Details

sample57.0ms

Algorithm

intervals

Results

22.0ms	52×	body	1280	valid
12.0ms	47×	body	640	valid
6.0ms	155×	body	80	valid
4.0ms	23×	body	320	valid
2.0ms	70×	body	80	nan
1.0ms	14×	body	160	valid

simplify117.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (9.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	108	6
4	310	4
5	792	4
6	4192	4
7	5002	4

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
8.0b	(log (/ x (+ x y)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
54×	`log-prod`
48×	`times-frac`
40×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
18×	`distribute-rgt-in` `distribute-lft-in`
13×	`distribute-lft-out`
10×	`add-exp-log`
8×	`associate-/r/`
7×	`pow1` `add-cbrt-cube`
4×	`flip3-+` `associate-r` `associate-/r*` `flip-+` `div-inv`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `log-div` `frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 123

Calls

3 calls:

5.0ms	(/ x (+ x y))
14.0ms	(* x (log (/ x (+ x y))))
4.0ms	(log (/ x (+ x y)))

series165.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ x (+ x y))
77.0ms	(* x (log (/ x (+ x y))))
46.0ms	(log (/ x (+ x y)))

simplify105.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	302	874
1	1266	813
2	4974	783
3	5001	783

prune257.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.7b	(log (/ (cbrt x) (cbrt (+ x y))))
2.7b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod` `log-prod`
84×	`*-un-lft-identity` `times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`distribute-lft-out`
10×	`add-exp-log`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `rem-log-exp` `associate-/r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `flip3-+` `pow1/3` `div-exp` `log-pow` `flip-+` `div-inv`

Counts

4 → 148

Calls

4 calls:

0.0ms	(cbrt x)
1.0ms	(cbrt x)
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series487.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt x)
170.0ms	(cbrt x)
71.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
73.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify73.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	318	1502
1	772	1456
2	2360	1424
3	5002	1350

prune517.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
29.3b	(log (* (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y)))) (/ x (cbrt (+ x y)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
20×	`prod-exp`
15×	`div-exp` `rem-log-exp`
13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`pow1` `add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-div` `flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`log-pow`
1×	`frac-times` `log-prod` `associate-r/` `pow-prod-down` `associate-l/`

Counts

4 → 78

Calls

4 calls:

2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
56.0ms	(log (* (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y)))) (/ x (cbrt (+ x y)))))

series464.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(cbrt (+ x y))
133.0ms	(cbrt (+ x y))
128.0ms	(cbrt (+ x y))
76.0ms	(log (* (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y)))) (/ x (cbrt (+ x y)))))

simplify71.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	179	487
1	582	436
2	2472	400
3	5001	395

prune318.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.4b	(expm1 (log1p (cbrt x)))
2.7b	(log (/ (cbrt x) (cbrt (+ x y))))
17.1b	(log (/ (expm1 (log1p (cbrt x))) (cbrt (+ x y))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

75×	`log-prod`
64×	`*-un-lft-identity`
63×	`times-frac`
60×	`cbrt-prod`
46×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log`
9×	`distribute-lft-out`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `rem-log-exp` `associate-/r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `flip3-+` `div-exp` `log-pow` `flip-+` `div-inv`
1×	`expm1-log1p` `pow1/3` `expm1-udef`

Counts

4 → 125

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(expm1 (log1p (cbrt x)))
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
5.0ms	(log (/ (expm1 (log1p (cbrt x))) (cbrt (+ x y))))

series697.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt x)
300.0ms	(expm1 (log1p (cbrt x)))
73.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
139.0ms	(log (/ (expm1 (log1p (cbrt x))) (cbrt (+ x y))))

simplify71.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	438	1217
1	882	1173
2	2472	1144
3	5001	1086

prune490.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

regimes84.0ms

Accuracy

17.3% (3.9b remaining)

Error of 4.9b against oracle of 1.0b and baseline of 5.7b

bsearch132.0ms

Steps

Iters	Range		Point
9	5.003531038945505e+82	4.123826930277484e+87	1.41249639531232e+87
9	0.008244135775532546	16112908.465778163	167.99809592077398

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	46
1	46	46

end0.0ms

sample1.7s

Algorithm

intervals

Results

676.0ms	1572×	body	1280	valid
357.0ms	1447×	body	640	valid
201.0ms	4844×	body	80	valid
141.0ms	825×	body	320	valid
87.0ms	2975×	body	80	nan
45.0ms	455×	body	160	valid