Details

sample106.0ms

Algorithm

intervals

Results

61.0ms

620×

body

valid

simplify89.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	47	14
1	110	13
2	335	13
3	1059	13
4	3442	13
5	5001	13

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 11.6b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* c z) (* t i))
3.8b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
5.0b	(* x (- (* y z) (* t a)))
5.6b	(* b (- (* c z) (* t i)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l` `add-log-exp`
5×	`sub-neg` `prod-diff`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-neg` `diff-log` `fma-udef`

Counts

4 → 82

Calls

4 calls:

4.0ms	(- (* c z) (* t i))
1.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
8.0ms	(* x (- (* y z) (* t a)))
6.0ms	(* b (- (* c z) (* t i)))

series707.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* c z) (* t i))
543.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
65.0ms	(* x (- (* y z) (* t a)))
63.0ms	(* b (- (* c z) (* t i)))

simplify53.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	376	645
1	1499	568
2	5001	568

prune418.0ms

Filtered

94 candidates to 73 candidates (77.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	78	16	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	16	95

Merged error: 3.4b

Counts

95 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
3.4b	(* (cbrt x) (- (* y z) (* t a)))
3.8b	(fma (- (* c a) (* y i)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (* b (- (* c z) (* t i)))))
5.6b	(* b (- (* c z) (* t i)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log`
18×	`distribute-rgt-in` `distribute-lft-in`
15×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
10×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sub-neg` `associate-*r/` `prod-diff`
7×	`associate-r`
4×	`cbrt-prod` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `*-commutative` `flip--` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 108

Calls

4 calls:

12.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
7.0ms	(* (cbrt x) (- (* y z) (* t a)))
1.0ms	(fma (- (* c a) (* y i)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (* b (- (* c z) (* t i)))))
6.0ms	(* b (- (* c z) (* t i)))

series1.1s

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
257.0ms	(* (cbrt x) (- (* y z) (* t a)))
633.0ms	(fma (- (* c a) (* y i)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (* b (- (* c z) (* t i)))))
68.0ms	(* b (- (* c z) (* t i)))

simplify73.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	557	1206
1	2447	956
2	5002	877

prune449.0ms

Filtered

120 candidates to 76 candidates (63.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	119	17	136

Merged error: 3.4b

Counts

136 → 17

localize28.0ms

Local error

Found 4 expressions with local error:

5.0b	(* x (- (* y z) (* t a)))
7.3b	(cbrt (- (* c z) (* t i)))
7.3b	(cbrt (- (* c z) (* t i)))
7.3b	(cbrt (- (* c z) (* t i)))

rewrite18.0ms

Algorithm

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×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow1/3` `associate-r` `associate-l`
2×	`sub-neg` `associate-*r/` `prod-diff`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

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

series405.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* x (- (* y z) (* t a)))
113.0ms	(cbrt (- (* c z) (* t i)))
113.0ms	(cbrt (- (* c z) (* t i)))
111.0ms	(cbrt (- (* c z) (* t i)))

simplify111.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	340	646
1	1165	598
2	4148	580
3	5001	580

prune476.0ms

Filtered

85 candidates to 74 candidates (87.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	86	16	102

Merged error: 3.4b

Counts

102 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

5.6b	(* b (- (* c z) (* t i)))
5.8b	(cbrt (- (* y z) (* t a)))
5.8b	(cbrt (- (* y z) (* t a)))
5.8b	(cbrt (- (* y z) (* t a)))

rewrite20.0ms

Algorithm

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×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow1/3` `associate-r` `associate-l`
2×	`sub-neg` `associate-*r/` `prod-diff`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

8.0ms	(* b (- (* c z) (* t i)))
3.0ms	(cbrt (- (* y z) (* t a)))
3.0ms	(cbrt (- (* y z) (* t a)))
4.0ms	(cbrt (- (* y z) (* t a)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* b (- (* c z) (* t i)))
110.0ms	(cbrt (- (* y z) (* t a)))
111.0ms	(cbrt (- (* y z) (* t a)))
113.0ms	(cbrt (- (* y z) (* t a)))

simplify109.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	335	646
1	1158	598
2	4180	580
3	5001	580

prune396.0ms

Filtered

85 candidates to 71 candidates (83.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	84	17	101

Merged error: 3.4b

Counts

101 → 17

regimes921.0ms

Accuracy

2.7% (7.5b remaining)

Error of 12.4b against oracle of 5.0b and baseline of 12.7b

bsearch123.0ms

Steps

Iters	Range		Point
9	4.429114526961516e+119	2.44312331398895e+128	7.530759318228735e+126

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	31
1	48	31

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.5s

19289×

body

valid

Details

sample106.0ms

simplify89.0ms

prune9.0ms

localize19.0ms

rewrite20.0ms

series707.0ms

simplify53.0ms

prune418.0ms

localize24.0ms

rewrite29.0ms

series1.1s

simplify73.0ms

prune449.0ms

localize28.0ms

rewrite18.0ms

series405.0ms

simplify111.0ms

prune476.0ms

localize24.0ms

rewrite20.0ms

series399.0ms

simplify109.0ms

prune396.0ms

regimes921.0ms

bsearch123.0ms

simplify2.0ms

end0.0ms

sample2.4s

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