Details

sample85.0ms

Algorithm

intervals

Results

49.0ms

619×

body

valid

simplify92.0ms

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: 13.4b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* c z) (* i a))
4.7b	(* x (- (* y z) (* t a)))
6.0b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
6.2b	(* 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	(- (* 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)))))
6.0ms	(* b (- (* c z) (* i a)))

series912.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* c z) (* i a))
68.0ms	(* x (- (* y z) (* t a)))
743.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
66.0ms	(* b (- (* c z) (* i a)))

simplify48.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (11.0ms)

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

prune400.0ms

Filtered

94 candidates to 73 candidates (77.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	79	15	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	15	95

Merged error: 5.6b

Counts

95 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

5.5b	(cbrt (- (* y z) (* t a)))
5.5b	(cbrt (- (* y z) (* t a)))
6.0b	(fma (- (* c t) (* i y)) j (- (* (* x (* (cbrt (- (* y z) (* t a))) (cbrt (- (* y z) (* t a))))) (cbrt (- (* y z) (* t a)))) (* b (- (* c z) (* i a)))))
6.2b	(* b (- (* c z) (* i a)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

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

series837.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt (- (* y z) (* t a)))
116.0ms	(cbrt (- (* y z) (* t a)))
542.0ms	(fma (- (* c t) (* i y)) j (- (* (* x (* (cbrt (- (* y z) (* t a))) (cbrt (- (* y z) (* t a))))) (cbrt (- (* y z) (* t a)))) (* b (- (* c z) (* i a)))))
65.0ms	(* b (- (* c z) (* i a)))

simplify120.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	386	810
1	1298	722
2	4702	694
3	5001	694

prune397.0ms

Filtered

80 candidates to 64 candidates (80.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	79	16	95

Merged error: 5.6b

Counts

95 → 16

localize23.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
3.4b	(* (cbrt x) (- (* y z) (* t a)))
6.0b	(fma (- (* c t) (* i y)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (* b (- (* c z) (* i a)))))
6.2b	(* b (- (* c z) (* i a)))

rewrite28.0ms

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

series1.1s

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
268.0ms	(* (cbrt x) (- (* y z) (* t a)))
647.0ms	(fma (- (* c t) (* i y)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (* b (- (* c z) (* i a)))))
66.0ms	(* b (- (* c z) (* i a)))

simplify76.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	554	1206
1	2443	956
2	5003	877

prune457.0ms

Filtered

120 candidates to 76 candidates (63.3%)

Pruning

17 alts after pruning (15 fresh and 2 done)

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

Merged error: 5.6b

Counts

136 → 17

localize28.0ms

Local error

Found 4 expressions with local error:

5.5b	(cbrt (- (* y z) (* t a)))
5.5b	(cbrt (- (* y z) (* t a)))
6.0b	(fma (- (* c t) (* i y)) j (- (* (* x (* (cbrt (- (* y z) (* t a))) (cbrt (- (* y z) (* t a))))) (* (cbrt (* (cbrt (- (* y z) (* t a))) (cbrt (- (* y z) (* t a))))) (cbrt (cbrt (- (* y z) (* t a)))))) (* b (- (* c z) (* i a)))))
6.2b	(* b (- (* c z) (* i a)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

4.0ms	(cbrt (- (* y z) (* t a)))
3.0ms	(cbrt (- (* y z) (* t a)))
1.0ms	(fma (- (* c t) (* i y)) j (- (* (* x (* (cbrt (- (* y z) (* t a))) (cbrt (- (* y z) (* t a))))) (* (cbrt (* (cbrt (- (* y z) (* t a))) (cbrt (- (* y z) (* t a))))) (cbrt (cbrt (- (* y z) (* t a)))))) (* b (- (* c z) (* i a)))))
6.0ms	(* b (- (* c z) (* i a)))

series853.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt (- (* y z) (* t a)))
117.0ms	(cbrt (- (* y z) (* t a)))
554.0ms	(fma (- (* c t) (* i y)) j (- (* (* x (* (cbrt (- (* y z) (* t a))) (cbrt (- (* y z) (* t a))))) (* (cbrt (* (cbrt (- (* y z) (* t a))) (cbrt (- (* y z) (* t a))))) (cbrt (cbrt (- (* y z) (* t a)))))) (* b (- (* c z) (* i a)))))
62.0ms	(* b (- (* c z) (* i a)))

simplify121.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	391	954
1	1328	842
2	4815	830
3	5001	830

prune402.0ms

Filtered

80 candidates to 64 candidates (80.0%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	14	14
Picked	0	1	1
Done	0	2	2
Total	80	17	97

Merged error: 5.6b

Counts

97 → 17

regimes908.0ms

Accuracy

-8% (8.0b remaining)

Error of 12.9b against oracle of 4.9b and baseline of 12.3b

bsearch203.0ms

Steps

Iters	Range		Point
8	-5.709131272659709e-202	-2.1363434946653318e-206	-3.1424918671022023e-204
9	-2.452115682527841e-142	-1.724531979937283e-147	-1.9127797830016308e-147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	49
1	59	49

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.5s

19064×

body

valid

Details

sample85.0ms

simplify92.0ms

prune9.0ms

localize19.0ms

rewrite18.0ms

series912.0ms

simplify48.0ms

prune400.0ms

localize25.0ms

rewrite15.0ms

series837.0ms

simplify120.0ms

prune397.0ms

localize23.0ms

rewrite28.0ms

series1.1s

simplify76.0ms

prune457.0ms

localize28.0ms

rewrite18.0ms

series853.0ms

simplify121.0ms

prune402.0ms

regimes908.0ms

bsearch203.0ms

simplify2.0ms

end0.0ms

sample2.4s

Profiling