Details

sample87.0ms

Algorithm

intervals

Results

51.0ms

617×

body

valid

simplify89.0ms

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

prune12.0ms

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: 12.0b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* c t) (* i y))
4.9b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
5.1b	(* b (- (* c z) (* i a)))
5.8b	(* x (- (* y z) (* t 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:

3.0ms	(- (* c t) (* i y))
1.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
6.0ms	(* b (- (* c z) (* i a)))
6.0ms	(* x (- (* y z) (* t a)))

series734.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* c t) (* i y))
564.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
65.0ms	(* b (- (* c z) (* i a)))
67.0ms	(* x (- (* y z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	423	646
1	1659	568
2	5001	568

prune439.0ms

Filtered

94 candidates to 71 candidates (75.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	73	21	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	21	95

Merged error: 4.4b

Counts

95 → 21

localize26.0ms

Local error

Found 4 expressions with local error:

4.9b	(fma (- (* c t) (* i y)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* i a)))))
5.1b	(* b (- (* c z) (* i a)))
5.8b	(* x (fma y z (- (* a t))))
49.7b	(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:

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

series3.7s

Counts

4 → 12

Calls

4 calls:

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)))))
70.0ms	(* b (- (* c z) (* i a)))
71.0ms	(* x (fma y z (- (* a t))))
25.0ms	(fma (- a) t (* a t))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	315	624
1	1247	538
2	5002	538

prune432.0ms

Filtered

82 candidates to 58 candidates (70.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	19	20
Picked	1	0	1
Done	0	0	0
Total	83	20	103

Merged error: 4.4b

Counts

103 → 20

localize23.0ms

Local error

Found 4 expressions with local error:

4.9b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* b (- (* i a))))))
5.2b	(* b (* c z))
5.8b	(* x (- (* y z) (* t a)))
6.4b	(* b (- (* i a)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

1.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* b (- (* i a))))))
5.0ms	(* b (* c z))
6.0ms	(* x (- (* y z) (* t a)))
5.0ms	(* b (- (* i a)))

series755.0ms

Counts

4 → 12

Calls

4 calls:

623.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* b (- (* i a))))))
26.0ms	(* b (* c z))
78.0ms	(* x (- (* y z) (* t a)))
27.0ms	(* b (- (* i a)))

simplify64.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	380	576
1	1736	498
2	5001	495

prune653.0ms

Filtered

94 candidates to 70 candidates (74.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	18	19
Picked	1	0	1
Done	0	0	0
Total	95	19	114

Merged error: 4.4b

Counts

114 → 19

localize31.0ms

Local error

Found 4 expressions with local error:

5.1b	(* b (- (* c z) (* i a)))
7.4b	(cbrt (- (* y z) (* t a)))
7.4b	(cbrt (- (* y z) (* t a)))
7.4b	(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:

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

series465.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* b (- (* c z) (* i a)))
131.0ms	(cbrt (- (* y z) (* t a)))
130.0ms	(cbrt (- (* y z) (* t a)))
130.0ms	(cbrt (- (* y z) (* t a)))

simplify124.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	336	646
1	1159	598
2	4181	580
3	5001	580

prune412.0ms

Filtered

85 candidates to 71 candidates (83.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	18	18
Picked	1	0	1
Done	0	0	0
Total	85	19	104

Merged error: 4.4b

Counts

104 → 19

regimes1.1s

Accuracy

-21% (9.4b remaining)

Error of 13.9b against oracle of 4.5b and baseline of 12.3b

bsearch176.0ms

Steps

Iters	Range		Point
8	1.3952650528872349e-176	3.3722698195245367e-172	1.4176851859825974e-176
5	-2.250415824177972e-247	-6.362356953122944e-248	-6.462588113691143e-248

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	25
1	54	25

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.7s

19172×

body

valid