Details

sample90.0ms

Algorithm

intervals

Results

50.0ms

627×

body

valid

simplify90.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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: 11.7b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* y z) (* t a))
4.0b	(* b (- (* c z) (* i a)))
4.9b	(* x (- (* y z) (* t a)))
6.0b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))

rewrite18.0ms

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

series717.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* y z) (* t a))
62.0ms	(* b (- (* c z) (* i a)))
68.0ms	(* x (- (* y z) (* t a)))
548.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	373	645
1	1485	568
2	5001	568

prune376.0ms

Filtered

94 candidates to 71 candidates (75.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	81	13	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Merged error: 5.4b

Counts

95 → 13

localize29.0ms

Local error

Found 4 expressions with local error:

4.0b	(* b (- (* c z) (* i a)))
4.9b	(* x (fma y z (- (* a t))))
6.0b	(fma (- (* c t) (* i y)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* i a)))))
50.1b	(fma (- a) t (* a t))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

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

series3.7s

Counts

4 → 12

Calls

4 calls:

74.0ms	(* b (- (* c z) (* i a)))
82.0ms	(* x (fma y z (- (* a t))))
3.5s	(fma (- (* c t) (* i y)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* i a)))))
25.0ms	(fma (- a) t (* a t))

simplify50.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	315	624
1	1242	538
2	5002	538

prune590.0ms

Filtered

82 candidates to 58 candidates (70.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	82	13	95

Merged error: 5.4b

Counts

95 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (cbrt b) (- (* c z) (* i a)))
2.5b	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))
4.9b	(* x (- (* y z) (* t a)))
6.0b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))))

rewrite31.0ms

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:

7.0ms	(* (cbrt b) (- (* c z) (* i a)))
13.0ms	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))
6.0ms	(* x (- (* y z) (* t a)))
1.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

291.0ms	(* (cbrt b) (- (* c z) (* i a)))
111.0ms	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))
76.0ms	(* x (- (* y z) (* t a)))
706.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))))

simplify87.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	559	1204
1	2479	956
2	5003	877

prune474.0ms

Filtered

120 candidates to 79 candidates (65.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	121	12	133

Merged error: 5.3b

Counts

133 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (cbrt x) (- (* y z) (* t a)))
2.9b	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
4.0b	(* b (- (* c z) (* i a)))
6.0b	(fma (- (* c t) (* i y)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (* b (- (* c z) (* i a)))))

rewrite30.0ms

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:

7.0ms	(* (cbrt x) (- (* y z) (* t a)))
13.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
6.0ms	(* b (- (* c z) (* i a)))
1.0ms	(fma (- (* c t) (* i y)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (* b (- (* c z) (* i a)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

295.0ms	(* (cbrt x) (- (* y z) (* t a)))
109.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
76.0ms	(* b (- (* c z) (* i a)))
709.0ms	(fma (- (* c t) (* i y)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (* b (- (* c z) (* i a)))))

simplify89.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	554	1206
1	2443	956
2	5001	877

prune414.0ms

Filtered

120 candidates to 77 candidates (64.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	120	12	132

Merged error: 5.3b

Counts

132 → 12

regimes734.0ms

Accuracy

25.6% (5.7b remaining)

Error of 10.6b against oracle of 4.9b and baseline of 12.6b

bsearch128.0ms

Steps

Iters	Range		Point
9	-6.415584159767308	-1.1216194205664065e-07	-1.9711435895315972

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	33
1	72	33
2	72	33

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.5s

18952×

body

valid