Details

sample29.0ms

Algorithm

intervals

Results

9.0ms	251×	body	80	valid
2.0ms	11×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	2×	body	2560	valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1498	6
6	3410	6
7	5001	6

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 24.2b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.7b	(+ x (/ (* (- y z) (- t x)) (- a z)))
17.8b	(/ (* (- y z) (- t x)) (- a z))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `associate-/l/`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
4×	`associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 81

Calls

3 calls:

9.0ms	(* (- y z) (- t x))
7.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
12.0ms	(/ (* (- y z) (- t x)) (- a z))

series306.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* (- y z) (- t x))
146.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
124.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify54.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	466	583
1	2158	534
2	5001	534

prune224.0ms

Filtered

90 candidates to 67 candidates (74.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	80	10	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	11	91

Merged error: 4.6b

Counts

91 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.5b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
36.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series729.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (- a z))
140.0ms	(cbrt (- a z))
291.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
156.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	744	1831
1	3287	1663
2	5001	1576

prune412.0ms

Filtered

146 candidates to 102 candidates (69.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	138	8	146
Fresh	4	5	9
Picked	1	0	1
Done	1	0	1
Total	144	13	157

Merged error: 4.6b

Counts

157 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
9.8b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log`
36×	`cbrt-div`
26×	`add-sqr-sqrt`
22×	`add-cbrt-cube`
17×	`associate-l`
16×	`-un-lft-identity` `times-frac` `associate-r*` `associate-/r/`
15×	`prod-exp` `cbrt-unprod`
14×	`flip3--` `flip--`
13×	`cbrt-prod`
12×	`cbrt-undiv` `div-exp`
10×	`add-cube-cbrt`
9×	`frac-times`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`associate-r/` `associate-l/`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 110

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
34.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
3.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series722.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (- a z))
142.0ms	(cbrt (- a z))
285.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
152.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify89.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	810	2470
1	3241	2130
2	5002	2090

prune507.0ms

Filtered

122 candidates to 90 candidates (73.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	121	14	135

Merged error: 4.6b

Counts

135 → 14

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
8.6b	(+ x (* (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 56

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
4.0ms	(+ x (* (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series605.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (- a z))
150.0ms	(cbrt (- a z))
151.0ms	(cbrt (- a z))
157.0ms	(+ x (* (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify42.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	270	944
1	858	858
2	5001	849

prune349.0ms

Filtered

68 candidates to 59 candidates (86.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	68	14	82

Merged error: 4.6b

Counts

82 → 14

regimes356.0ms

Accuracy

14.9% (6.9b remaining)

Error of 10.6b against oracle of 3.7b and baseline of 11.8b

bsearch91.0ms

Steps

Iters	Range		Point
8	1.561074351064423e-112	1.0064026256720376e-107	2.7182630617525346e-110
5	-5.768469913273354e-73	-2.8755540344936286e-73	-2.919906856904198e-73

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	54
1	49	54

end0.0ms

sample808.0ms

Algorithm

intervals

Results

303.0ms	7884×	body	80	valid
71.0ms	455×	body	640	valid
53.0ms	278×	body	1280	valid
45.0ms	396×	body	320	valid
19.0ms	253×	body	160	valid
6.0ms	18×	body	2560	valid