Details

analyze909.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
2.3%	97.4%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
24.9%	74.9%	0.2%	13
33.2%	66.5%	0.2%	14

sample24.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	34×	body	80	invalid

simplify90.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4952	11
1	4952	11

prune12.0ms

Filtered

1 candidates to 1 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: 0.0b

Counts

2 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
70×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
26×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
9×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/r` `associate-/l`
4×	`pow1` `associate-/r/`
3×	`flip3--` `associate-l` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

2 → 102

Calls

2 calls:

8.0ms	(/ (- z t) (- z a))
18.0ms	(* y (/ (- z t) (- z a)))

series24.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(/ (- z t) (- z a))
16.0ms	(* y (/ (- z t) (- z a)))

simplify49.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5083	1163

prune119.0ms

Filtered

70 candidates to 108 candidates (-54.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	102	8	110

Merged error: 0.0b

Counts

110 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- z a))
0.2b	(* (- z t) (/ 1 (- z a)))
2.7b	(* y (* (- z t) (/ 1 (- z a))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
32×	`times-frac`
31×	`add-exp-log`
24×	`add-cube-cbrt`
22×	`associate-r`
19×	`add-cbrt-cube`
13×	`prod-exp`
11×	`pow1`
8×	`associate-r/` `associate-l*` `distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`flip3--` `div-exp` `flip--`
5×	`associate-/r*`
4×	`frac-times` `pow-prod-down` `associate-*l/` `associate-/r/`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`un-div-inv` `*-commutative` `div-inv`
1×	`pow-flip` `frac-2neg` `clear-num` `inv-pow`

Counts

3 → 119

Calls

3 calls:

5.0ms	(/ 1 (- z a))
13.0ms	(* (- z t) (/ 1 (- z a)))
15.0ms	(* y (* (- z t) (/ 1 (- z a))))

series30.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(/ 1 (- z a))
9.0ms	(* (- z t) (/ 1 (- z a)))
16.0ms	(* y (* (- z t) (/ 1 (- z a))))

simplify49.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5847	1082

prune119.0ms

Filtered

74 candidates to 128 candidates (-73.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	128	8	136

Merged error: 0.0b

Counts

136 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (/ (- z t) (- z a))) (cbrt (/ (- z t) (- z a))))
4.3b	(cbrt (/ (- z t) (- z a)))
4.3b	(cbrt (/ (- z t) (- z a)))
4.3b	(cbrt (/ (- z t) (- z a)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

333×	`*-un-lft-identity`
277×	`cbrt-prod`
273×	`add-sqr-sqrt`
229×	`times-frac`
106×	`distribute-lft-out--`
93×	`add-cube-cbrt`
78×	`difference-of-squares`
58×	`swap-sqr`
34×	`associate-r` `associate-l`
14×	`associate-/r/`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `flip3--` `flip--` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 276

Calls

4 calls:

35.0ms	(* (cbrt (/ (- z t) (- z a))) (cbrt (/ (- z t) (- z a))))
7.0ms	(cbrt (/ (- z t) (- z a)))
7.0ms	(cbrt (/ (- z t) (- z a)))
7.0ms	(cbrt (/ (- z t) (- z a)))

series138.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cbrt (/ (- z t) (- z a))) (cbrt (/ (- z t) (- z a))))
34.0ms	(cbrt (/ (- z t) (- z a)))
31.0ms	(cbrt (/ (- z t) (- z a)))
30.0ms	(cbrt (/ (- z t) (- z a)))

simplify96.0ms

Algorithm

egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4994	5276
1	4994	5276

prune225.0ms

Filtered

170 candidates to 288 candidates (-69.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	288	8	296

Merged error: 0.0b

Counts

296 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
7.0b	(* (* y (* (cbrt (- z t)) (cbrt (- z t)))) (/ (cbrt (- z t)) (- z a)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
46×	`associate-r`
40×	`cbrt-prod` `times-frac`
30×	`cbrt-div`
26×	`add-cube-cbrt`
25×	`add-exp-log`
21×	`associate-*r/`
18×	`add-cbrt-cube`
16×	`frac-times` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
13×	`pow1`
12×	`associate-*l/` `prod-exp` `cbrt-unprod`
6×	`pow-prod-down`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow1/3` `div-exp`
2×	`associate-/r/`
1×	`associate-l` `*-commutative` `div-inv`

Counts

4 → 132

Calls

4 calls:

3.0ms	(cbrt (- z t))
3.0ms	(cbrt (- z t))
3.0ms	(cbrt (- z t))
26.0ms	(* (* y (* (cbrt (- z t)) (cbrt (- z t)))) (/ (cbrt (- z t)) (- z a)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- z t))
26.0ms	(cbrt (- z t))
26.0ms	(cbrt (- z t))
19.0ms	(* (* y (* (cbrt (- z t)) (cbrt (- z t)))) (/ (cbrt (- z t)) (- z a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4993	2137
1	4993	2137

prune120.0ms

Filtered

96 candidates to 144 candidates (-50.0%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	143	9	152

Merged error: 0b

Counts

152 → 9

regimes659.0ms

Accuracy

2.6% (1.4b remaining)

Error of 1.4b against oracle of 0.0b and baseline of 1.5b

bsearch46.0ms

Steps

Iters	Range		Point
10	1.1677708886023657e-120	6.542874286260532e-109	4.314373561989049e-114
9	-2.3208289882322565e-98	-1.4900453834063606e-106	-3.5486213838242893e-100

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	31
1	44	31

end0.0ms

sample602.0ms

Algorithm

intervals

Results

299.0ms	7999×	body	80	valid
30.0ms	754×	body	80	invalid
0.0ms	1×	body	1280	valid

Details

analyze909.0ms

sample24.0ms

simplify90.0ms

prune12.0ms

localize8.0ms

rewrite30.0ms

series24.0ms

simplify49.0ms

prune119.0ms

localize10.0ms

rewrite38.0ms

series30.0ms

simplify49.0ms

prune119.0ms

localize15.0ms

rewrite80.0ms

series138.0ms

simplify96.0ms

prune225.0ms

localize12.0ms

rewrite41.0ms

series96.0ms

simplify52.0ms

prune120.0ms

regimes659.0ms

bsearch46.0ms

simplify1.0ms

end0.0ms

sample602.0ms

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