Details

sample3.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 1.062012%

Guaranteed chance to sample good point: 19.272054%

Results

8.0ms	201×	body	80	valid
3.0ms	19×	body	640	valid
2.0ms	12×	body	1280	valid
2.0ms	14×	body	320	valid
2.0ms	38×	body	80	invalid
1.0ms	10×	body	160	valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

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: 22.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.8b	(+ x (/ (* (- y z) (- t x)) (- a z)))
15.4b	(/ (* (- y z) (- t x)) (- a z))

rewrite34.0ms

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)))
16.0ms	(/ (* (- y z) (- t x)) (- a z))

series95.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- y z) (- t x))
51.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
35.0ms	(/ (* (- 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

prune151.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	79	11	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	11	91

Merged error: 3.9b

Counts

91 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.4b	(+ 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))
35.0ms	(* (/ (- 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)))))

series157.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt (- a z))
26.0ms	(cbrt (- a z))
56.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
48.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	752	1839
1	3320	1671
2	5001	1580

prune197.0ms

Filtered

103 candidates to 146 candidates (-41.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	140	6	146
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	142	15	157

Merged error: 3.9b

Counts

157 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt (- a z)))
0.6b	(cbrt (cbrt (- a z)))
1.1b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
11.1b	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
100×	`cbrt-prod`
98×	`times-frac`
76×	`*-un-lft-identity`
69×	`add-exp-log`
61×	`associate-r`
48×	`cbrt-div`
42×	`add-cbrt-cube`
38×	`add-cube-cbrt`
29×	`associate-l`
27×	`cbrt-undiv` `div-exp`
24×	`prod-exp` `cbrt-unprod`
19×	`distribute-lft-out--` `difference-of-squares`
18×	`associate-/r/`
15×	`flip3--` `flip--`
12×	`unswap-sqr`
9×	`frac-times`
6×	`pow1` `add-log-exp`
5×	`associate-r/` `associate-l/`
3×	`div-inv`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 189

Calls

4 calls:

3.0ms	(cbrt (cbrt (- a z)))
3.0ms	(cbrt (cbrt (- a z)))
62.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
3.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series161.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (cbrt (- a z)))
26.0ms	(cbrt (cbrt (- a z)))
57.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
50.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1141	4254
1	5002	3782

prune257.0ms

Filtered

153 candidates to 201 candidates (-31.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	3	10	13
Picked	1	0	1
Done	0	1	1
Total	203	13	216

Merged error: 3.9b

Counts

216 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt (- a z)))
0.6b	(cbrt (cbrt (- a z)))
0.6b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x))))
10.9b	(+ x (* (/ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

44×	`cbrt-div`
26×	`cbrt-prod`
25×	`add-exp-log`
20×	`frac-times` `flip3--` `flip--`
18×	`add-sqr-sqrt`
17×	`associate-l`
16×	`*-un-lft-identity`
15×	`add-cbrt-cube`
14×	`associate-*r/`
11×	`prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt`
9×	`pow1`
8×	`associate-/r/`
7×	`associate-*l/`
6×	`times-frac` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow-prod-down` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `unswap-sqr`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 106

Calls

4 calls:

3.0ms	(cbrt (cbrt (- a z)))
3.0ms	(cbrt (cbrt (- a z)))
24.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x))))
4.0ms	(+ x (* (/ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (cbrt (- a z)))
25.0ms	(cbrt (cbrt (- a z)))
179.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x))))
52.0ms	(+ x (* (/ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	752	1862
1	2443	1660
2	5001	1623

prune131.0ms

Filtered

88 candidates to 118 candidates (-34.1%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	117	14	131

Merged error: 3.9b

Counts

131 → 14

regimes769.0ms

Accuracy

5.5% (7.4b remaining)

Error of 11.6b against oracle of 4.2b and baseline of 12.1b

bsearch64.0ms

Steps

Iters	Range		Point
7	7.498554674984581e-144	1.3951435904162493e-142	3.8885248754173e-143
9	-1.2831581258770894e-54	-5.310794507512987e-63	-6.201676580706831e-60

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	51
1	46	51

end0.0ms

sample4.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 1.062012%

Guaranteed chance to sample good point: 19.272054%

Results

288.0ms	6582×	body	80	valid
66.0ms	457×	body	640	valid
53.0ms	1067×	body	80	invalid
51.0ms	250×	body	1280	valid
47.0ms	424×	body	320	valid
25.0ms	266×	body	160	valid
5.0ms	21×	body	2560	valid

Details

sample3.8s

simplify66.0ms

prune4.0ms

localize9.0ms

rewrite34.0ms

series95.0ms

simplify54.0ms

prune151.0ms

localize13.0ms

rewrite52.0ms

series157.0ms

simplify90.0ms

prune197.0ms

localize17.0ms

rewrite88.0ms

series161.0ms

simplify58.0ms

prune257.0ms

localize24.0ms

rewrite39.0ms

series285.0ms

simplify70.0ms

prune131.0ms

regimes769.0ms

bsearch64.0ms

simplify2.0ms

end0.0ms

sample4.6s

Profiling