Details

analyze2.0s (21.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
0%	99.6%	0.4%	11
0%	99.6%	0.4%	12
0%	99.6%	0.4%	13
0%	99.6%	0.4%	14

sample90.0ms (1%)

Algorithm

1×

intervals

Results

26.0ms	332×	body	80	invalid
20.0ms	256×	body	80	valid

simplify381.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (379.0ms)

Iter	Nodes	Cost
0	4955	29
1	4955	29

prune12.0ms (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: 12.3b

Counts

2 → 1

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
5.0b	(* b (- (* c z) (* i a)))
5.4b	(* j (- (* c t) (* i y)))
5.7b	(* x (- (* y z) (* t a)))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`associate-*r/`
11×	`sub-neg`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
8×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`frac-sub`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate--l+` `associate--r+`
1×	`diff-log`

Counts

4 → 85

Calls

4 calls:

8.0ms	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
6.0ms	(* b (- (* c z) (* i a)))
6.0ms	(* x (- (* y z) (* t a)))
6.0ms	(* j (- (* c t) (* i y)))

series128.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
20.0ms	(* x (- (* y z) (* t a)))
18.0ms	(* b (- (* c z) (* i a)))
18.0ms	(* j (- (* c t) (* i y)))

simplify43.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5173	1548

prune297.0ms (3.2%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	73	24	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	24	98

Merged error: 7.9b

Counts

98 → 24

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

5.7b	(* x (- (* y z) (* t a)))
6.9b	(cbrt (- (* z c) (* a i)))
6.9b	(cbrt (- (* z c) (* a i)))
6.9b	(cbrt (- (* c z) (* i a)))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube`
4×	`flip3--` `flip--` `add-log-exp`
3×	`pow1/3` `associate-r` `associate-l`
2×	`sub-neg` `associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

6.0ms	(* x (- (* y z) (* t a)))
4.0ms	(cbrt (- (* z c) (* a i)))
4.0ms	(cbrt (- (* c z) (* i a)))
4.0ms	(cbrt (- (* z c) (* a i)))

series133.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(cbrt (- (* z c) (* a i)))
37.0ms	(cbrt (- (* c z) (* i a)))
37.0ms	(cbrt (- (* z c) (* a i)))
18.0ms	(* x (- (* y z) (* t a)))

simplify46.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4933	894
1	4933	894

prune260.0ms (2.8%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	1	22	23
Picked	1	0	1
Done	0	0	0
Total	72	25	97

Merged error: 7.9b

Counts

97 → 25

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

5.7b	(* x (- (* y z) (* t a)))
7.0b	(cbrt (- (* c t) (* i y)))
7.0b	(cbrt (- (* t c) (* y i)))
7.0b	(cbrt (- (* t c) (* y i)))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube`
4×	`flip3--` `flip--` `add-log-exp`
3×	`pow1/3` `associate-r` `associate-l`
2×	`sub-neg` `associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

6.0ms	(* x (- (* y z) (* t a)))
4.0ms	(cbrt (- (* t c) (* y i)))
3.0ms	(cbrt (- (* t c) (* y i)))
3.0ms	(cbrt (- (* c t) (* i y)))

series129.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(cbrt (- (* t c) (* y i)))
36.0ms	(cbrt (- (* t c) (* y i)))
36.0ms	(cbrt (- (* c t) (* i y)))
19.0ms	(* x (- (* y z) (* t a)))

simplify42.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4954	894
1	4954	894

prune261.0ms (2.8%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	1	23	24
Picked	1	0	1
Done	0	0	0
Total	72	26	98

Merged error: 7.9b

Counts

98 → 26

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

5.7b	(* x (- (* y z) (* t a)))
6.3b	(cbrt (* b (- (* z c) (* a i))))
6.3b	(cbrt (* b (- (* z c) (* a i))))
6.3b	(cbrt (* b (- (* z c) (* a i))))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `associate-*r/`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity` `add-cbrt-cube`
4×	`flip3--` `flip--` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `associate-r` `associate-l`
2×	`sub-neg`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

6.0ms	(* x (- (* y z) (* t a)))
5.0ms	(cbrt (* b (- (* z c) (* a i))))
5.0ms	(cbrt (* b (- (* z c) (* a i))))
5.0ms	(cbrt (* b (- (* z c) (* a i))))

series144.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(cbrt (* b (- (* z c) (* a i))))
42.0ms	(cbrt (* b (- (* z c) (* a i))))
40.0ms	(cbrt (* b (- (* z c) (* a i))))
18.0ms	(* x (- (* y z) (* t a)))

simplify46.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5135	831

prune92.0ms (1%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	25	25
Picked	1	0	1
Done	0	0	0
Total	67	26	93

Merged error: 7.9b

Counts

93 → 26

regimes2.3s (24.9%)

Accuracy

Total 4.1b remaining (33.7%)

Threshold costs 0b (0%)

bsearch72.0ms (0.8%)

Steps

Iters	Range		Point
4	2.325961380890472e-208	4.075739402764228e-208	3.3107706184898416e-208
7	-1.347507180155637e-122	-3.6929323227213327e-124	-3.731049634329954e-124

simplify19.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	707	83
1	707	83

end0.0ms (0%)

sample2.6s (27.7%)

Algorithm

1×

intervals

Results

935.0ms	11085×	body	80	invalid
656.0ms	8000×	body	80	valid

Details

analyze2.0s (21.8%)

sample90.0ms (1%)

simplify381.0ms (4.1%)

prune12.0ms (0.1%)

localize20.0ms (0.2%)

rewrite28.0ms (0.3%)

series128.0ms (1.4%)

simplify43.0ms (0.5%)

prune297.0ms (3.2%)

localize35.0ms (0.4%)

rewrite19.0ms (0.2%)

series133.0ms (1.4%)

simplify46.0ms (0.5%)

prune260.0ms (2.8%)

localize29.0ms (0.3%)

rewrite17.0ms (0.2%)

series129.0ms (1.4%)

simplify42.0ms (0.4%)

prune261.0ms (2.8%)

localize30.0ms (0.3%)

rewrite22.0ms (0.2%)

series144.0ms (1.5%)

simplify46.0ms (0.5%)

prune92.0ms (1%)

regimes2.3s (24.9%)

bsearch72.0ms (0.8%)

simplify19.0ms (0.2%)

end0.0ms (0%)

sample2.6s (27.7%)

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