.0ms	(-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
6.0ms	(/.f64 0.5 (hypot.f64 1.0 x))
6.0ms	(/.f64 1.0 (hypot.f64 1.0 x))
11.0ms	(-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4939	1071
1	4939	1071

prune153.0ms

Filtered

73 candidates to 98 candidates (-34.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	95	6	101

Merged error: 13.8b

Counts

101 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1.0 (hypot.f64 1.0 x))
0.0b	(log.f64 (-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x))))
0.1b	(exp.f64 (log.f64 (-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x)))))
1.5b	(-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
14×	`log-prod_binary64`
12×	`times-frac_binary64`
9×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
8×	`log-div_binary64`
7×	`add-exp-log_binary64` `exp-sum_binary64`
6×	`pow1_binary64` `flip3--_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `frac-sub_binary64`
4×	`exp-diff_binary64` `exp-prod_binary64`
3×	`associate-/r_binary64` `diff-log_binary64` `associate-/l_binary64`
2×	`sub-neg_binary64` `log-pow_binary64`
1×	`associate--l-_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `associate--l+_binary64`

Counts

4 → 90

Calls

4 calls:

3.0ms	(/.f64 1.0 (hypot.f64 1.0 x))
10.0ms	(log.f64 (-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x))))
13.0ms	(exp.f64 (log.f64 (-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x)))))
10.0ms	(-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/.f64 1.0 (hypot.f64 1.0 x))
26.0ms	(log.f64 (-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x))))
9.0ms	(exp.f64 (log.f64 (-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x)))))
9.0ms	(-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4881	1326
1	4881	1326

prune146.0ms

Filtered

70 candidates to 102 candidates (-45.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	103	5	108

Merged error: 13.8b

Counts

108 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (/.f64 (-.f64 (pow.f64 (-.f64 1.0 0.5) 3) (pow.f64 (/.f64 0.5 (hypot.f64 1.0 x)) 3)) (+.f64 (.f64 (-.f64 1.0 0.5) (-.f64 1.0 0.5)) (.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (+.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (-.f64 1.0 0.5))))))
0.1b	(pow.f64 (/.f64 0.5 (hypot.f64 1.0 x)) 3)
0.1b	(exp.f64 (log.f64 (/.f64 (-.f64 (pow.f64 (-.f64 1.0 0.5) 3) (pow.f64 (/.f64 0.5 (hypot.f64 1.0 x)) 3)) (+.f64 (.f64 (-.f64 1.0 0.5) (-.f64 1.0 0.5)) (.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (+.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (-.f64 1.0 0.5)))))))
1.4b	(-.f64 (pow.f64 (-.f64 1.0 0.5) 3) (pow.f64 (/.f64 0.5 (hypot.f64 1.0 x)) 3))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

424×	`add-sqr-sqrt_binary64`
378×	`log-prod_binary64`
296×	`times-frac_binary64`
256×	`*-un-lft-identity_binary64`
208×	`frac-add_binary64`
189×	`exp-sum_binary64`
168×	`difference-of-squares_binary64`
167×	`unpow-prod-down_binary64` `cube-prod_binary64`
148×	`associate-/r/_binary64`
142×	`flip3--_binary64` `flip--_binary64`
136×	`frac-times_binary64`
102×	`add-cube-cbrt_binary64`
100×	`associate-*r/_binary64`
91×	`distribute-lft-out--_binary64`
71×	`sqr-pow_binary64`
52×	`associate-*l/_binary64`
34×	`flip3-+_binary64` `flip-+_binary64`
10×	`add-exp-log_binary64`
7×	`difference-cubes_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64`
5×	`cube-div_binary64`
4×	`div-inv_binary64` `exp-prod_binary64`
3×	`pow-unpow_binary64`
2×	`rem-log-exp_binary64` `log-pow_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `log-div_binary64` `frac-sub_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `rem-exp-log_binary64` `exp-diff_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 495

Calls

4 calls:

54.0ms	(log.f64 (/.f64 (-.f64 (pow.f64 (-.f64 1.0 0.5) 3) (pow.f64 (/.f64 0.5 (hypot.f64 1.0 x)) 3)) (+.f64 (.f64 (-.f64 1.0 0.5) (-.f64 1.0 0.5)) (.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (+.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (-.f64 1.0 0.5))))))
5.0ms	(pow.f64 (/.f64 0.5 (hypot.f64 1.0 x)) 3)
60.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (pow.f64 (-.f64 1.0 0.5) 3) (pow.f64 (/.f64 0.5 (hypot.f64 1.0 x)) 3)) (+.f64 (.f64 (-.f64 1.0 0.5) (-.f64 1.0 0.5)) (.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (+.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (-.f64 1.0 0.5)))))))
28.0ms	(-.f64 (pow.f64 (-.f64 1.0 0.5) 3) (pow.f64 (/.f64 0.5 (hypot.f64 1.0 x)) 3))

series245.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(log.f64 (/.f64 (-.f64 (pow.f64 (-.f64 1.0 0.5) 3) (pow.f64 (/.f64 0.5 (hypot.f64 1.0 x)) 3)) (+.f64 (.f64 (-.f64 1.0 0.5) (-.f64 1.0 0.5)) (.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (+.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (-.f64 1.0 0.5))))))
13.0ms	(pow.f64 (/.f64 0.5 (hypot.f64 1.0 x)) 3)
83.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (pow.f64 (-.f64 1.0 0.5) 3) (pow.f64 (/.f64 0.5 (hypot.f64 1.0 x)) 3)) (+.f64 (.f64 (-.f64 1.0 0.5) (-.f64 1.0 0.5)) (.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (+.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (-.f64 1.0 0.5)))))))
21.0ms	(-.f64 (pow.f64 (-.f64 1.0 0.5) 3) (pow.f64 (/.f64 0.5 (hypot.f64 1.0 x)) 3))

simplify200.0ms

Algorithm

egg-herbie

Counts

507 → 507

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5672	34409

prune4.0s

Filtered

268 candidates to 507 candidates (-89.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	504	3	507
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	507	5	512

Merged error: 13.7b

Counts

512 → 5

regimes244.0ms

Accuracy

0% (0.3b remaining)

Error of 15.2b against oracle of 14.9b and baseline of 15.2b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	106	62
1	106	62

end0.0ms

sample1.0s

Algorithm

intervals

Results

608.0ms	2812×	body	1280	valid
161.0ms	4056×	body	80	valid
112.0ms	650×	body	640	valid
37.0ms	311×	body	320	valid
16.0ms	171×	body	160	valid

Details

analyze1.0ms

sample42.0ms

simplify23.0ms

prune2.0ms

localize7.0ms

rewrite15.0ms

series42.0ms

simplify60.0ms

prune73.0ms

localize13.0ms

rewrite22.0ms

series41.0ms

simplify65.0ms

prune153.0ms

localize15.0ms

rewrite39.0ms

series50.0ms

simplify52.0ms

prune146.0ms

localize26.0ms

rewrite203.0ms

series245.0ms

simplify200.0ms

prune4.0s

regimes244.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling